This study presents a new concept related to the quality and usability of multispectral (MS) and panchromatic (PAN) data sets captured by very-/extremely high-resolution (VHR/EHR) satellite MS scanners. Despite the ever-increasing resolution and spectral coverage capabilities of modern instruments, MS datasets suffer from the presence of aliasing originating from the insufficient sampling step size, corresponding to a high value of the modulation transfer function (MTF) of the instrument at the Nyquist frequency. Another source of degradation is the local misalignment between interpolated MS and PAN, originating from different viewpoints along the orbit of the instruments in the presence of discontinuities of the imaged surface. Here, we propose a procedure to harmonize MS and PAN datasets: aliasing artifacts of MS are suppressed; local MS-to-MS and MS-to-PAN shifts are damped. This is feasible for the unimodality of the MS and PAN instruments. Harmonization of MS towards PAN is achieved by injecting the least squares (LS) residue of the multivariate linear regression of the interpolated bands captured by each MS scanner towards the lowpass-filtered PAN. Experiments with two (MS-PAN) and three (MS1-MS2-PAN) on-board instruments show that an almost perfect alignment and a significant reduction of aliasing patterns are achieved. MS pansharpening greatly benefits from harmonized datasets. When the latter are used for the fusion and as references of spectral and spatial qualities of fusion products, inconsistencies noticed and complained about in the literature vanish. The procedure is in real time, fully automated, and does not require additional or ancillary information.

This work presents a pre-processing patch to automatically realign the multispectral (MS) spectrometers of WorldView-2 or WorldView-3. Once the resampled bands have been accurately overlaid onto the Pan image, established component substitution pansharpening algorithms can recover their original top performance, which had been diminished in the passage from a 4-band (a unique MS spectrometer) to an 8-band setup (two separate MS spectrometers). The misalignment arises because the three instruments onboard Worldview-2 (four on WorldView-3) – namely, old MS, new MS, and Pan – share the same optics and thus cannot have parallel optical axes. Consequently, they image the same swath area from different positions along the orbit. Local height changes (hills, buildings, trees, etc.) originate local shifts among the datasets. The three images can be accurately aligned only if the digital elevation surface model is exactly known. The proposed alignment procedure is fully automated and does not require any additional or ancillary information, but relies on the unimodality of the MS and Pan sensors.

The paper presents an original method for the spatial resolution enhancement of the hyperspectral (HS) data from PRISMA (Italian acronym for Hyperspectral Precursor of the Application Mission) by means of the Sentinel-2 visible and near infrared (VNIR) and shortwave infrared (SWIR) bands at 10 and 20 m spatial resolution, and the 5 m panchromatic (PAN) band also acquired by the PRISMA satellite. Firstly, the 20 m bands of Sentinel-2 are hypersharpened to 10 m by means of the four 10 m VNIR bands of the same instrument. Then, the 10 m hypersharpened bands of Sentinel-2 are used to sharpen the 30 m bands of PRISMA to 10 m as well, still according to the hypersharpening protocol. Eventually, the 10 m hypersharpened bands of PRISMA are pansharpened to 5 m by means of the Pan image of the same satellite. Results show that the nested hypersharpening followed by pansharpening is better than plain HS pansharpening, both visually and according to established full-scale indexes of spectral and spatial consistence.

In this paper, we propose a totally unsupervised procedure to cope with the residual local misalignment between a higher-resolution panchromatic (Pan) image and a series of lower-resolution multispectral (MS) bands, preliminarily interpolated to the pixel size of Pan. The proposed method exploits the different resolutions of the MS and Pan datasets to force the former to match a lowpass version of the latter. Specifically, the space-varying residue of the multivariate regression between resampled MS bands and lowpass-filtered Pan image, which locally measures the extent of MS-to-Pan misalignment, is injected into each the MS bands, after being weighted by the pixel-varying multiplicative injection gain of each band. Tests on a GeoEye-1 image, with space-varying shifts, highlight improvements in the spatial alignment.

Several tasks of remote sensing entail the measurement of the similarity/dissimilarity of a test multiband image to a reference multiband image. To this purpose, several indices has been developed over the last two decades. The most widely used indices are normalized to avoid dependence on the data format. In this work, we will focus on such indices and provide a novel insight on their behaviors. Spectral indices are those performing crossed measurements between couple of different bands of the test and reference image. Wherever crossed measurements do not occur, the index is purely spatial, or better radiometric. Both theoretical insights and simulations performed on a GeoEye dataset, with the products of twelve pansharpening methods, show that their performance ranking does not depend on the data format for purely radiometric indices, while it significantly depends on the data format, either spectral radiance or digital numbers (DN), for a purely spectral index, like the spectral angle mapper (SAM). The dependence on the data format is weak for indices that balance the spectral and radiometric similarity, like the family of indices, Q2n, based on hypercomplex algebra.

Pansharpening usually refers to the fusion of a high spatial resolution panchromatic image with a low spatial resolution multispectral image. One of the most debated issue in this research field regards the quality assessment of fused products. The two exploited quality assessments are at reduced resolution and at full resolution. The former is an accurate procedure, but the main drawback is that it works on synthetic (with lower spatial resolutions) products. The latter is able to work at full resolution paying it with a reduced accuracy due to the absence of a ground-truth. In this work, we will focus on the assessment at full resolution by introducing a new measure of spatial consistency based on multivariate linear regression of the panchromatic image towards the multispectral bands. Simulations with an IKONOS dataset and six fusion methods show that the proposed spatial index is the ideal counterpart of Khan's spectral consistency index.

In this letter, we propose a simple yet robust procedure to combat the residual local misalignment between the image data sets that are usually processed for pansharpening: a higher resolution panchromatic (Pan) image and a series of lower resolution multispectral (MS) bands, preliminarily interpolated to the pixel size of Pan. Unlike a conventional coregistration, which requires a preliminary orthorectification enforced by an accurate digital surface model, the proposed method automatically exploits the characteristics of the Pan image to alleviate the effects of misalignment on fusion products, whichever is the method chosen for pansharpening. More specifically, the space-varying residue of the multivariate regression between resampled MS bands and low-pass-filtered Pan image, which locally measures the extent of MS-to-Pan misalignments, is injected into the MS bands after being weighted by the projection coefficients of each band. Tests on simulated Pléiades images demonstrate that global shifts up to five pixels along each direction are perfectly compensated. Tests on a true GeoEye-1 image, whose shifts are space-varying and of unknown extent, highlight the attained improvement in spatial alignment.

In this letter, we show that pansharpening of visible/near-infrared (VNIR) bands takes advantage from a correction of the path-radiance term introduced by the atmosphere during the fusion process. This holds whenever the fusion mechanism emulates the radiative transfer model ruling the acquisition of the Earth's surface from space, that is, for methods exploiting a contrast-based injection model of spatial details extracted from the panchromatic (Pan) image into the interpolated multispectral (MS) bands. Such methods are high-pass modulation (HPM), Brovey transform, synthetic variable ratio (SVR), University of New Brunswick pansharp, smoothing filter-based intensity modulation, and spectral distortion minimization. The path radiance should be estimated and subtracted from each band before the product by Pan is accomplished and added back after. Both empirical and model-based estimation techniques of MS path radiances are compared within the framework of optimized SVR and HPM algorithms. Simulations carried out on QuickBird and IKONOS data highlight that haze correction of MS before fusion is always beneficial, especially on vegetated areas and in terms of spectral quality.

In this work, the authors investigate the behaviors of the two main classes of pansharpening methods: those based on component substitution (CS) or spectral methods and those based on multiresolution analysis (MRA) or spatial methods, in the presence of temporal and/or instrumental misalignments between the multispectral (MS) and panchromatic (Pan) data sets, that is, whenever MS and Pan are not jointly acquired at the same time and/or from the same platform. Starting from the mathematical formulation of CS and MRA pansharpening and from the spectral model between the Pan and MS channels, estimated through the multivariate linear regression between MS and spatially degraded Pan, it is proven that both CS and MRA methods may lose geometric sharpness in the case of a spectral mismatch, but spatial methods preserve the spectral diversity of the original MS data set regardless of the date or instrument of Pan image acquisition. Conversely, spectral methods also suffer from a loss of spectral fidelity to the original MS data set that is inversely related to the success of the spectral match between MS and Pan, measured by the coefficient of determination of the multivariate regression. An experimental setup exploiting GeoEye-1 and QuickBird data sets demonstrates the validity and intrinsic limitations of the proposed theoretical models. Depending of the target application, one class of methods may be preferred to another: Whenever spectral fidelity of pansharpened products to the original MS data sets is crucial, spectral methods should be avoided, and spatial methods are to be preferred.

In this paper, the authors investigate the statistical matching of the panchromatic (Pan) image to the multispectral (MS) bands, also known as the histogram matching, for the two main classes of pansharpening methods, i.e., those based on component substitution (CS) or spectral methods and those based on multiresolution analysis (MRA) or spatial methods. Also, hybrid methods combining CS with MRA, like the widespread additive wavelet luminance proportional (AWLP), are investigated. It is shown that all spectral, spatial, and hybrid methods must perform a dynamics matching of the enhancing Pan to the individual MS bands for MRA or a combination of them (the component that shall be substituted) for CS. For hybrid methods, the problem is more complex and both types of histogram matching may be suitable. Such an intersensor balance may be either explicit or implicitly performed by the detail-injection model, e.g., the popular projective and multiplicative injection models. An experimental setup exploiting IKONOS and WorldView-2 data sets demonstrates that a correct histogram matching is the key to attain extra performance from established methods. As a first result of this paper, the AWLP method has been revisited and its performance significantly improved by simply performing the histogram matching of Pan to the individual MS bands, rather than to the intensity component, thereby losing the original proportionality feature.

The majority of multispectral (MS) pansharpening methods may be labeled as spectral or spatial, depending on whether the geometric details that shall be injected into the interpolated MS bands are extracted from the panchromatic (P) image by means of a spectral transformation of MS pixels or a spatial transformation of the P image, achieved by means of linear shift-invariant digital filters. Spectral methods are known as component substitution; spatial methods are based on multiresolution analysis (MRA). In this paper, the authors show that, under the most general conditions, MRA-based pansharpening is characterized by a unique separable low-pass filter, which can be parametrically optimized based on the modulation transfer function (MTF) of the MS instrument, possibly followed by decimation and interpolation stages. This happens for the discrete wavelet transform (DWT) and its undecimated version (UDWT), for the “à-trous” wavelet (ATW) transform and its decimated version, i.e., the generalized Laplacian pyramid (GLP), and for nonseparable wavelet transforms, such as the nonsubsampled contourlet transform (NSCT). Hybrid methods, in which MRA fusion is performed on the intensity component derived from a spectral transformation, are equivalent to MRA fusion with a specific detail injection model. ATW and GLP are preferable to DWT, UDWT, and NSCT, because of computational benefits and of a looser choice of the low-pass filter, unconstrained from the requirement of generating a perfect reconstruction filter bank. Ultimately, GLP outperforms ATW, because its decimation and interpolation stages allow the aliasing impairments intrinsically present in the original MS bands to be removed from the pansharpened product.

Pansharpening aims at fusing a multispectral and a panchromatic image, featuring the result of the processing with the spectral resolution of the former and the spatial resolution of the latter. In the last decades, many algorithms addressing this task have been presented in the literature. However, the lack of universally recognized evaluation criteria, available image data sets for benchmarking, and standardized implementations of the algorithms makes a thorough evaluation and comparison of the different pansharpening techniques difficult to achieve. In this paper, the authors attempt to fill this gap by providing a critical description and extensive comparisons of some of the main state-of-the-art pansharpening methods. In greater details, several pansharpening algorithms belonging to the component substitution or multiresolution analysis families are considered. Such techniques are evaluated through the two main protocols for the assessment of pansharpening results, i.e., based on the full- and reduced-resolution validations. Five data sets acquired by different satellites allow for a detailed comparison of the algorithms, characterization of their performances with respect to the different instruments, and consistency of the two validation procedures. In addition, the implementation of all the pansharpening techniques considered in this paper and the framework used for running the simulations, comprising the two validation procedures and the main assessment indexes, are collected in a MATLAB toolbox that is made available to the community.

In this paper state-of-the-art and advanced methods for multispectral pansharpening are reviewed and evaluated on two very high resolution datasets acquired by IKONOS-2 (four bands) and WorldView-2 (eight bands). The experimental analysis allows us to highlight the performances of the two main pansharpening approaches (i.e. component substitution and multiresolution analysis).

In the past few decades, several methods have been developed for despeckling synthetic aperture radar (SAR) images. A considerable number of them have been derived under the assumption of a fully-developed speckle model in which the multiplicative speckle noise is supposed to be a white process. Unfortunately, the transfer function of SAR acquisition systems can introduce a statistical correlation, which decreases the despeckling efficiency of such filters. In this paper, a whitening method is proposed for processing a complex image acquired by a SAR system. We demonstrate that the proposed approach allows the successful application of classical despeckling algorithms. First, we perform an estimation of the SAR system frequency response based on some statistical properties of the acquired image and by using realistic assumptions. Then, a decorrelation process is applied on the acquired image, taking into account the presence of point targets. Finally, the image is despeckled. The experimental results show that the despeckling filters achieve better performance when they are preceded by the proposed whitening method; furthermore, the radiometric characteristics of the image are preserved.

A nonparametric method for unsupervised change detection in multipass synthetic aperture radar (SAR) imagery is described. The method relies on a novel feature capturing the structural change between two SAR images and is robust to the statistical change that may be originated by speckle and coregistration inaccuracies. The proposed method starts from the scatterplot of the amplitude levels in the two images and applies the mean-shift (MS) algorithm to find the modes of the underlying bivariate distribution. If we assume that the two images have been preliminarily coregistered and calibrated on one another, then all the modes lying outside the main diagonal correspond to the structural changes across the two observations. The value of the probability density function (PDF) in any of the off-diagonal modes found by the MS algorithm is translated into a value of conditional information. This value is assigned to all image pixels generating the corresponding cluster in the scatterplot. Thus, a feature is obtained on a per-pixel basis. Experimental results on simulated changes and true SAR images acquired by the COSMO-SkyMed satellite constellation show that the proposed feature exhibits significantly better discrimination capability than the classical log-ratio (LR). Advantages over a preliminary version of the method without MS regularization and over another nonparametric method based on Kullback-Leibler divergence are also demonstrated. The method is robust when it is applied to SAR images with different acquisition angles, whose effects are deemphasized compared to the actual scene changes.

This paper presents a fast method suitable for pansharpening of MS imagery. Key points of the novel method, which falls in the category of component substitution (CS) methods, are optimization of the intensity component, achieved through multivariate regression of Pan to MS, and adjustment of the modulus of the spatial detail vector to be injected, based on a minimization of spatial distortion. Spatial distortion is measured at full scale according to the QNR protocol on land cover classes defined by NDVI thresholding. Experiments carried out on IKONOS data demonstrate that results are competitive with those of the most advanced methods, with a computational complexity comparable with that of Brovey transform fusion, which is the baseline version of the proposed method.

This paper describes the most recent achievements in speckle reduction of COSMO-SkyMed (CSK@) synthetic aperture radar (SAR) data. An advanced multiresolution despeckling filter, based on undecimated wavelet transform (UDWT) and maximum a-posteriori (MAP) estimation has been specialized and optimized to CSKê data, both single- and multi-look. The tradeoff between performances and computational complexity has been investigated: Laplacian-Gaussian and generalized Gaussian (GG) priors for MAP estimation in UDWT domain differ by one order of magnitude in computation cost. Pre-processing of point targets and segmentation of wavelet planes has been exploited to effectively handle the heterogeneity of the data. Besides traditional supervised methods to evaluate the quality of despeckling, a novel procedure, fully automated, based on bivariate analysis of noisy and denoised image has been devised.

This paper presents an unsupervised nonparametric method for change detection in multitemporal synthetic aperture radar (SAR) imagery. The proposed method relies on a novel feature capable of capturing the structural changes between the two images and discarding almost completely the statistical changes due to speckle patterns or co-registration inaccuracies. This feature utilizes the scatterplots of the amplitude levels in the two SAR images and applies a fast version of the mean-shift (MS) algorithm to find the modes of the underlying bivariate distribution. The value of the probability density function (PDF) is translated to a value of conditional information and given to all image pixels originating such modes. Experimental results have been carried out with simulated changes and true SAR images acquired by the COSMO-SkyMed satellite constellation. The proposed feature exhibits significantly better discrimination capability than both the classical log-ratio (LR) and is particularly robust if applied to SAR images having different processing and/or acquisition angles.

The undecimated wavelet transform and the maximum a posteriori probability (MAP) criterion have been applied to the problem of synthetic-aperture-radar image despeckling. The MAP solution is based on the assumption that wavelet coefficients have a known distribution. In previous works, the generalized Gaussian (GG) function has been successfully employed. Furthermore, despeckling methods can be improved by using a classification of wavelet coefficients according to their texture energy. A major drawback of using the GG distribution is the high computational cost since the MAP solution can be found only numerically. In this letter, a new modeling of the statistics of wavelet coefficients is proposed. Observations of the estimated GG shape parameters relative to the reflectivity and to the speckle noise suggest that their distributions can be approximated as a Laplacian and a Gaussian function, respectively. Under these hypotheses, a closed form solution of the MAP estimation problem can be achieved. As for the GG case, classification of wavelet coefficients according to their texture content may be exploited also in the proposed method. Experimental results show that the fast MAP estimator based on the Laplacian-Gaussian assumption and on the classification of coefficients reaches almost the same performances as the GG version in terms of speckle removal, with a gain in computational cost of about one order of magnitude.

The undecimated wavelet transform and the maximum a posteriori (MAP) criterion have been applied to the problem of despeckling SAR images. The solution is based on the assumption that the wavelet coefficients have a known distribution. In previous works, the generalized Gaussian function has been successfully employed. In this case, a major problem is the computational cost, since the solution can be found only numerically. In this work, a different modeling is proposed. The observation of the experimental histograms of the wavelet coefficients related to the reflectivity and to speckle noise demonstrates that their distributions can be approximated as a Laplacian and a Gaussian function, respectively. Under these hypotheses, a closed form solution of the MAP estimation problem can be achieved. In addition, a closed form estimator based on the MMSE criterion also exists. The experimental results show that the fast MAP and MMSE estimators reach almost the same performances of their generalized Gaussian based counterparts in terms of speckle removal, with a computational gain of about one order of magnitude.

In this work, maximum a posteriori (MAP) despeckling, implemented in the multiresolution domain defined by the undecimated discrete wavelet transform (UDWT), will carried out on very high resolution (VHR) SAR images and compared with earlier multiresolution approaches developed by the authors. The MAP solution in UDWT domain has been specialized to SAR imagery. Every UDWT subband is segmented into statistically homogeneous segments and one generalized Gaussian (GG) PDF (variance and shape factor) is estimated for each segment. This solution allows to effectively handle scene heterogeneity as imaged by the VHR SAR system. Segmentation exploits a Tree Structured Markov Random Field (TSMRF), which is a low complexity MRF segmentation that allows the estimation of the number of segments and the segmentation itself to be carried out at same time. Experiments performed on a single-look VHR X-band SAR images demonstrate that the segmented approach is effective whenever the classical circular Gaussian model of complex reflectivity may no longer hold.

This paper presents a novel method for the spatial quality improvement of low resolution hyperspectral (HS) images by making use of a high resolution panchromatic (Pan) image. Since the introduction of all the details extracted from the Pan image into the upscaled HS images may result in spectral and spatial distortions, a detail injection model based on the optimization of QNR spatial quality index is proposed. This proposed model produces pansharpened images while preserving spectral fidelity. Also, to speed up the fusion process we propose to use the Universal Image Quality Index (UIQI) for dimensionality reduction before performing pansharpening. Finally, a comparison of the proposed method is presented with some existing pansharpening methods.

This work focuses on the assessment of noise parameters characterizing the hyperspectral images collected by a new generation high resolution sensor manufactured by Selex Galileo S.p.A., in Italy, and named Hyper SIM-GA, which is an imaging spectrometer operating in the push-broom configuration, with 512 bands (2 nm bandwidth) and 256 bands (6 nm bandwidth) in the V-NIR and SWIR wavelengths, respectively. To this purpose, an original method suitable for estimating the noise introduced by optical imaging systems is described. The power of the signal-dependent photonic noise is decoupled from that of the signal-independent noise generated by the electronic circuitry. The method relies on the multivariate regression of local sample mean and variance. Statistically homogeneous pixels produce scatter-points that are clustered along a straight line, whose slope and intercept measure the signal-dependent and the signal-independent components of the noise power, respectively. Experimental results on radiance data acquired by SIM-GA, highlight the accuracy of the proposed method and its robustness to image textures that may lead to a gross overestimation of the noise.

In this letter a novel method suitable for the lossless compression of hyperspectral imagery is presented. The proposed method generalizes two previous algorithms, in which the concept of nearest neighbor (NN) prediction implemented through either one or two lookup tables (LUTs) was introduced. NowMLUTs are defined on each of theNprevious bands, from which prediction is calculated. The decision among one of theNmiddotMpossible prediction values is based on the closeness of the values contained in the LUTs to an advanced prediction carried out from the values in the sameNprevious bands. Such a prediction is provided by either of two spectral predictors recently developed by the authors. Experimental results carried out on the AVIRIS'97 data set show improvements up to 18% over the baseline LUT-NN algorithm. However, preliminary results carried out on raw data show that all LUT-based methods are not suitable for on-board compression, since they take advantage uniquely of the data artifacts that may be originated by the on-ground calibration procedure.

Quality assessment of pansharpening methods is not an easy task. Quality-assessment indexes, like Q4, spectral angle mapper, and relative global synthesis error, require a reference image at the same resolution as the fused image. In the absence of such a reference image, the quality of pansharpening is assessed at a degraded resolution only. The recently proposed index of Quality Not requiring a Reference (QNR) is one among very few tools available for assessing the quality of pansharpened images at the desired high resolution. However, it would be desirable to cross the outcomes of several independent quality-assessment indexes, in order to better determine the quality of pansharpened images. In this paper, we propose a method to assess fusion quality at the highest resolution, without requiring a high-resolution reference image. The novel method makes use of digital filters matching the modulation transfer functions (MTFs) of the imaging-instrument channels. Spectral quality is evaluated according to Wald's spectral consistency property. Spatial quality measures interscale changes by matching spatial details, extracted from the multispectral bands and from the panchromatic image by means of the high-pass complement of MTF filters. Eventually, we highlight the necessary and sufficient condition criteria for quality-assessment indexes by developing a pansharpening method optimizing the QNR spatial index and assessing the quality of fused images by using the proposed protocol.

The nonsubsampled contourlet transform (NSCT) is a powerful and versatile tool that allows a multiresolution and directional representation to be achieved. In this paper, we propose an extension of two despeckling algorithms, proposed to restore SAR images and based on the undecimated separable wavelet transform, to work into the NSCT domain. The signal is modeled as affected by a multiplicative noise. The noise-free NSCT coefficients are estimated from the observed ones according to either the maximum-a-posteriori (MAP) or the linear minimum mean square error (LMMSE) criterion. The results show that the proposed restoration algorithms highly benefit from the fact of working into a multiresolution and multidirectional domain.

This paper presents a novel algorithm suitable for the lossless compression of hyperspectral imagery. The algorithm generalizes two previous algorithms, in which the concept nearest neighbor (NN) prediction implemented through lookup tables (LUTs) was introduced. Here, the set of LUTs, two or more, say M, on each band are allowed to span more than one previous band, say N bands, and the decision among one of the NM possible prediction values is based on the closeness of the value contained in the LUT to an advanced prediction, spanning N previous bands as well, provided by a top-performing scheme recently developed by the authors and featuring a classified spectral prediction. Experimental results carried out on the AVIRIS '97 dataset show improvements up to 15% over the baseline LUT-NN algorithm. However, preliminary results carried out on raw data show that all LUT-based methods are not suitable for on-board compression, since they take advantage uniquely of the sparseness of data histograms, which is originated by the on-ground calibration procedure.

In this paper, we propose an extension of two despeckling algorithms, proposed to denoise SAR images and based on the undecimated separable wavelet transform, to work with the nonsubsampled contourlet transform (NSCT). The NSCT is a powerful and versatile nonseparable transform that allows a multiresolution and directional representation to be achieved. The SAR signal is modeled as affected by a multiplicative noise. The noise-free NSCT coefficients are estimated from the observed ones according to either the maximum-a-posteriori (MAP) or the linear minimum mean square error (LMMSE) criterion. The results show that the proposed de-speckling algorithms highly benefit from the fact of working into a multiresolution and multidirectional domain.

Quality assessment of pansharpening methods is not a trivial task. The generally used indexes i.e., Q4, SAM and ERGAS require a reference image at the same resolution as the fused image. Since, this reference image is not available the quality of pansharpening algorithms is tested at degraded resolution. However, this does not provide the means to assess the quality of fused images at the desired high resolution. In this paper we propose a method to assess the fusion quality at high resolution by making use of modulation transfer function filters in the frame works of Wald's spectral consistency protocol and Zhou's spatial quality protocol. The results are compared with the recently proposed QNR quality index which also does not require a reference high resolution multispectral image, Zhou's protocol, Q4, ERGAS and SAM.

Quality Without Reference (QNR) index can be used to globally assess the quality of pansharpened images without the need of a reference high resolution multispectral (MS) image. The QNR index relies on local calculation of the Q4 index. Exploiting the local Q4 calculation property of the QNR index, we propose an injection model for pansharpening. The injection model determines the weight of extracted panchromatic (Pan) details that are to be added into the upscaled MS images to obtain the best QNR index. The QNR index calculates spectral distortion of the fused images with respect to the low resolution MS images and spatial distortion of the fused images with respect to the high resolution Pan image. Hence, the QNR optimized fused image is spectrally consistent with the low resolution MS image and spatially consistent with the high resolution Pan image.

In this paper, a novel despeckling algorithm based on undecimated wavelet decomposition and maximumaposterioriestimation is proposed. Such a method represents an improvement with respect to the filter presented by the authors, and it is based on the same conjecture that the probability density functions (pdfs) of the wavelet coefficients follow a generalized Gaussian (GG) distribution. However, the approach introduced here presents two major novelties: 1) theoretically exact expressions for the estimation of the GG parameters are derived: such expressions do not require further assumptions other than the multiplicative model with uncorrelated speckle, and hold also in the case of a strongly correlated reflectivity; 2) a model for the classification of the wavelet coefficients according to their texture energy is introduced. This model allows us to classify the wavelet coefficients into classes having different degrees of heterogeneity, so thatadhocestimation approaches can be devised for the different sets of coefficients. Three different implementations, characterized by different approaches for incorporating into the filtering procedure the information deriving from the segmentation of the wavelet coefficients, are proposed. Experimental results, carried out on both artificially speckled images and true synthetic aperture radar images, demonstrate that the proposed filtering approach outperforms the previous filters, irrespective of the features of the underlying reflectivity.

Multi-temporal analysis of Synthetic Aperture Radar (SAR) images has gained an ever increasing attention due to the availability of several satellite platforms with different revisit times and to the intrinsic capability of the SAR system of producing all-weather observations. As a drawback, automated analysis in general and change detection in particular are made difficult by the inherent noisiness of SAR imagery. Even if a pre-processing step aimed at speckle reduction is adopted, most of algorithms borrowed from computer vision cannot be profitably used. In this work, a novel pixel feature suitable for change analysis is derived from information-theoretic concepts. It does not require preliminary de-speckling and capable of providing accurate change maps from a couple of SAR images. The rationale is that the negative of logarithm of the probability of an amplitude level in one image conditional to the level of the same pixel in the other image conveys an information on the amount of change occurred between the two passes. Experimental results carried out on two couples of multi-temporal SAR images demonstrate that the proposed IT feature outperform the Log-Ratio in terms of capability of discriminating changes.

This paper presents two novel image fusion methods, suitable for sharpening of hyperspectral (HS) images by means of a panchromatic (Pan) observation: the HS bands expanded to the finer scale of the Pan image are sharpened by adding the spatial details which are calculated by the PAN image. Since a direct, unconditioned injection of Pan details gives unsatisfactory results, a new injection model is proposed, which provides the optimum injection simulating fusion at degraded scale by minimizing the mean square error. Fusion tests are carried out both on spatially degraded data to objectively compare the proposed scheme to some fusion methods and on full resolution image data.

This work focuses on quality assessment of fusion of hyperspectral (HS) images with high-resolution panchromatic (Pan) data. A novel fidelity index suitable for HS images is defined from the theory of hypercomplex numbers (2n-ons). Both spectral and spatial distortion measurements are encapsulated in a unique score index. Some fusion methods capable to selectivity inject spatial-frequencies from the higher-resolution Pan image to the coarser HS bands are used for testing and comparisons. Experimental results are presented on Hyperion and ALI data sets.

This letter presents an original approach that exploits classified spectral prediction for lossless/near-lossless hyperspectral-image compression. Minimum-mean-square-error spectral predictors are calculated, one for each small spatial block of each band, and are classified (clustered) to yield a user-defined number of prototype predictors that are capable of matching the spectral features of different classes of pixel spectra for each wavelength. Such predictors are used to achieve a prediction, either crisp or fuzzy. Unlike most of the methods reported in the literature, the proposed approach exploits a purely spectral prediction that is suitable in compressing the data in band-interleaved-by-line format, as they are available at the output of the onboard instrument. In that case, the training phase, i.e., clustering and refining of predictors for each wavelength, may be moved offline. Experimental results on Airborne Visible InfraRed Imaging Spectrometer data show improvements over the most advanced methods in the literature, with a computational complexity that is far lower than that of analogous methods by the same and other authors.

In January 2006, the Data Fusion Committee of the IEEE Geoscience and Remote Sensing Society launched a public contest for pansharpening algorithms, which aimed to identify the ones that perform best. Seven research groups worldwide participated in the contest, testing eight algorithms following different philosophies [component substitution, multiresolution analysis (MRA), detail injection, etc.]. Several complete data sets from two different sensors, namely, QuickBird and simulated Pleiades, were delivered to all participants. The fusion results were collected and evaluated, both visually and objectively. Quantitative results of pansharpening were possible owing to the availability of reference originals obtained either by simulating the data collected from the satellite sensor by means of higher resolution data from an airborne platform, in the case of the Pleiades data, or by first degrading all the available data to a coarser resolution and saving the original as the reference, in the case of the QuickBird data. The evaluation results were presented during the special session on data fusion at the 2006 international geoscience and remote sensing symposium in Denver, and these are discussed in further detail in this paper. Two algorithms outperform all the others, the visual analysis being confirmed by the quantitative evaluation. These two methods share the same philosophy: they basically rely on MRA and employ adaptive models for the injection of high-pass details.

In this work we investigate the use of Shannon's information theory for the goal of devising quality scores of image fusion results that do not require reference originals. In particular, the mutual information between resampled original and fused MS bands is used to measure the spectral quality, while the mutual information between the Pan image and the fused bands yields a measure of spatial quality. The rationale is that the normalized mutual information calculated either between any couple of bands, or between each MS band and the Pan image, should be unchanged after fusion, i.e., when passing from the coarse scale of the MS data to the fine scale of the Pan image. Experimental results carried out on QuickBird and Ikonos data demonstrate that the results provided by the proposed information-theoretic method are in trend with analysis performed on spatially degraded data by means of such parameters as Walds's ERGAS, Wang and Bovik's QI, and the novel Q4 score index based on quaternion theory and recently proposed by the authors. However, the novel method requires no reference and is therefore directly applicable in all practical cases

Segmentation algorithms are often used in many image processing applications like compression, restoration, content extraction, and classification. In particular as for content extraction works carried out in the past decade have demonstrated that multi-frequency fully polarimetric SAR observations are particularly interesting, thanks to physical properties of the backscattered signal at various frequencies and polarizations. To achieve a good classification, the main difficulty is that SAR images are often embedded in heavy speckle. Segmentation of multi/hyperspectral (optical) imagery is obtained by means of algorithms based on image models, which exploit the spatial dependencies of land-covers. Unfortunately, speckle noise hides such spatial dependencies in observed SAR data. With the aim of investigating on a content extraction algorithm capable of discriminating cover classes present in the observed SAR image, heterogeneity features are used here to emphasize spatial dependencies in the data. Thus, observed pixel values are mapped into features, that take "similar" values on "similar" textures. This allows for using the same procedure of the optical case. Obviously, homogeneity/heterogeneity feature and segmentation quality are fundamental for classification accuracy. Here, the problem is tackled through the joint use of information theoretic SAR features and of a segmentation algorithm based on Markov Random Fields (MRFs).

In this paper, a new despeckling method based on undecimated wavelet decomposition and maximum a posteriori MIAP) estimation is proposed. Such a method relies on the assumption that the probability density function (pdf) of each wavelet coefficient is generalized Gaussian (GG). The major novelty of the proposed approach is that the parameters of the GG pdf are taken to be space-varying within each wavelet frame. Thus, they may be adjusted to spatial image context, not only to scale and orientation. Since the MAP equation to be solved is a function of the parameters of the assumed pdf model, the variance and shape factor of the GG function are derived from the theoretical moments, which depend on the moments and joint moments of the observed noisy signal and on the statistics of speckle. The solution of the MAP equation yields the MAP estimate of the wavelet coefficients of the noise-free image. The restored SAR image is synthesized from such coefficients. Experimental results, carried out on both synthetic speckled images and true SAR images, demonstrate that MAP filtering can be successfully applied to SAR images represented in the shift-invariant wavelet domain, without resorting to a logarithmic transformation.

A method to despeckle SAR images based on a maximum a posteriori (MAP) estimation strategy in the undecimated wavelet domain is proposed. The method uses the assumption that the wavelet coefficient probability density functions (PDFs) are generalized Gaussians. The parameters of such distributions are computed by using the moments and the cumulants of the PDFs of the processes that constitute the SAR image, i.e., radar reflectivity and speckle noise. Experimental results demonstrate that the theory of MAP filtering can be successfully applied to SAR images represented in the shift-invariant wavelet domain.

Segmentation algorithms are often used in many image processing applications like compression, restoration, content extraction, and classification. In particular as for the content extraction, works carried out in the past decade have demonstrated that multi-frequency fully polarimetric SAR observations content are particularly interesting, thanks to physical properties of the backscattered signal at various frequencies and polarizations. To achieve a good classification, the main difficulty is that SAR images are often embedded in heavy speckle. Segmentation of multi/hyperspectral (optical) imagery is obtained by means of algorithms based on image models, which exploit the spatial dependencies of landcovers. Unfortunately, speckle noise hides such spatial dependencies in observed SAR data. With the aim of investigating on a content extraction algorithm capable of discriminating cover classes present in the observed SAR image, homogeneity/heterogeneity features are used here to emphasize spatial dependencies in the data. Thus, observed pixel values are mapped into features, that take "similar" values on "similar" textures. This allows for using the same procedure of the optical case. Obviously, homogeneity/heterogeneity feature and segmentation quality are fundamental for classification accuracy. Here, the problem is tackled through the joint use of information-theoretic SAR features and of a segmentation algorithm based on Markov Random Fields (MRFs).

This paper presents a novel scheme for lossless/near-lossless hyperspectral image compression, that exploits a classified spectral prediction. MMSE spectral predictors are calculated for small spatial blocks of each band and are classified (clustered) to yield a user-defined number of prototype predictors for each wavelength, capable of matching the spatial features of different classes of pixel spectra. Unlike most of the literature, the proposed method employs a purely spectral prediction, that is suitable for compressing the data in band-interleaved-by-line (BIL) format, as they are available at the output of the on-board spectrometer. In that case, the training phase, i.e., clustering of predictors for each wavelength, may be moved off-line. Thus, prediction will be slightly less fitting, but the overhead of predictors calculated on-line is saved. Although prediction is purely spectral, hence ID, spatial correlation is removed by the training phase of predictors, aimed at finding statistically homogeneous spatial classes matching the set of prototype spectral predictors. Experimental results on AVIRIS data show improvements over the most advanced methods in the literature, with a computational complexity far lower than that of analogous methods by other authors.

This paper presents a novel image fusion method, suitable for pan-sharpening of multispectral (MS) bands, based on multiresolution analysis (MRA). The low-resolution MS bands are sharpened by injecting highpass directional details extracted from the high-resolution panchromatic (Pan) image by means of the curvelet transform, which is a nonseparable MRA, whose basis function are directional edges with progressively increasing resolution. The advantage with respect to conventional separable MRA, either decimated or not, is twofold: directional detail coefficients matching image edges may be preliminarily soft-thresholded to achieve denoising better than in the separable wavelet domain; modeling of the relationships between high-resolution detail coefficients of MS bands and of the Pan image is more fitting, being carried out in a directional wavelet domain. Experiments carried out on a very-high resolution MS + Pan QuickBird image show that the proposed curvelet method quantitatively outperforms state-of-the art image fusion methods, in terms of geometric, radiometric, and spectral fidelity

A heterogeneity feature, calculable from synthetic aperture radar (SAR) images on a per-pixel basis, but relying on global image statistics, is defined and discussed. Starting from the multiplicative speckle and texture models relating the amount of texture and speckle to the local mean and variance at every pixel, such a feature is rigorously derived from Shannon's information theory as the conditional information of local standard deviation to local mean. Thanks to robust statistical estimation, it is very little sensitive to the noise affecting SAR data, and thus capable of capturing subtle variations of texture whenever they are embedded in a heavy speckle. Experimental results carried out on two SAR images with different degrees of noisiness demonstrate that the proposed feature is likely to be useful for a variety of automated segmentation and classification tasks.

This paper critically reviews state of the art and advanced methods for multispectral (MS) and panchromatic (Pan) image fusion based on either intensity-hue-saturation (IHS) transformation, or redundant multiresolution analysis (MRA). In either case, lower-resolution MS bands are sharpened by injecting details taken from the higher-resolution Pan image. Crucial point is modeling the relationships between detail coefficients of a generic MS band and the Pan image at the same resolution. Once calculated at the coarser resolution, where both types of data are available, such a model shall be extended to the finer resolution to weight the Pan details to be injected. Two injection models embedded in an "a trous" wavelet decomposition will be compared on a test set of very high resolution QuickBird MS+Pan data. One works on approximations and provides a partial unmixing of coarse MS pixels via high-resolution Pan. Another is based on spectral fidelity of original and merged MS data. Fusion comparisons on spatially degraded data, whose high-resolution MS originals are available for reference, show that the former performs better than the latter, in terms of both spatial and spectral fidelity

This letter focuses on quality assessment of fusion of multispectral (MS) images with high-resolution panchromatic (Pan) observations. A new quality index suitable for MS imagery having four spectral bands is defined from the theory of hypercomplex numbers, or quaternions. Both spectral and radiometric distortion measurements are encapsulated in a unique measurement, simultaneously accounting for local mean bias, changes in contrast, and loss of correlation of individual bands, together with spectral distortion. Results are presented and discussed on very high-resolution QuickBird data, through comparisons between state-of-the-art and advanced MS+Pan merge algorithms.

This work presents a novel multisensor image fusion algorithm, which extends panchrmomatic sharpening of multispectral (MS) data through intensity modulation to the integration of MS and synthetic aperture radar (SAR) imagery. The method relies on SAR texture, extracted by ratioing the despeckled SAR image to its low-pass approximation. SAR texture is used to modulate the generalized intensity (GI) of the MS image, which is given by a linear transform extending intensity-hue-saturation transform to an arbitrary number of bands. Before modulation, the GI is enhanced by injection of high-pass details extracted from the available panchrmomatic image by means of the "a/spl grave/-trous" wavelet decomposition. The texture-modulated panchrmomatic-sharpened GI replaces the GI calculated from the resampled original MS data. Then, the inverse transform is applied to obtain the fusion product. Experimental results are presented on Landsat-7 Enhanced Thematic Mapper Plus and European Remote Sensing 2 satellite images of an urban area. The results demonstrate accurate spectral preservation on vegetated regions, bare soil, and also on textured areas (buildings and road network) where SAR texture information enhances the fusion product, which can be usefully applied for both visual analysis and classification purposes.

In this paper, LLMMSE filtering is performed in the undecimated wavelet domain by means of an adaptive rescaling of detail coefficients. The amplitude of each coefficient is divided by the variance ratio of the noisy coefficient to the noise-free one. All the above quantities are analytically calculated from the speckled image, the speckle variance, and the wavelet filters only, without assuming any model to describe the underlying backscatter. Empirical criteria based on distributions of multiresolution coefficient of variation calculated in the undecimated wavelet domain are introduced to mitigate the rescaling of coefficients in highly heterogeneous areas where the speckle is not fully developed. Experiments carried out on both simulated speckled images and true SAR images demonstrate that the visual quality of results is excellent in terms of both background smoothing and preservation of edge sharpness, textures, and point targets. The absence of decimation in the wavelet decomposition avoids the typical impairments produced by critically-subsampled wavelet-based denoising.

This work presents an unsupervised method capable to provide estimates of temporal coherence starting from a couple of multilook detected SAR images of the same scene. The method relies on a robust measurement of the temporal correlation of speckle patterns occurring between the two pass dates. Thanks to the accurate speckle assessment, the temporal correlation coefficient (TCC) of speckle between two overlapped images taken different times is estimated. A nonlinear transformation aimed at decorrelating the data across time while retaining the multiplicative noise model is defined starting from the pixel the pixel geometric mean and ratio of the two overlapped observations. Such a reversible transformation is applied to the couple of images to expedite assessment of temporal speckle patterns correlation. The TCC of speckles is estimated from the noise variances of a transformed couple of images by inverting the relationship yielding the noise variances of the transformed data. Experiments are carried out on two SAR observations from the ERS-1/2 Tandem mission. Starting form the SLC pair, coherence is first estimated to be used as reference. Then, detected 5-looks images are produced and TCC is measured on square blocks, to yield the desired coherence estimate. A linear regression fit shows a good degree of matching with the true coherence values, which holds also on textured areas. Experiments show a good degree of accuracy, when the TCC of speckles is estimated on 32 /spl times/ 32 blocks of geometric mean and ratio of detected 5-looks amplitude images. The method yields acceptable results also in the presence of strong reflectors and textures (urban area) where intensity-based coherence estimators generally fail.

Goal of this work is to investigate lossy compression methodologies from the viewpoint of spectral distortion introduced in hyperspectral pixel vectors, besides that of radiometric distortion. The main result of this analysis is that, for a given compression ratio, near-lossless methods, i.e., with constrained pixel error, either absolute or relative, are more suitable for preserving the spectral discrimination capability among pixel vectors, which is perhaps the main source of spectral information. Therefore, whenever a lossless compression is not practicable, near-lossless compression is recommended in such applications where spectral quality is crucial.

This work presents a viable solution to the problem of merging a multispectral image with an arbitrary number of bands with a higher resolution panchromatic observation. The proposed method relies on the generalized Laplacian pyramid, which is a multiscale oversampled structure in which spatial details are mapped on different scales. The goal is to selectively perform spatial-frequencies spectrum substitution from an image to another with the constraint of thoroughly retaining the spectral information of the coarser data. To this end, a vector injection model has been defined: at each pixel, the detail vector to be added is always parallel to the approximation. Furthermore, its components are scaled by factors measuring the ratio of local gains between the multispectral and panchromatic data. Such a model is calculated at a coarser resolution where both types of data are available and extended to the finer resolution by embedding the modulation transfer function of the multispectral scanner into the multiresolution analysis. In this way, the interband structure model can be extended to the higher resolution without the drawback of the poor enhancement occurring when the model assumes MTFs close to be ideal. Results are presented and discussed on very high resolution QuickBird data of an urban area.

In this work, a new strategy for the analysis of hyperspectral data is described and assessed. The image is segmented into spatially homogeneous areas by means of a three-steps procedure: split the whole hyperspectral image into homogeneous square blocks of different sizes, merge adjacent homogeneous blocks into connected regions, and merge non-adjacent homogeneous blocks into unconnected regions. A reduced data set (RDS) is produced by applying the projection pursuit (PP) algorithm to each of the segments in which the original hyperspectral image has been partitioned based on a spatial homogeneity criterion of pixel spectra. Few significant spectral pixels are extracted from each segment. This operation allows to dramatically reduce the size of the set while maintaining the main information relative to the whole image. The "best" elements of a basis that represents the RDS are searched for. Algorithms that can be used for this task are whichever methods capable to reduce spectral features: e.g., principal component analysis (PCA) or PP. The best elements representing RDS may constitute a good approximation of the best elements found for the whole hyperspectral image, as the features of RDS are very similar to the features of the original hyperspectral data. Therefore, once the basis has been calculated from RDS, it is used to decompose the whole hyperspectral data set. Experiments were carried out on AVIRIS data, for which ground truth was available. Results show that the PCA based on the RDS, even if suboptimal in the MMSE sense with respect to the conventional PCA, increases the separability of thematic classes, which is favored when pixel vectors in the transformed domain are homogeneously spread around their class centers.

This work reports about an original application concerning lossy compression of multispectral (XS) and panchromatic (Pan) images collected by spaceborne platforms. Generally, the former is a set of three or four narrow-band spectral images, while the latter is a single broadband observation imaged in the visible and near-infrared wavelengths. Since high resolution spectral observations having high SNR are difficult to obtain, and especially to transmit, the Pan image, having resolution typically four times that of XS, but slightly lower SNR, is added to the XS data and used with the main purpose of expediting both visual and automatic identification tasks, possibly through an integration (merge) with the lower resolution XS data. Whenever XS data at the same resolution of the Pan data and with adequate SNR were hypothetically available on board, the bottleneck of downlink to receiving stations would impose severe limitations in the bit rate, so that a lossy compression would be mandatory. The consequence of the loss of information is a distortion, both radiometric and especially spectral, which may be easily quantified.

This paper presents an unsupervised method capable to provide estimates of temporal coherence starting from a pair of multilook detected synthetic aperture radar (SAR) images of the same scene. The method relies on robust measurements of the temporal correlation of speckle patterns between the two pass dates. To this end, a nonlinear transformation aimed at decorrelating the data across time while retaining the multiplicative noise model is defined as the pixel geometric mean and ratio of the two overlapped images. The temporal correlation coefficient (TCC) of speckle is analytically derived from the noise variances, measured in the transformed pair of images as regression coefficients of local standard deviation to local mean, calculated on homogeneous, i.e., nontextured, pixels. Such pixels are identified based on the observation that homogeneous areas produce clustered scatter-points that are aligned along the regression line. Experiments were carried out on two pairs of multitemporal SAR observations, from the European Remote Sensing 1/2 (ERS-1/2) tandem mission and from the 1994 SIR-C mission. A good fit with the true coherence values was found, irrespective of the presence of textures; when the true coherence was unavailable, the estimated coherence results match the available ground truth data.

In this paper, methods to denoise images corrupted by a signal-dependent additive distortion are proposed. The noise model is parametric to take into account different noise generation processes. Noise reduction is approached as a Wiener-like filtering performed in a shift-invariant wavelet domain by means of an adaptive rescaling of the coefficients of an undecimated decomposition. The scaling factor is computed by using the statistics estimated from the degraded image and the parameters of the noise model. The absence of decimation in the wavelet decomposition avoids the ringing impairments produced by critically-subsampled wavelet-based denoising. Experimental results demonstrate that excellent background smoothing as well as preservation of edge sharpness and texture can be obtained.

In this paper, LLMMSE filtering is performed in the undecimated wavelet domain by means of an adaptive rescaling of detail coefficients. The amplitude of each coefficient is divided by the variance ratio of the noisy coefficient to the noise-free one. All the above quantities are analytically calculated from the speckled image, the speckle variance, and the wavelet filters only, without assuming any model to describe the underlying backscatter. Empirical criteria based on distributions of multiresolution C/sub v/ calculated in the undecimated wavelet domain are introduced to mitigate the rescaling of coefficients in highly heterogeneous areas where the speckle is not fully developed, to definitely avoid the slight blurring noticed in some textures and the perceivable smearing of point targets. Experiments carried out on SAR images demonstrate that the visual quality of results is excellent in terms of both background smoothing and preservation of edge sharpness, textures, and point targets. The absence of decimation in the wavelet decomposition avoids the typical impairments produced by critically-subsampled wavelet-based denoising.

This work describes a nonparametric algorithm suitable for scene classification, either supervised or not, starting from a number of pixel features derived from SAR observations. Pixel vectors composed by simple features derived from the backscatter coefficients of one or more bands and/or polarizations are iteratively clustered into dynamically upgraded classes. Possible "a priori" knowledge coming from ground truth data may be used to initialize the procedure, but is not mandatory. Experiments on MAC-91 NASA/JPL AIRSAR data on the Montespertoli test site show that seven features derived from each of L-HV and P-HV observations are capable to discriminate seven agricultural cover classes with an overall pixel accuracy of 60%, when the algorithm learns from 10% of the truth data and classifies the remaining 90%.

Aim of this paper is investigating the use of overcomplete bases for the representation of hyperspectral image data. The idea is building an overcomplete basis starting from several orthogonal or nonorthogonal bases and picking a set of vectors fitting pixel spectra to the largest extent. This technique, denoted also as mixed-transform analysis (MTA), has been successfully used to represent speech and images. The main problems in using MTA for hyperspectral data analysis are: (1) choice of bases (at least two) that potentially convey maximum spectral information; (2) computation of projections in the non-orthogonal representation. Selection of vectors from the overcomplete basis can be made in different ways. A large variety of bases has been taken into consideration, including several types of wavelets with compact support. Representation of data as a linear combination of the selected basis vector is complicated by the fact that these vectors are non-orthogonal. The computational cost is extremely high when a large set of data is to be processed. For these reasons, an iterative approach is used to find the coefficients of the linear combination of vectors, so that the residual function has minimum energy. Experimental results carried out on hyperspectral data collected in AVIRIS Moffett Field '97 show the joint use of two different bases, possibly including a wavelet, is preferable to a unique orthogonal basis in terms of energy compaction, as well as of significance of the outcome components.

This letter describes a context-based entropy coding suitable for any causal spatial differential pulse code modulation (DPCM) scheme performing lossless or near-lossless image coding. The proposed method is based on partitioning of prediction errors into homogeneous classes before arithmetic coding. A context function is measured on prediction errors lying within a two-dimensional (2-D) causal neighborhood, comprising the prediction support of the current pixel, as the root mean square (RMS) of residuals weighted by the reciprocal of their Euclidean distances. Its effectiveness is demonstrated in comparative experiments concerning both lossless and near-lossless coding. The proposed context coding/decoding is strictly real-time.

This paper presents an application of fuzzy-logic techniques to the reversible compression of grayscale images. With reference to a spatial differential pulse code modulation (DPCM) scheme, prediction may be accomplished in a space-varying fashion either as adaptive, i.e., with predictors recalculated at each pixel, or as classified, in which image blocks or pixels are labeled in a number of classes, for which fitting predictors are calculated. Here, an original tradeoff is proposed; a space-varying linear-regression prediction is obtained through fuzzy-logic techniques as a problem of matching pursuit, in which a predictor different for every pixel is obtained as an expansion in series of a finite number of prototype nonorthogonal predictors, that are calculated in a fuzzy fashion as well. To enhance entropy coding, the spatial prediction is followed by context-based statistical modeling of prediction errors. A thorough comparison with the most advanced methods in the literature, as well as an investigation of performance trends and computing times to work parameters, highlight the advantages of the proposed fuzzy approach to data compression.

This paper compares two general and formal solutions to the problem of fusion of multispectral images with high-resolution panchromatic observations. The former exploits the undecimated discrete wavelet transform, which is an octave bandpass representation achieved from a conventional discrete wavelet transform by omitting all decimators and upsampling the wavelet filter bank. The latter relies on the generalized Laplacian pyramid, which is another oversampled structure obtained by recursively subtracting from an image an expanded decimated lowpass version. Both the methods selectively perform spatial-frequencies spectrum substitution from an image to another. In both schemes, context dependency is exploited by thresholding the local correlation coefficient between the images to be merged, to avoid injection of spatial details that are not likely to occur in the target image. Unlike other multiscale fusion schemes, both the present decompositions are not critically subsampled, thus avoiding possible impairments in the fused images, due to missing cancellation of aliasing terms. Results are presented and discussed on SPOT data.

Speckle reduction is approached as a minimum mean-square error (MMSE) filtering performed in the undecimated wavelet domain by means of an adaptive rescaling of the detail coefficients, whose amplitude is divided by the variance ratio of the noisy coefficient to the noise-free one. All the above quantities are analytically calculated from the speckled image, the variance and autocorrelation of the fading variable, and the wavelet filters only, without resorting to any model to describe the underlying backscatter. On the test image Lena corrupted by synthetic speckle, the proposed method outperforms Kuan's local linear MMSE filtering by almost 3-dB signal-to-noise ratio. When true synthetic aperture radar (SAR) images are concerned, empirical criteria based on distributions of multiscale local coefficient of variation, calculated in the undecimated wavelet domain, are introduced to mitigate the rescaling of coefficients in highly heterogeneous areas where the speckle does not obey a fully developed model, to avoid blurring strong textures and point targets. Experiments carried out on widespread test SAR images and on a speckled mosaic image, comprising synthetic shapes, textures, and details from optical images, demonstrate that the visual quality of the results is excellent in terms of both background smoothing and preservation of edge sharpness, textures, and point targets. The absence of decimation in the wavelet decomposition avoids typical impairments often introduced by critically subsampled wavelet-based denoising.

This paper presents an original application of fuzzy logic to the restoration of images affected by white noise, possibly nonstationary and/or signal dependent. Space-varying linear MMSE estimation is stated as a problem of matching pursuits, in which the estimator is obtained as a series expansion of a finite number of prototype estimators, fitting the spatial features of the different statistical classes encountered, e.g., edges and textures. Such estimators are calculated in a fuzzy fashion through an automatic training procedure. The space-varying coefficients of the expansion are stated as degrees of fuzzy membership of a pixel to each of the estimators. Besides the fact that neither "a priori" knowledge of the noise model is required nor a particular signal model is assumed, a performance comparison highlights the advantages of the proposed approach. Results on simulated noisy versions of Lenna show a steady SNR improvement of almost 3 dB over Kuan's LLMMSE filtering and over 2 dB over wavelet thresholding, irrespective of noise model and intensity.

Near-lossless compression, yielding a strictly bounded reconstruction error, is extended to preserve the radiometric resolution of data produced by coherent imaging systems. A noncausal DPCM, based on the rational Laplacian pyramid (RLP), recently introduced by the authors for despeckling, is adjusted to this purpose. The baseband icon of the RLP is DPCM encoded, the intermediate layers are uniformly quantized, and the bottom layer is logarithmically quantized. As a consequence, the relative error, i.e., pixel ratio of original to decoded image, can be strictly bounded by the quantization step size of the bottom layer of the RLP.

The impact of a regularization of motion vectors (MVs) on the performance of a block-DCT based video coder (H.263) is addressed. Postprocessing is accomplished by exploiting both the spatial correlation of the vector field and the confidence of the estimated block vectors. A previously proposed adaptive scheme for MV smoothing, based on the theory of vector median filters, is adjusted and embedded into an H.263 coder. With a bit stream that is perfectly H.263-compatible, results are improved, especially for very low bit rates and complex motion of the scene.

Near-lossless compression yielding strictly bounded reconstruction error is proposed for high-quality compression of remote sensing images. A classified causal differential pulse code modulation scheme is presented for optical data, either multi/hyperspectral three-dimensional (3-D) or panchromatic two-dimensional (2-D) observations. It is based on a classified linear-regression prediction, followed by context-based arithmetic coding of the outcome prediction errors and provides excellent performances, both for reversible and for irreversible (near-lossless) compression. Coding times are affordable thanks to fast convergence of training. Decoding is always real time. If the reconstruction errors fall within the boundaries of the noise distributions, the decoded images will be virtually lossless even though encoding was not strictly reversible.

This work focuses on estimating the information conveyed to a user by hyperspectral image data. The goal is establishing the extent to which an increase in spectral resolution enhances the amount of usable information. Indeed, a tradeoff exists between spatial and spectral resolution due to physical constraints of multi-band sensors imaging with a prefixed SNR. After describing an original method developed for the automatic estimation of variance and correlation of the noise introduced by hyperspectral imagers, lossless interband data compression is exploited to measure the useful information content of hyperspectral data. In fact, the bit rate achieved by the reversible compression process takes into account both the contribution of the "observation" noise (i.e., information regarded as statistical uncertainty, but whose relevance to a user is null) and the intrinsic information of radiance sampled and digitized through an ideally noise-free process. An entropic model of the decorrelated image source is defined and, once the parameters of the noise, assumed to be Gaussian and stationary, have been measured, such a model is inverted to yield an estimate of the information content of the noise-free source from the code rate. Results are reported and discussed on both simulated and AVIRIS data.

This paper presents an error bounded encoder suitable for near lossless image compression. The scheme is a classified spatial DPCM, enhanced by a fuzzy clustered initialization and an iterative joint adjustment of predictors and block partition into classes, followed by context based statistical modeling and arithmetic coding of prediction residuals. Prediction errors are quantized with user defined odd step sizes in order to allow rate control with a minimum peak error over the whole image, so as to exactly limit the local distortion. The performances of the method are superior with respect to other similar schemes, thanks to its flexibility and robustness to changes in type of image and desired distortion level. Decoding is always performed in real time, as predictors are trained at the encoder only.

In this letter, we investigate the problem of fusion of data collected by sensors having different ground and wavelength resolutions. This is a typical problem encountered in the interpretation of remotely sensed images. The approach that is proposed here is based on the use of cosine-modulated uniform filter banks. We assume that the ratio of the sampling periods of the input data is not integer and show how to design the filter banks so that spectra from different signals can be integrated with a minimum distortion.

This paper describes a computational method for estimating the body reflectance function of color surfaces. The experimental apparatus consists of a vision system having seven spectral channels whose wavelength sensitivities cover the visible spectrum. The estimation of the spectral-reflectance function is based on finite-dimensional linear models. In order to use digitized imaged data to evaluate the surface reflectance, a procedure for bypassing the problem of unknown illuminant spectral-power distribution was devised. For the simple objects utilized (color checker charts), it is found that an accuracy greater than 97% can be achieved.

An effective method for lossless image compression is presented. It relies on a classified linear-regression prediction obtained through fuzzy techniques, followed by context based modeling of the outcome prediction errors, to enhance entropy coding. The present scheme is a reworking of the fuzzy encoder presented at ICIP'98 (FDC). Now, predictors, instead of pixel intensity patterns, are fuzzy-clustered to find out optimized MMSE prediction classes, and a novel membership function measuring the fitness of prediction is adopted. Size and shape of causal neighborhoods supporting prediction, as well as number of predictors to be blended, may be chosen by user and settle the tradeoff between coding performances and computational costs. The encoder exhibits impressive performances, thanks to the skill of predictors in fitting data patterns as well as to context modeling.

A novel method for estimating the shape factor of a generalized Gaussian probability density function (PDF) is presented and assessed. It relies on matching the entropy of the modeled distribution with that of the empirical data. The entropic approach is suitable for real-time applications and yields results that are accurate also for low values of the shape factor and small data sample. Modeling of wavelet coefficients for entropy coding is addressed and experimental results on true image data are reported and discussed.

This paper describes an original application of fuzzy logic to the reversible compression of multispectral data. The method consists of a space spectral varying prediction followed by context-based classification and arithmetic coding of the outcome residuals. Prediction of a pixel to be encoded is obtained from the fuzzy-switching of a set of linear regression predictors. Pixels both on the current band and on previously encoded bands may be used to define a causal neighborhood. The coefficients of each predictor are calculated so as to minimize the mean-squared error for those pixels whose intensity level patterns lying on the causal neighborhood, belong in a fuzzy sense to a predefined cluster. The size and shape of the causal neighborhood, as well as the number of predictors to be switched, may be chosen by the user and determine the tradeoff between coding performances and computational cost. The method exhibits impressive results, thanks to the skill of predictors in fitting multispectral data patterns, regardless of differences in sensor responses.

Vector median filtering has been recently proposed as an effective method to refine estimated velocity fields. Here, the use of a weighted vector median filtering is suggested to improve the regularization of the optic flow field across motion boundaries. Information about the confidence of the estimated pixel velocities is exploited for the choice of the filter weights. Experimental results, on both synthetic and real-world sequences, show the effectiveness of the proposed procedure.

A distributed implementation of a new method for reversible compression of both 2D and 3D data is presented. A classified prediction is first trained through fuzzy clustering; then, data decorrelation is accomplished by prediction in a fuzzy fashion. Context-based adaptive arithmetic coding is tailored to the prediction errors to enhance entropy coding. Results and comparisons with other schemes are presented and discussed together with computational issues.

Speckle filtering in synthetic aperture radar (SAR) images is a key point to facilitate applicative tasks. A filter aimed at speckle reduction should energetically smooth homogeneous regions, while preserving point targets, edges, and linear features. A compromise, however, should be arranged on textured areas. In this work, a ratio Laplacian pyramid (RLP) is introduced to match the signal-dependent nature of speckle noise. Local statistics filtering is applied to the different spatial resolutions of the RLP of a speckled image. For natural scenes, each pyramid layer is characterized by an signal-to-noise ratio (SNR) increasing as resolution decreases. Thus, each filter may be adjusted to achieve adaptivity also across scales. In addition, the estimation of the local statistics driving the filter is more accurate thanks to the multiresolution framework. A complete procedure is setup, and a general formulation, in which the variance of speckle is theoretically derived at each resolution, is developed. Experiments carried out on remotely sensed optical images corrupted with synthetic speckle, as well as on true SAR images, show the potentiality of the pyramid-based approach compared with other established despeckle algorithms, in terms both of SNR improvements and of enhancement in visual quality.

Signal-dependent noise may be described by a unique parametric model yielding additive, multiplicative, and film-grain noise. For such a model, adaptive filtering can be written as local linear minimum mean square error (LLMMSE) filtering. Multiresolution processing is exploited to achieve adaptivity also across scale, as SNR increases with the scale of the decomposition, in natural images. A generalized Laplacian pyramid is designed to match the signal-dependent nature of noise, thus allowing LLMMSE filtering to be carried out on its layers. Results from images affected by several types of synthetic noise are superior to those achieved without multiresolution context, by 1 to 2 dB on an average.

The idea of the present scheme is to apply a directional version of geometric filter (complementary-hull) to the different sub-bands into which the noisy image is decomposed by the S-transform, a dyadic Haar wavelet yielding integer valued coefficients. The hull algorithm is applied only on the direction(s) along which the signal is more structured. The number of iterations is adjusted to the SNR of the sub-bands, so as to preserve spatial details to the largest extent. Comparisons with the standard geometric filter are presented for images affected by synthetic multiplicative (speckle) noise. Results are pretty superior to those achieved without multiresolution context, both visually and in terms of SNR.

In this paper, the effects of quantization noise feedback on the entropy of Laplacian pyramids are investigated. This technique makes it possible for the maximum absolute reconstruction error to be easily and strongly upper-bounded (near-lossless coding), and therefore, allows reversible compression. The entropy-minimizing optimum quantizer is obtained by modeling the first-order distributions of the differential signals as Laplacian densities, and by deriving a model for the equivalent memoryless entropy. A novel approach, based on an enhanced Laplacian pyramid, is proposed for the compression, either lossless or lossy, of gray-scale images. Major details are prioritized through a content-driven decision rule embedded in a uniform threshold quantizer with noise feedback. Lossless coding shows improvements over reversible Joint Photographers Expert Group (JPEG) and the reduced-difference pyramid schemes, while lossy coding outperforms JPEG, with a significant peak signal-to-noise ratio (PSNR) gain. Also, subjective quality is higher even at very low bit rates, due to the absence of the annoying impairments typical of JPEG. Moreover, image versions having resolution and SNR that are both progressively increasing are made available at the receiving end from the earliest retrieval stage on, as intermediate steps of the decoding procedure, without any additional cost.

In the field of video coding the issues of backward prediction and standards conversion have focused an increasing attention towards techniques for an effective estimation of the true interframe motion. The problem of restoration of motion vector-fields computed by means of a standard block matching algorithm is addressed. The restoration must be carried out carefully by exploiting both the spatial correlation of the vector-field, and the significance of the obtained vectors as measures of the reliability of the previous estimation step. A novel approach matching both the above requirements is presented. Based on the theory of vector-median filters an adaptive scheme is developed and results are discussed.

In this work, it is shown that the generalized recursive interpolation (GRINT) proposed is the most effective progressive technique for inter-frame reversible compression of tomographic sections that typically occur in the medical field. An image sequence is decimated by a factor 2, first along rows only, then along columns only, and eventually along slices only, recursively in a sequel, thus creating a gray-level hyperpyramid whose number of voxels halves at every level. The top of the pyramid (root) is stored and then directionally interpolated by means of a 1D kernel. Interpolation errors with the underlying equally-sized hyperlayer are stored as well. The same procedure is repeated, until the image sequence is completely decomposed. The advantage of the novel scheme with respect to other noncausal DPCM schemes is twofold: firstly interpolation is performed from all error-free values, thereby reducing the variance of residuals; secondly different correlation values along rows, columns and sections can be exploited for a better decorrelation.

A novel criterion is introduced for eliminating false contours detected as zero-crossings in images processed by means of a Laplacian-of-Gaussian filter. Each candidate contour point is given a score and is retained only if such a value exceeds a threshold which is related to image contrast and independent of the noise. After all the zero-crossings of a contour have been classified, the whole contour is either accepted or rejected depending on its percentage of validated contour points. The threshold percentage is stated a function of the signal-to-noise ratio. The algorithm effectively copes with images taken practically under any possible environmental conditions during acquisition. Experiments carried out on images of structured markers show that the procedure is robust to noise and suitable for real-time applications in which an image segmentation is demanded.

The Laplacian pyramid (LP) is appropriate for lossy image compression; conversely, the reduced-difference pyramid (RDP), having as many data as pixels, gives a better performance with lossless encoding. A reduced LP is designed by discarding the anti-aliasing filter and adopting a half-band interpolator, thus retaining three over four of the LP coefficients. Lossless coding outperforms both LP and RDP, especially when dealing with medical images.

In this paper results of investigations about the effects of channel errors in the transmission of images compressed by means of techniques based on Discrete Cosine Transform (DCT) and Vector Quantization (VQ) are presented. Since compressed images are heavily degraded by noise in the transmission channel, more seriously for what concern VQ-coded images, theoretical studies and simulations are presented in order to define and evaluate this degradation. Some channel coding schemes are proposed in order to protect information during transmission. Hamming codes (7,4), (15,11) and (31,26) have been used for DCT-compressed images; more powerful codes, such as Golay (23,12), for VQ-compressed images. Performances attainable with soft- decoding techniques are also evaluated; better quality images have been obtained than using classical hard decoding techniques. All tests have been carried out to simulate the transmission of a digital image from HDTV signal over an AWGN channel with PSK modulation.

In this paper we have studied what performances can be obtained by mapping processing image algorithms on parallel architectures. For this reason we have focused our attention on a particular problems we have studied a processing chain to detect ship wakes in SAR images. It allowed us to test low and medium level algorithms. Because of the noisy nature of SAR images great attention has been put on the choice of the most appropriate filtering technique. It has been done both through theoretical considerations on the nature of noise and experimental results on filtered images. The chain has been implemented on a sequential machine like MicroVAX II and on some parallel architectures based on eight transputers IMS T800. The performances obtained in this way have been discussed and some general considerations have been deduced from them.