Speckle noise produces a strong degradation in SAR images, characterized by a multiplicative model. Its removal is an important step of any processing chain exploiting such data. To perform this task, several model-based despeckling methods were proposed in the past years as well as, more recently, deep learning approaches. However, most of the latter ones need to be trained on a large number of pairs of noisy and clean images that, in the case of SAR images, can only be produced with the aid of synthetic noise. In this paper, we propose a self-supervised learning method based on the use of Deep Image Prior, which is extended to deal with speckle noise. The major advantage of the proposed approach lies in its ability to perform denoising without requiring any reference clean image during training. A new loss function is introduced in order to reproduce a multiplicative noise having statistics close to those of a typical speckle noise and composed also by a guidance term derived from model-based denoisers. Experimental results are presented to show the effectiveness of the proposed method and compare its performance with other reference despeckling algorithms. • A self-supervised learning method for SAR despeckling, denoted as S3DIP, is proposed. • The Deep Image Prior (DIP) approach is extended introducing a learnable noise matrix. • A histogram loss based on the knowledge of the speckle noise statistics is designed. • Existing model-based denoisers are exploited through the use of a guidance loss. • S3DIP outperforms both DIP and existing model-based denoisers on the intended task.

The NDSA technique, proposed for estimating the IWV (Integrated Water Vapor) through a tropospheric radio link, operates by transmitting two sinusoidal signals at K band and gauging their reception power. This enables the estimation of IWV based on the different signals’attenuation. In 2018, an instrument prototype was finalized for the first measurement campaign, showcasing the NDSA method. In this paper we describe the improved version of the instrument, used for a second campaign in 2022, the procedures for its characterization and generation of data, and some of the campaign outcomes.

Accurate quantitative precipitation estimation (QPE) methods are essential for weather forecasting and for prevention of hydrogeological risk. QPE becomes even more important when facing severe precipitation events. In this letter, a comparison among different rainfall estimation methods is presented, using a severe event that occurred in Italy as a case study. In particular, the focus is on a merging method based on the dynamic adaptation of the Z–R relationship according to the spatiotemporal evolution of the observed phenomenon. Through a cross-validation analysis, we quantitatively assess the effectiveness of such a method: compared with the others, it performs better on the average, while it can outperform them in critical rainfall conditions, confirming its potential for localizing and monitoring areas with greatest risks.

In this paper, we address the problem of combating the effect of the nonlinearities of the transmit-receive chain in solid-state radars, which are typically generated by the power amplifier in transmission. This issue is of particular importance in meteorological radar applications, as they require transmit pulses featuring very low autocorrelation sidelobes, which are significantly raised due to nonlinearities. In this work, we describe an adaptive predistortion design method based on an iterative approach in the spectral domain. The proposed method has been validated by means of hardware using a customized software radio and driving an amplifier into saturation. Two different ideal, highly performing pulse compression waveforms, expressly designed for weather radar applications, were sent to its input. The experimental results demonstrate the benefits of the proposed approach to design the digital predistortion module.

This paper illustrates the first results of the analysis carried out to check the possibility to provide an estimate of the Integrated Liquid Water (ILW) content along a microwave link established between the multifrequency transmitter and the receiver on board a couple of Low Earth Orbiting (LEO) satellites. The ILW estimate is provided through the power ratio of the received signals at 32 and 17 GHz. The results have been obtained using a simulation tool developed for LEO satellites orbiting in the same plane and along the same angular direction (co-rotating satellites), assuming some high-resolution atmospheric scenarios generated by using the WRF (Weather Research and Forecasting) numerical weather prediction model.

Recently, inversion of Integral Water Vapor (IWV) measurements, obtained through the use of the Normalized Differential Spectral Absorption (NDSA) has been proposed to retrieve the tropospheric Water Vapor (WV) content. In this paper, the results of the application of the External Reconstruction Tomographic Algorithm (ERTA) to that problem are presented. The results have been obtained by considering a measurement scenario composed of LEO satellites orbiting in the same plane and along the same angular direction (co-rotating satellites).

This article addresses the problem of radar pulse compression. First, a matched filter at the receiver is assumed and a method to design a transmit waveform characterized by an autocorrelation function with a narrow mainlobe and low sidelobes is proposed. After that, a mismatched filter is considered and a method to design the optimum linear filter receiver is proposed. In both cases, the pursued objectives are minimum sidelobe energy and peak level through a strategy based on quadratic and nonlinear optimization. In this article, we focus particularly on the case of ground weather radars, where the problem of pulse compression is particularly challenging.

To decide whether a digital video has been captured by a given device, multimedia forensic tools usually exploit characteristic noise traces left by the camera sensor on the acquired frames. This analysis requires that the noise pattern characterizing the camera and the noise pattern extracted from video frames under analysis are geometrically aligned. However, in many practical scenarios this does not occur, thus a re-alignment or synchronization has to be performed. Current solutions often require time consuming search of the realignment transformation parameters. In this paper, we propose to overcome this limitation by searching scaling and rotation parameters in the frequency domain. The proposed algorithm tested on real videos from a well-known state-of-the-art dataset shows promising results.

The use of the normalized differential spectral attenuation (NDSA) approach in the microwaves and (later) in the millimeter waves has been recently introduced to retrieve information about integrated water vapor (IWV) content from attenuation measurements along microwave links between two low Earth orbit (LEO) satellites. NDSA was originally proposed for a configuration of two counter-rotating satellites, to achieve vertical profiles of water vapor (WV) from IWV measurements. In this paper, we analyze the exploitability of the NDSA approach in the case of a constellation of corotating LEO satellites in order to estimate the WV content in a 2-D field lying in the orbital plane of the satellites. The WV retrieval is formalized as the solution of an inverse problem. Simulation results are presented in order to demonstrate the feasibility of the proposed approach: a complete acquisition system composed of transmitting and receiving LEO satellites, including tropospheric scintillation effects, has been modeled, and the reconstruction of 2-D maps of the atmospheric WV from multiple IWV measurements is shown.

Orthogonal Frequency Division Multiplexing (OFDM) transmission technique has been considered for the 4G LTE-Advanced system because of its high performance and low complexity. In the new 5G scenario this type of modulation is not properly suited because of the additional requirements for very high spectral efficiency, low latency and low out-of-band (OOB) emissions. Thus, new waveforms have been chosen to replace it and effectively deal with these problems. Particularly, recently proposed multicarrier techniques as the Generalized Frequency Division Multiplexing (GFDM) and the Filter Bank Multicarrier (FBMC) modulations are two of the main candidates techniques for the new 5G standard. As for classical OFDM technique, the channel estimation is a crucial functionality for the all multicarrier approaches. In this paper we generalize a recently proposed method for the computation of the MSE on the time-frequency domain for pilot based channel estimation techniques in multicarrier system. This method permits to determine the most suitable channel estimation algorithm for a given wireless channel as well as to define the suitable pilot density in order to afford a target MSE value for a given SNR level. Hence, in this paper a general design tool for multicarrier systems is proposed.

This paper presents a study for the estimation of 2-D maps of atmospheric water vapour content from integrated water vapour measurements carried out by a constellation of co-rotating low earth orbit satellites. The proposed method uses the normalised differential spectral attenuation (NDSA) approach - able to achieve integrated water vapour content information from attenuation measurements over microwave links among the satellites - and tomographic techniques to solve the inverse problem of atmospheric water vapour field reconstruction. Simulation results demonstrate the feasibility of the proposed approach to retrieve a 2-D map of the atmospheric water vapour content. This study has been developed under the framework of the ANISAP project funded by the European Space Agency.

The normalised differential spectral attenuation (NDSA) approach has been recently introduced to retrieve integrated water vapour (IWV) content information from attenuation measurements over microwave links between two low earth orbit (LEO) satellites. In the original formulation, two counter-rotating satellites were considered in order to achieve vertical profiles of water vapour. In this paper, an extension of the method to the case of a constellation of co-rotating LEO satellites is proposed. Simulation results demonstrate the feasibility of the proposed approach to retrieve 2-D maps of the atmospheric water vapour content from IWV measurements.

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.

The definition of LTE and LTE-Advanced standards aims at improving the performance of cellular networks with the final goal of a fair competition between wired and wireless communication systems. In order to guarantee excellent performance, one of the crucial challenge to cope with is the introduction of advanced channel estimation techniques for Multiple Inputs Multiple Outputs (MIMO) systems. In this paper, we will review and compare several Pilot-Based Channel Estimation algorithms for MIMO LTE downlink communications. Channel estimation algorithms will be analysed for different multi-antenna schemes, namely 2×2 and 4×4 with Alamouti space-frequency coding. The performance of all of these schemes will be considered both for uncoded and coded systems. The simulation results will be obtained for a multipath fading channel, assuming high speed mobility for the mobile terminals.

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.

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 the area of music information retrieval (MIR), automatic music transcription is considered one of the most challenging tasks, for which many different techniques have been proposed. This paper presents a new method for polyphonic music transcription: a system that aims at estimating pitch, onset times, durations, and intensity of concurrent sounds in audio recordings, played by one or more instruments. Pitch estimation is carried out by means of a front-end that jointly uses a constant-Q and a bispectral analysis of the input audio signal; subsequently, the processed signal is correlated with a fixed 2-D harmonic pattern. Onsets and durations detection procedures are based on the combination of the constant-Q bispectral analysis with information from the signal spectrogram. The detection process is agnostic and it does not need to take into account musicological and instrumental models or other a priori knowledge. The system has been validated against the standard Real-World Computing (RWC)-Classical Audio Database. The proposed method has demonstrated good performances in the multipleF0 tracking task, especially for piano-only automatic transcription at MIREX 2009.

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.

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.

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.

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.

Normalized differential spectral attenuation (NDSA) is a novel differential measurement method to estimate the total content of water vapor [integrated water vapor (IWV)] along a tropospheric propagation path between two low Earth orbit (LEO) satellites. A transmitter onboard the first LEO satellite and a receiver onboard the second one are required. The NDSA approach is based on the simultaneous estimates of the total attenuation at two relatively close frequencies in the Ku/K-bands and of a "spectral sensitivity parameter" that can be directly converted into IWV. The spectral sensitivity has the potential to determine the water vapor contribution, to cancel out all spectrally flat unwanted contributions, and to limit the impairments due to tropospheric scintillation. In this paper, we focus on the measurement accuracy of the spectral sensitivity parameter. Specifically, we examine this accuracy at three different frequencies and for two models of atmospheric structure. We first provide an approximate expression of the accuracy and then validate this expression through Monte Carlo simulations based on microwave propagation models.

The multiband UWB approach is well-seen as one of the most promising technique for short range communications due to its compatibility towards 802.11 family. In this contribution we aim to present a multiband UWB system using cross-polarized antenna, a channel model taking into account also the mutual orientation of Tx and Rx antennas and, at last, several time-frequency codes for accessing the channel in a multi-piconets environment

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.

In this paper, we investigate the performance of a generic filterbank transceiver in the presence of a carrier frequency offset. We propose a theoretical model to compute the error probability in the case of a generic frequency-selective channel. Moreover, the proposed method is also extended to deal with nonuniform, i.e., wavelet, transceivers. The accuracy of the model is evaluated by means of computer simulations, using several types of filterbank transceivers. Systems based on cyclic prefix (CP) and zero padding (ZP) are considered to avoid interblock interference (IBI) in frequency-selective channels. The analytical results obtained with the proposed method allow us to quickly compare different systems, characterized by a different filterbank selectivity, as well as by different methods to combat IBI (ZP or CP).

We investigate the performance of filterbank-based MC-CDMA systems in the presence of a carrier frequency offset. We propose a semi-analytical method to compute the error probability when both generic transmit filters and arbitrary linear receivers are used, considering a multipath fading channel in the downlink. In particular, systems based on cyclic prefix (CP) and zero padding (ZP) are considered to avoid inter-block interference (IBI). The accuracy of the method is evaluated by means of computer simulations, considering several types of filterbank-based MC-CDMA systems, and it is shown to be very accurate. The analytical results obtained with the proposed method allow us to compare, in a fast way, different systems characterized by different methods to combat IBI (ZP or CP), as well as by different receiver structures.

We investigate the performance of a transceiver based on wavelet packet modulation in presence of a carrier frequency offset. We propose a theoretical model to compute the error probability in the case of an uniform frequency subdivision, considering both the AWGN channel and an arbitrary frequency-selective channel. Then, we extend the proposed method to deal with nonuniform, i.e. wavelet, transceivers. The accuracy of the model is evaluated by means of computer simulations.

We investigate the performance of filterbank transceivers in the presence of a dispersive time-variant channel. It is well-known that filterbank transceivers can be adapted to the channel transfer function to yield intersymbol interference (ISI) cancellation. When the channel is time-variant, several problems arise, since the transceiver should be changed whenever the channel evolves. We allow both the transmitter and the receiver to change and satisfy the ISI-free condition, under the assumption of a zero padded block transmission. In this case, the transmitter-receiver pair can be computed by using a singular value decomposition (SVD) of the channel matrix. A fast receiver adaptation based on SVD tracking is presented. Simulation results show that minimum performance loss can be achieved for our reduced complexity receiver.

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.

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.

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.

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.

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.

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.

In this study we propose a new method to design pseudo-QMF prototype filters to implement near perfect reconstruction (NPR) cosine-modulated filter banks. The method is based on the eigenfilter approach, that is simple to implement, but, nevertheless, is very efficient in designing high attenuation prototype filters. The method also allows to design complex coefficient prototypes that can be used to build nonuniform filter banks. The effectiveness of the method is demonstrated by means of some examples of design of both uniform and nonuniform filter banks.

The eigenfilter approach is applied to designing Infinite Impulse Response (IIR) filters having an arbitrary magnitude frequency response. A causal rational transfer function having an arbitrary number of poles and zeros is achieved. The procedure works in the frequency domain. Some numerical examples showing the application of the presented method to the design of multiband filters with different gains and different magnitude shape in each band are presented.

A method of designing non-uniform FIR filter banks is presented. It is based on the cosine modulation of more than one prototype, having different passbands. The method aims at the cancellation of the main component of aliasing: this imposes constraints on the prototypes, which become dependent of each other. The method is simple and requires numerical optimization only for the narrowest prototype, being the others derived in a straightforward way from this one. For this reason, the method seems particularly suitable when banks with a large number of coefficients must be designed.

Digital high-definition TV (HDTV) signals are generally compressed to reduce transmission bandwidth requirements. A compression algorithm for the bit rate reduction of an HDTV image using the wavelet transform is presented. The major problems related to the transmission of a compressed HDTV signal are analyzed. Transmission is examined both on a noisy channel and an asynchronous transfer mode (ATM) network. The effects of channel noise on the reconstructed image are determined, and a solution to mitigate the degradation of the image quality is presented. A model for the output bit rate of the HDTV coder is derived and used to simulate the transmission of an ATM multiplexer so that the network's main performance parameters can be determined.>