This paper develops a practical method for image resolution enhancement. The method optimizes the spatially constrained Wiener filter for an efficiently parameterized model of the image autocorrelation based on a Markov random field (MRF) with affine transformation. The paper presents a closed-form solution to parameterize the model for an image. The enhancement method is computationally efficient, because it is formulated as convolution with a small kernel. Because the kernel is small, it can be optimized efficiently and only a small portion of the MRF autocorrelation model is required. Because the autocorrelation model parameters and optimal filter can be computed quickly, the method can be optimized locally for adaptive processing. Experimental results indicate that the new method can balance the error-budget tradeoff between signal error and aliasing error.

Cubic convolution is a popular method for image interpolation. Traditionally, the piecewise-cubic kernel has been derived in one dimension with one parameter and applied to two-dimensional (2-D) images in a separable fashion. However, images typically are statistically nonseparable, which motivates this investigation of nonseparable cubic convolution. This paper derives two new nonseparable, 2-D cubic-convolution kernels. The first kernel, with three parameters (designated 2D-3PCC), is the most general 2-D, piecewise-cubic interpolator defined on [-2, 2] x [-2, 2] with constraints for biaxial symmetry, diagonal (or 90 degrees rotational) symmetry, continuity, and smoothness. The second kernel, with five parameters (designated 2D-5PCC), relaxes the constraint of diagonal symmetry, based on the observation that many images have rotationally asymmetric statistical properties. This paper also develops a closed-form solution for determining the optimal parameter values for parametric cubic-convolution kernels with respect to ensembles of scenes characterized by autocorrelation (or power spectrum). This solution establishes a practical foundation for adaptive interpolation based on local autocorrelation estimates. Quantitative fidelity analyses and visual experiments indicate that these new methods can outperform several popular interpolation methods. An analysis of the error budgets for reconstruction error associated with blurring and aliasing illustrates that the methods improve interpolation fidelity for images with aliased components. For images with little or no aliasing, the methods yield results similar to other popular methods. Both 2D-3PCC and 2D-5PCC are low-order polynomials with small spatial support and so are easy to implement and efficient to apply.

This paper formulates a two-dimensional, piecewise-cubic interpolator that accounts for non-separable and rotationally asymmetric scene statistics. The resulting kernel has five parameters and is designated 2D-5PCC. As a low-order polynomial with small spatial support, the kernel is easy to implement and efficient to apply. A closed-form solution, developed in this paper, yields the optimal parameter values for scene ensembles characterized by autocorrelation or power spectrum. Experiments indicate that 2D-5PCC yields higher fidelity interpolations than several other popular methods.

This paper formulates two-dimensional parametric cubic convolution for one-pass image restoration and reconstruction and derives a closed-form solution for the mean-square optimal parameters. The approach improves on traditional separable cubic convolution and relaxes the interpolation constraint to support restoration. The resulting kernel has five parameters and is designated 2D-5PCC-R. The closed-form solution for the optimal parameters is based on a continuous-discrete-continuous system model that accounts for the scene ensemble, acquisition blurring, sampling, noise, and processing. The analysis of the model leads to a simultaneous solution for five linear equations in the five parameters

The paper develops two-dimensional (2D), nonseparable, piecewise cubic convolution (PCC) for image interpolation. Traditionally, PCC has been implemented based on a one-dimensional (1D) derivation with a separable generalization to two dimensions. However, typical scenes and imaging systems are not separable, so the traditional approach is suboptimal. We develop a closed-form derivation for a two-parameter, 2D PCC kernel with support [-2,2] x [-2,2] that is constrained for continuity, smoothness, symmetry, and flat-field response. Our analyses, using several image models, including Markov random fields, demonstrate that the 2D PCC yields small improvements in interpolation fidelity over the traditional, separable approach. The constraints on the derivation can be relaxed to provide greater flexibility and performance.

The information content in remote sensing imagery depends upon various factors such as spatial and radiometric resolutions, spatial scale of the features to be imaged, radiometric contrast between different target types, and the type and amount of noise present in the imagery. Various statistical and textural measures are used to characterize image information content, based upon which different image processing techniques are employed to quantify this parameter. Previous work in this area have resulted in three different approaches for quantifying the image information content, primarily based on interpretability, mutual information, and entropy. These approaches, although well refined, are difficult to apply to all types of remote sensing imagery. We have developed an approach based on the use of classification accuracy to quantify image information content, since loss of information occurs if pixels in the image are wrongly classified. Using this approach, we have separately developed negative exponential models relating information content to image parameters such as spatial and spectral resolution. In this paper, we describe a preliminary unified information content model and assess its performance using hyperspectral AVIRIS imagery. The model combines the effects of the above parameters and takes into account the interrelationships between them with respect to information contained within the image. Using the model, appropriate trade-offs between the parameters can be investigated for obtaining a specific value for image information content for a particular application.

This paper describes a technique for restoring and reconstructing a scene from overlapping images. In situations where there are multiple, overlapping images of the same scene, it may be desirable to create a single image that most closely approximates the scene, based on the data in all of the available images. For example, successive swaths acquired by NASA's moderate imaging spectrometer (MODIS) will overlap, particularly at wide scan angles, creating a severe visual artifact in the output image. Resampling the overlapping swaths to produce a more accurate image on a uniform grid requires restoration and reconstruction. The one-pass restoration and reconstruction technique developed in this paper yields mean-square optimal resampling, based on a comprehensive end-to-end system model that accounts for image overlap and is subject to user-defined and data-availability constraints on the spatial support of the filter.

This paper describes two-dimensional, non-separable, piecewise polynomial convolution for image reconstruction. We investigate a two-parameter kernel with support [-2,2]/spl times/[-2,2] and constrained for smooth reconstruction. The performance reconstructing a sampled random Markov field is superior to the traditional one-dimensional cubic convolution algorithm.

A Source Specific Model for Global Earth Data (SSM-GED) is a lossless compression method for large images that captures global redundancy in the data and achieves a significant improvement over CALIC and DCXT-BT/CARP, two leading lossless compression schemes. The Global Land 1-km Advanced Very High Resolution Radiometer (AVHRR) data, which contains 662 Megabytes (MB) per band, is an example of a large data set that requires decompression of regions of the data. For this reason, SSM-GED compresses the AVHRR data as a collection of subwindows. This approach defines the statistical parameters for the model prior to compression. Unlike universal models that assume no a priori knowledge of the data, SSM-GED captures global redundancy that exists among all of the subwindows of data. The overlap in parameters among subwindows of data enables SSM-GED to improve the compression rate by increasing the number of parameters and maintaining a small model cost for each subwindow of data.

Describes the design of small convolution kernels for the restoration and reconstruction of Advanced Very High Resolution Radiometer (AVHRR) images. The kernels are small enough to be implemented efficiently by convolution, yet effectively correct degradations and increase apparent resolution. The kernel derivation is based on a comprehensive, end-to-end system model that accounts for scene statistics, image acquisition blur, sampling effects, sensor noise, and postfilter reconstruction. The design maximizes image fidelity subject to explicit constraints on the spatial support and resolution of the kernel. The kernels can be designed with finer resolution than the image to perform partial reconstruction for geometric correction and other remapping operations. Experiments demonstrate that small kernels yield fidelity comparable to optimal unconstrained filters with less computation.>

An approach is presented for subband coding of images. This process not only accounts for the aliasing effects due to non-ideal subband filters, but also takes into account the degradations introduced in the transmission due to channel noise, undersampling of the source, and optical blur introduced by the acquisition device. It is shown that the resultant restored image is far superior to any others formed by either simple reconstruction or restoration.>

An algorithm is developed for defining small kernels that are conditioned on the important components of the imaging process: the nature of the scene, the point-spread function of the image-gathering device, sampling effects, noise, and post-filter interpolation. Subject to constraints on the spatial support of the kernel, the algorithm generates the kernal values that minimize the expected mean-square error of the estimate of the scene characteristic. This development is consistent with the derivation of the spatially unconstrained Wiener characteristic filter, but leads to a small, spatially constrained convolution kernel. Simulation experiments demonstrate that the algorithm is more flexible than traditional small-kernel techniques and yields more accurate estimates.>

In this paper we are concerned with the end-to-end performance of image gathering, coding, and restoration as a whole rather than as a chain of independent tasks. Our approach evolves from the pivotal relationship that exists between the spectral information density of the transmitted signal and the restorability of images from this signal. The information theoretical assessment accounts for the information density and efficiency of the acquired signal as a function of the image-gathering system design and the radiance-field statistics, and for the information efficiency and data compression that can be gained by combining image gathering with coding to reduce the signal redundancy and irrelevancy. The redundancy reduction is concerned mostly with the statistical properties of the acquired signal, and the irrelevancy reduction is concerned mostly with the visual properties of the scene and the restored image. The results of this assessment lead to intuitively appealing insights about image gathering and coding for digital restoration. Foremost is the realization that images can be restored with better quality and from less data as the information efficiency of the transmitted data is increased, providing that the restoration correctly accounts for the image gathering and coding processes and effectively suppresses the image-display degradations. High information efficiency, in turn, can be attained only by minimizing imagegathering degradations as well as signal redundancy. Another important realization is that the critical constraints imposed on both image gathering and natural vision limit the maximum acquired information density to ~ 4 binary information units (bifs). This information density requires ~ 5-bit encoding for transmission and recording when lateral inhibition is used to compress the dynamic range of the signal (irrelevancy reduction). This number of encoding levels is close (perhaps fortuitously) to the upper limit of the ~ 40 intensity levels that each nerve fiber can transmit, via pulses, from the retina to the visual cortex within ~l/20 sec to avoid prolonging reaction times. If the data are digitally restored as an image on film for ‘best’ visual quality, then the information density may often be reduced to ~3 bifs or even less, depending on the scene, without incurring perceptual degradations because of the practical limitations that are imposed on the restoration. These limitations are not likely to be found in the nervous system of human beings, so that the higher information density of ^4 bifs that the eye can acquire probably contributes effectively to the improvement in visual quality that we always experience when we view a scene directly rather than through the media of image gathering and restoration.

Most digital image restoration algorithms are inherently incomplete because they are conditioned on a discrete-input, discrete-output model which only accounts for blurring during image gathering and additive noise. For those restoration applications where sampling and reconstruction (display) are important the restoration algorithm should be based on a more comprehensive end-to-end model which also accounts for the potentially important noise-like effects of aliasing and the low- pass filtering effects of interpolative reconstruction. In this paper we demonstrate that, although the mathematics of this more comprehensive model is more complex, the increase in complexity is not so great as to prevent a complete development and analysis of the associated minimum mean- square error (Wiener) restoration filter. We also survey recent results related to the important issue of implementing this restoration filter, in the spatial domain, as a computationally efficient small convolution kernel.