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Compression of Hyperspectral Scenes through integer-to-integer Spectral Graph transforms

REMOTE SENSING 2019年第19期11卷 2290-2290页

作者： Tzamarias, Dion Eustathios Olivier Chow, Kevin Blanes, Ian Serra-Sagrista, Joan Univ Autonoma Barcelona Dept Informat & Commun Engn Campus UAB E-08193 Barcelona Spain

Hyperspectral images are depictions of scenes represented across many bands of the electromagnetic spectrum. The large size of these images as well as their unique structure requires the need for specialized data compression algorithms. The redundancies found between consecutive spectral components and within components themselves favor algorithms that exploit their particular structure. One novel technique with applications to hyperspectral compression is the use of spectral graph filterbanks such as the GraphBior transform, that leads to competitive results. Such existing graph based filterbank transforms do not yield integer coefficients, making them appropriate only for lossy image compression schemes. We propose here two integer-to-integer transforms that are used in the biorthogonal graph filterbanks for the purpose of the lossless compression of hyperspectral scenes. Firstly, by applying a Triangular Elementary Rectangular Matrix decomposition on GraphBior filters and secondly by adding rounding operations to the spectral graph lifting filters. We examine the merit of our contribution by testing its performance as a spatial transform on a corpus of hyperspectral images;and share our findings through a report and analysis of our results.

关键词： hyperspectral image coding graph filterbanks integer-to-integer transforms graph signal processing

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Reversible Resampling of integer Signals

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2009年第2期57卷 516-525页

作者： Hao, Pengwei Univ London Dept Comp Sci London E1 4NS England Peking Univ Ctr Informat Sci Beijing 100871 Peoples R China

Except some extremely special cases, signal resampling was generally considered to be irreversible because of strong attenuation of high frequencies after interpolation. In this paper, we prove that signal resampling based on polynomial interpolation can be reversible even for integer signals, i.e., the original signal can be reconstructed losslessly from the resampled data. By using matrix factorization, we also propose a reversible method for uniform shifted resampling and uniform scaled and shifted resampling. The new factorization yields three elementary integer-reversible matrices. The method is actually a new way to compute linear transforms and a lossless integer implementation of linear transforms with the factor matrices. It can be applied to integer signals by in-place integer-reversible computation, which needs no auxiliary memory to keep the original sample data for the transformation during the process or for "undo" recovery after the process. Some examples of low-order resampling solutions are also presented in this paper and our experiments show that the resampling error relative to the original signal is comparable to that of the traditional irreversible resampling.

关键词： Factorial polynomials integer-to-integer transforms PLUS factorization of matrices resampling Stirling numbers

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Generalized multiple description coding with correlating transforms

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IEEE TRANSACTIONS ON INFORMATION THEORY 2001年第6期47卷 2199-2224页

作者： Goyal, VK Kovacevic, J Bell Labs Murray Hill NJ 07974 USA

Multiple description ND) coding is source coding in which several descriptions of the source are produced such that various reconstruction qualities are obtained from different subsets of the descriptions. Unlike multiresolution or layered source coding, there is no hierarchy of descriptions;thus, MD coding is suitable for packet erasure channels or networks without priority provisions. Generalizing work by Orchard, Wang, Vaishampayan, and Reibman, a transform-based approach is developed for producing AT descriptions of an N-tuple source, M less than or equal to N. The descriptions are sets of transform coefficients, and th transform coefficients of different descriptions are correlated so that missing coefficients can be estimated. Several transform optimization results are presented for memoryless Gaussian sources, including a complete solution of the N = 2, M = 2 case with arbitrary weighting of the descriptions. The technique is effective only when independent components of the source have differing variances. Numerical studies show that this method performs well at low redundancies, as compared to uniform MD scalar quantization.

关键词： erasure channels integer-to-integer transforms packet networks robust source coding

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Matrix factorizations for parallel integer transformation

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2006年第12期54卷 4675-4684页

作者： She, Yiyuan Hao, Pengwei Paker, Yakup Peking Univ Ctr Informat Sci Beijing 100871 Peoples R China Queen Mary Univ London Dept Comp Sci London E1 4NS England Peking Univ Ctr Informat Sci Beijing 100871 Peoples R China

integer mapping is critical for lossless source coding and has been used for multicomponent image compression in the new international image compression standard JPEG 2000. In this paper, starting from block factorizations for any nonsingular transform matrix, we introduce two types of parallel elementary reversible matrix (PERM) factorizations which are helpful for the parallelization of perfectly reversible integer transforms. With improved degree of parallelism and parallel performance, the cost of multiplications and additions can be, respectively, reduced to O(log N) and O(log(2) N) for an N by N transform matrix. These make PERM factorizations an effective means of developing parallel integer transforms for large matrices. We also present a scheme to block the matrix and allocate the load of processors for efficient transformation.

关键词： integer-to-integer transforms lossless compression matrix factorization parallel algorithms parallel architectures

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Optimal filter banks for multiple description coding: Analysis and synthesis

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IEEE TRANSACTIONS ON INFORMATION THEORY 2002年第7期48卷 2036-2052页

作者： Dragotti, PL Servetto, SD Vetterli, M Swiss Fed Inst Technol LCAV EPFL CH-1015 Lausanne Switzerland

Multiple description (MD) coding is a source coding technique for information transmission over unreliable networks. In MD coding, the coder generates several different descriptions of the same signal and the decoder can produce a useful reconstruction of the source with any received subset of these descriptions. In this paper, we study the problem of MD coding of stationary Gaussian sources with memory. First, we compute an approximate MD rate distortion region for these sources, which we prove to be asymptotically tight at high rates. This region generalizes the MD rate distortion region of El Gamal, Cover, and Ozarow for memoryless Gaussian sources. Then, we develop an algorithm for the design of optimal two-channel biorthogonal filter banks for MD coding of Gaussian sources. We show that optimal filters are obtained by allocating the redundancy over frequency with a reverse "water-filling" strategy. Finally, we present experimental results which show the effectiveness of our filter banks in the low complexity, low rate regime.

关键词： filter bank design integer-to-integer transforms multiple description (MD) coding rate distortion functions robust source coding

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integer polar coordinates for compression

Integer polar coordinates for compression

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IEEE International Symposium on Information Theory

作者： Ba, Demba E. Goyal, Vivek K. MIT Cambridge MA 02139 USA

ISBN: (纸本)9781424413973

This paper introduces a family of integer-to-integer approximations to the Cartesian-to-polar coordinate transformation and analyzes its application to lossy compression. A high-rate analysis is provided for an encoder that first uniformly scalar quantizes, then transforms to "integer polar coordinates," and finally separately entropy codes angle and radius. For sources separable in polar coordinates, the performance (at high rate) is shown to match that of entropy-constrained unconstrained polar quantization-where the angular quantization is allowed to depend on the radius. Thus, for sources separable in polar coordinates but not separable in rectangular coordinates-including certain Gaussian scale mixtures-the proposed system performs better than any transform code. Furthermore, unlike unconstrained polar quantization, integer polar coordinates are appropriate for lossless compression of integer-valued vectors. Combination of integer polar coordinates with integer-to-integer transform coding is also discussed.

关键词： entropy coding Gauss circle problem Gaussian scale mixtures high-rate quantization theory integer-to-integer transforms spherical coordinates transform coding

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SAR Image Compression Using integer to integer Transformations, Dimensionality Reduction, and High Correlation Modeling

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Journal of Computer and Communications 2022年第2期10卷 19-32页

作者： Sergey Voronin Independent Researcher Reston VA USA

In this document, we present new techniques for near-lossless and lossy compression of SAR imagery saved in PNG and binary formats of magnitude and phase data based on the application of transforms, dimensionality reduction methods, and lossless compression. In particular, we discuss the use of blockwise integer to integer transforms, subsequent application of a dimensionality reduction method, and Burrows-Wheeler based lossless compression for the PNG data and the use of high correlation based modeling of sorted transform coefficients for the raw floating point magnitude and phase data. The gains exhibited are substantial over the application of different lossless methods directly on the data and competitive with existing lossy approaches. The methods presented are effective for large scale processing of similar data formats as they are heavily based on techniques which scale well on parallel architectures.

关键词： SAR Imagery integer-to-integer transforms Dimensionality Reduction High Correlation Modeling Lossy and Lossless Compression

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