ICA based algorithms for computing optimal 1-D linear block transforms in variable high-rate source coding

International audienceThe Karhunen-Loève Transform (KLT) is optimal for transform coding of Gaussian sources, however, it is not optimal, in general, for non-Gaussian sources. Furthermore, under the high-resolution quantization hypothesis, nearly everything is known about the performance of a transform coding system with entropy constrained scalar quantization and mean-square distortion. It is then straightforward to find a criterion that, when minimized, gives the optimal linear transform under the abovementioned conditions. However, the optimal transform computation is generally considered as a difficult task and the Gaussian assumption is then used in order to simplify the calculus. In this paper, we present the abovementioned criterion as a contrast of independent component analysis modified by an additional term which is a penalty to non-orthogonality. Then we adapt the icainf algorithm by Pham in order to compute the transform minimizing the criterion either with no constraint or with the orthogonality constraint. Finally, experimental results show that the transforms we introduced can (1) outperform the KLT on synthetic signals, (2) achieve slightly better PSNR for high-rates and better visual quality (preservation of lines and contours) for medium-to-low rates than the KLT and 2-D DCT on grayscale natural images

Kernel methods for measuring independence

We introduce two new functionals, the constrained covariance and the kernel mutual information, to measure the degree of independence of random variables. These quantities are both based on the covariance between functions of the random variables in reproducing kernel Hilbert spaces (RKHSs). We prove that when the RKHSs are universal, both functionals are zero if and only if the random variables are pairwise independent. We also show that the kernel mutual information is an upper bound near independence on the Parzen window estimate of the mutual information. Analogous results apply for two correlation-based dependence functionals introduced earlier: we show the kernel canonical correlation and the kernel generalised variance to be independence measures for universal kernels, and prove the latter to be an upper bound on the mutual information near independence. The performance of the kernel dependence functionals in measuring independence is verified in the context of independent component analysis

Discrete Wavelet Transforms

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

Compression d'images satellite par post-transformées dans le domaine ondelettes

Le CNES s'intéresse aux nouvelles transformées pour accroître les performances de la compression d'images à bord des satellites d'observation de la Terre. Dans cette thèse nous étudions les post-transformées. Elles sont appliquées après la transformée en ondelettes. Chaque bloc de coefficients d'ondelettes est de nouveau transformé dans une base sélectionnée dans un dictionnaire par minimisation d'un critère débit-distorsion. Nous commençons par mettre en évidence des dépendances entre coefficients d'ondelettes qui limitent les performances en compression. Nous étudions ensuite la transformée en bandelettes par blocs, qui est à l'origine des post-transformées, et nous en optimisons les paramètres pour la compression d'images satellite. En particulier nous adaptons la méthode d'optimisation de Shoham et Gersho à la sélection de la meilleure base de bandelettes. Nous en déduisons une formule du multiplicateur de Lagrange optimal quiintervient dans le critère de sélection. Dans un deuxième temps, nous analysons les dépendances entre coefficients d'ondelettes qui ne sont pas prises en comptes par les bandelettes et nous définissons de nouvelles bases de post-transformées. Les bases construites par ACP minimisent les corrélations entre coefficients post-transformés et compactent l'énergie de chaque bloc sur un petit nombre de coefficients. Cette propriété est exploitée lors du codage entropique. Enfin, nous modifions le critère de sélection des bases pour adapter la post-transformée à une compression progressive. Nous employons alors la post-transformée de Hadamard dans le codeur du CCSDS le tout ayant une faible complexité calculatoire. ABSTRACT : The French Space Agency, CNES, is interested in the transforms derived from the wavelets in order to increase the image compression efficiency on-board of Earth observation satellites. In this thesis, the post-transforms are studied. They are employed after the wavelet transform. Each block of wavelet coefficients is further transformed in a basis selected among a dictionary by minimization of a rate- istortion criterion. First, we emphasize dependencies between wavelet coefficients limiting the compression efficiency. Then, we study the bandelet transform by blocks, from which the post-transforms derive, and we optimize its parameter for the compression of satellite images. Particularly, we adapt Shoham and Gersho optimization method to the problem of the selection of the best bandelet basis. We deduce from these results an expression of the optimal Lagrangian multiplier used in the rate-distortion criterion. Next, we analyze dependencies between wavelet coefficient which are not exploited by the bandelet transform and we define new post-transform bases. Bases build by PCA minimize the correlations between post-transformed coefficients and compact the energy of each block on a small number of coefficients. This feature is exploited during the entropy coding process. Last, we modify the bases selection criterion to adapt the post-transform to progressive compression schemes. We then employ the Hadamard post-transform with the CCSDS image encoder to obtain a low computational complexity yet efficient compression schem

Fast Algorithms for Mutual Information Based Independent Component Analysis

This paper provides fast algorithms to perform independent component analysis based on the mutual information criterion. The main ingredient is the binning technique and the use of cardinal splines, which allows the fast computation of the density estimator over a regular grid. Using a discretized form of the entropy, the criterion can be evaluated quickly together with its gradient, which can be expressed in terms of the score functions. Both off-line and on-line separation algorithms have been developed. Our density, entropy and score estimators also have their own interest