Results 11  20
of
68
ON THE COMPRESSION OF TWODIMENSIONAL PIECEWISE SMOOTH FUNCTIONS
, 2001
"... It is well known that wavelets provide good nonlinear approximation of onedimensional (1D) piecewise smooth functions. However, it has been shown that the use of a basis with good approximation properties does not necessarily lead to a good compression algorithm. The situation in 2D is much more ..."
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Cited by 39 (4 self)
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It is well known that wavelets provide good nonlinear approximation of onedimensional (1D) piecewise smooth functions. However, it has been shown that the use of a basis with good approximation properties does not necessarily lead to a good compression algorithm. The situation in 2D is much more complicated since wavelets are not good for modeling piecewise smooth signals (where discontinuities are along smooth curves). The purpose of this work is to analyze the performance of compression algorithms for 2D piecewise smooth functions directly in a rate distortion context. We consider some simple image models and compute rate distortion bounds achievable using oracle based methods. We then present a practical compression algorithm based on optimal quadtree decomposition that, in some cases, achieve the oracle performance.
Image Decomposition: Separation of Texture from Piecewise Smooth Content
, 2003
"... This paper presents a novel method for separating images into texture and piecewise smooth parts. The proposed approach is based on a combination of the Basis Pursuit Denoising (BPDN) algorithm and the TotalVariation (TV) regularization scheme. The basic idea promoted in this paper is the use of tw ..."
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Cited by 23 (4 self)
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This paper presents a novel method for separating images into texture and piecewise smooth parts. The proposed approach is based on a combination of the Basis Pursuit Denoising (BPDN) algorithm and the TotalVariation (TV) regularization scheme. The basic idea promoted in this paper is the use of two appropriate dictionaries, one for the representation of textures, and the other for the natural scene parts. Each dictionary is designed for sparse representation of a particular type of imagecontent (either texture or piecewise smooth). The use of BPDN with the two augmented dictionaries leads to the desired separation, along with noise removal as a byproduct. As the need to choose a proper dictionary for natural scene is very hard, a TV regularization is employed to better direct the separation process. Experimental results validate the algorithm's performance.
Multipledescription coding by dithered deltasigma quantization
 in Data Compression Conference, 2007. DCC ’07, (Snowbird, UT
, 2007
"... We address the connection between the multipledescription (MD) problem and DeltaSigma quantization. The inherent redundancy due to oversampling in DeltaSigma quantization, and the simple linearadditive noise model resulting from dithered lattice quantization, allow us to construct a symmetric and ..."
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Cited by 13 (8 self)
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We address the connection between the multipledescription (MD) problem and DeltaSigma quantization. The inherent redundancy due to oversampling in DeltaSigma quantization, and the simple linearadditive noise model resulting from dithered lattice quantization, allow us to construct a symmetric and timeinvariant MD coding scheme. We show that the use of a noise shaping filter makes it possible to trade off central distortion for side distortion. Asymptotically as the dimension of the lattice vector quantizer and order of the noise shaping filter approach infinity, the entropy rate of the dithered DeltaSigma quantization scheme approaches the symmetric twochannel MD ratedistortion function for a memoryless Gaussian source and MSE fidelity criterion, at any sidetocentral distortion ratio and any resolution. In the optimal scheme, the infiniteorder noise shaping filter must be minimum phase and have a piecewise flat power spectrum with a single jump discontinuity. An important advantage of the proposed design is that it is symmetric in rate and distortion by construction, so the coding rates of the descriptions are identical and there is therefore no need for source splitting. Index Terms deltasigma modulation, dithered lattice quantization, entropy coding, joint sourcechannel coding, multipledescription coding, vector quantization. I.
The multiresolution directional filter banks
, 2006
"... Abstract—In this paper, we introduced a class of directional filter banks (DFBs) having the previously proposed uniform DFB (uDFB) as a special case. Except for the uDFB, each DFB in this class can be used to decompose an image yielding up to 12 directions while maintaining perfect reconstruction an ..."
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Cited by 13 (4 self)
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Abstract—In this paper, we introduced a class of directional filter banks (DFBs) having the previously proposed uniform DFB (uDFB) as a special case. Except for the uDFB, each DFB in this class can be used to decompose an image yielding up to 12 directions while maintaining perfect reconstruction and maximal decimation. A multiresolution representation can be obtained by repeating the same decomposition at the lowpass band. The permissible property of the filter banks in cases of being implemented by a tree structure and by direct implementation is discussed. The result shows that only one DFB in the class, called the uniform quincunx DFB (uqDFB), satisfies the permissible property when being implemented directly without using the tree structure. The nonuniform quincunx DFB (nuqDFB) is then constructed from the uqDFB by merging its two lowpass subbands. An alternative structure for constructing the nuqDFB is presented. The new structure, while yielding the same frequency partitioning, allows the DFB to be realized with complexity comparable to that of the separable wavelet filter bank. The connection between the discrete filter bank and the continuous directional wavelet is also established. Numerical experiments on directional feature extractions, image denoising and nonlinear approximation are presented at the end of the paper to demonstrate the potential of the nuqDFB. Index Terms—Contourlet, curvelet, diamond filter, directional decomposition, directional filter bank (DFB), feature extraction, multidimensional filter bank, multiresolution directional filter bank (DFB), multiresolution representation, nonlinear approximation, permissibility, quincunx, wavelet. I.
Rate distortion behavior of sparse sources
 in Technical report, EPFL
, 2001
"... Abstract—The rate distortion behavior of sparse memoryless sources is studied. Such sources serve as models for sparse representations and can be used for the performance analysis of “sparsifying ” transforms like the wavelet transform, as well as nonlinear approximation schemes. Under the Hamming d ..."
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Cited by 12 (0 self)
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Abstract—The rate distortion behavior of sparse memoryless sources is studied. Such sources serve as models for sparse representations and can be used for the performance analysis of “sparsifying ” transforms like the wavelet transform, as well as nonlinear approximation schemes. Under the Hamming distortion criterion, R(D) is shown to be almost linear for sources emitting sparse binary vectors. For continuous random variables, the geometric mean is proposed as a sparsity measure and shown to lead to upper and lower bounds on the entropy, thereby characterizing asymptotic R(D) behavior. Three models are analyzed more closely under the mean squared error distortion measure: continuous spikes in random discrete locations, power laws matching the approximately scaleinvariant decay of wavelet coefficients, and Gaussian mixtures. The latter are versatile models for sparse data, which in particular allow to bound the suitably defined coding gain of a scalar mixture compared to that of a corresponding unmixed transform coding system. Such a comparison is interesting for transforms with known coefficient decay, but unknown coefficient ordering, e.g. when the positions of highestvariance coefficients are unknown. The use of these models and results in distributed coding and compressed sensing scenarios is also discussed. Index Terms—Sparse signal representations, rate distortion theory, memoryless systems, entropy, transform coding. I.
A new family of nonredundant transforms using hybrid wavelets and directional filter banks
, 2007
"... We propose a new family of nonredundant geometrical image transforms that are based on wavelets and directional filter banks. We convert the wavelet basis functions in the finest scales to a flexible and rich set of directional basis elements by employing directional filter banks, where we form a n ..."
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Cited by 11 (1 self)
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We propose a new family of nonredundant geometrical image transforms that are based on wavelets and directional filter banks. We convert the wavelet basis functions in the finest scales to a flexible and rich set of directional basis elements by employing directional filter banks, where we form a nonredundant transform family, which exhibits both directional and nondirectional basis functions. We demonstrate the potential of the proposed transforms using nonlinear approximation. In addition, we employ the proposed family in two key image processing applications, image coding and denoising, and show its efficiency for these applications.
On Twochannel Filter Banks with Directional Vanishing Moments
, 2005
"... The contourlet transform was proposed to address the limited directional resolution of the separable wavelet transform. In order to guarantee good nonlinear approximation behavior, the directional filters in the contourlet filter bank require sharp frequency response which incurs a large support siz ..."
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Cited by 10 (5 self)
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The contourlet transform was proposed to address the limited directional resolution of the separable wavelet transform. In order to guarantee good nonlinear approximation behavior, the directional filters in the contourlet filter bank require sharp frequency response which incurs a large support size. We seek to isolate the key filter property that ensures good approximation. In this direction, we propose filters with directional vanishing moments (DVM). These filters, we show, annihilate information along a given direction. We study twochannel filter banks with DVM filters. We provide conditions under which the design of DVM filter banks is possible. A complete characterization of the product filter is thus obtained. We propose a design framework that avoids twodimensional factorization using the mapping technique. The filters designed, when used in the contourlet transform, exhibit nonlinear approximation comparable to the conventional filters while being shorter and therefore providing better visual quality with less ringing artifacts.
Blind Source Separation: the Sparsity Revolution
, 2008
"... Over the last few years, the development of multichannel sensors motivated interest in methods for the coherent processing of multivariate data. Some specific issues have already been addressed as testified by the wide literature on the socalled blind source separation (BSS) problem. In this conte ..."
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Cited by 7 (5 self)
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Over the last few years, the development of multichannel sensors motivated interest in methods for the coherent processing of multivariate data. Some specific issues have already been addressed as testified by the wide literature on the socalled blind source separation (BSS) problem. In this context, as clearly emphasized by previous work, it is fundamental that the sources to be retrieved present some quantitatively measurable diversity. Recently, sparsity and morphological diversity have emerged as a novel and effective source of diversity for BSS. We give here some essential insights into the use of sparsity in source separation and we outline the essential role of morphological diversity as being a source of diversity or contrast between the sources. This paper overviews a sparsitybased BSS method coined Generalized Morphological Component Analysis (GMCA) that takes advantages of both morphological diversity and sparsity, using recent sparse overcomplete or redundant signal representations. GMCA is a fast and efficient blind source separation method. In remote sensing applications, the specificity of hyperspectral data should be accounted for. We extend the proposed GMCA framework to deal with hyperspectral data. In a general framework, GMCA provides a basis for multivariate data analysis in the scope of a wide range of classical multivariate data restorate. Numerical results are given in color image denoising and inpainting. Finally, GMCA is applied to the simulated ESA/Planck data. It is shown to give effective astrophysical component separation.
Depth and DepthColor Coding using Shapeadaptive Wavelets
, 2009
"... We present a novel depth and depthcolor codec aimed at freeviewpoint 3DTV. The proposed codec uses a shapeadaptive wavelet transform and an explicit encoding of the locations of major depth edges. Unlike the standard wavelet transform, the shapeadaptive transform generates small wavelet coeffic ..."
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Cited by 7 (1 self)
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We present a novel depth and depthcolor codec aimed at freeviewpoint 3DTV. The proposed codec uses a shapeadaptive wavelet transform and an explicit encoding of the locations of major depth edges. Unlike the standard wavelet transform, the shapeadaptive transform generates small wavelet coefficients along depth edges, which greatly reduces the bits required to represent the data. The wavelet transform is implemented by shapeadaptive lifting, which enables fast computations and perfect reconstruction. We derive a simple extension of typical boundary extrapolation methods for lifting schemes to obtain as many vanishing moments near boundaries as away from them. We also develop a novel rateconstrained edge detection algorithm, which integrates the idea of significance bitplanes into the Canny edge detector. Together with a simple chain code, it provides an efficient way to extract and encode edges. Experimental results on synthetic and real data confirm the effectiveness of the proposed codec, with PSNR gains of more than 5 dB for depth images and significantly better visual quality for synthesized novel view images.
Efficient decentralized approximation via selective gossip
 IEEE Journal of Selected Topics in Signal Processing
, 2011
"... Abstract—Recently, gossip algorithms have received much attention from the wireless sensor network community due to their simplicity, scalability and robustness. Motivated by applications such as compression and distributed transform coding, we propose a new gossip algorithm called Selective Gossi ..."
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Cited by 5 (3 self)
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Abstract—Recently, gossip algorithms have received much attention from the wireless sensor network community due to their simplicity, scalability and robustness. Motivated by applications such as compression and distributed transform coding, we propose a new gossip algorithm called Selective Gossip. Unlike traditional randomized gossip which computes the average of scalar values, we run gossip algorithms in parallel on the elements of a vector. The goal is to compute only the entries which are above a defined threshold in magnitude, i.e., significant entries. Nodes adaptively approximate the significant entries while abstaining from calculating the insignificant ones. Consequently, network lifetime and bandwidth are preserved. We show that with the proposed algorithm nodes reach consensus on the values of the significant entries and on the indices of insignificant ones. We illustrate the performance of our algorithm with a field estimation application. For regular topologies, selective gossip computes an approximation of the field using the wavelet transform. For irregular network topologies, we construct an orthonormal transform basis using eigenvectors of the graph Laplacian. Using two real sensor network datasets we show substantial communication savings over randomized gossip. We also propose a decentralized adaptive threshold mechanism such that nodes estimate the threshold while approximating the entries of the vector for computing the bestterm approximation of the data. Index Terms—Distributed algorithms, field estimation, sparse approximation, wireless sensor networks. I.