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A new, fast, and efficient image codec based on set partitioning in hierarchical trees
 In IEEE Transactions on Circuits and Systems for Video Technology
, 1996
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Quantization
 IEEE TRANS. INFORM. THEORY
, 1998
"... The history of the theory and practice of quantization dates to 1948, although similar ideas had appeared in the literature as long ago as 1898. The fundamental role of quantization in modulation and analogtodigital conversion was first recognized during the early development of pulsecode modula ..."
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Cited by 700 (12 self)
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The history of the theory and practice of quantization dates to 1948, although similar ideas had appeared in the literature as long ago as 1898. The fundamental role of quantization in modulation and analogtodigital conversion was first recognized during the early development of pulsecode modulation systems, especially in the 1948 paper of Oliver, Pierce, and Shannon. Also in 1948, Bennett published the first highresolution analysis of quantization and an exact analysis of quantization noise for Gaussian processes, and Shannon published the beginnings of rate distortion theory, which would provide a theory for quantization as analogtodigital conversion and as data compression. Beginning with these three papers of fifty years ago, we trace the history of quantization from its origins through this decade, and we survey the fundamentals of the theory and many of the popular and promising techniques for quantization.
Splines: A Perfect Fit for Signal/Image Processing
 IEEE SIGNAL PROCESSING MAGAZINE
, 1999
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Adaptive Wavelet Thresholding for Image Denoising and Compression
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 2000
"... The first part of this paper proposes an adaptive, datadriven threshold for image denoising via wavelet softthresholding. The threshold is derived in a Bayesian framework, and the prior used on the wavelet coefficients is the generalized Gaussian distribution (GGD) widely used in image processing ..."
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Cited by 263 (4 self)
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The first part of this paper proposes an adaptive, datadriven threshold for image denoising via wavelet softthresholding. The threshold is derived in a Bayesian framework, and the prior used on the wavelet coefficients is the generalized Gaussian distribution (GGD) widely used in image processing applications. The proposed threshold is simple and closedform, and it is adaptive to each subband because it depends on datadriven estimates of the parameters. Experimental results show that the proposed method, called BayesShrink, is typically within 5% of the MSE of the best softthresholding benchmark with the image assumed known. It also outperforms Donoho and Johnstone's SureShrink most of the time. The second part
Image compression via joint statistical characterization in the wavelet domain
, 1997
"... We develop a statistical characterization of natural images in the wavelet transform domain. This characterization describes the joint statistics between pairs of subband coefficients at adjacent spatial locations, orientations, and scales. We observe that the raw coefficients are nearly decorrelate ..."
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Cited by 207 (29 self)
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We develop a statistical characterization of natural images in the wavelet transform domain. This characterization describes the joint statistics between pairs of subband coefficients at adjacent spatial locations, orientations, and scales. We observe that the raw coefficients are nearly decorrelated, but their magnitudes are highly correlated. A linear magnitude predictor coupled with both multiplicative and additive uncertainties accounts for the joint coefficient statistics of a wide variety of images including photographic images, graphical images, and medical images. In order to directly demonstrate the power of this model, we construct an image coder called EPWIC (Embedded Predictive Wavelet Image Coder), in which subband coefficients are encoded one bitplane at a time using a nonadaptive arithmetic encoder that utilizes probabilities calculated from the model. Bitplanes are ordered using a greedy algorithm that considers the MSE reduction per encoded bit. The decoder uses the statistical model to predict coefficient values based on the bits it has received. The ratedistortion performance of the coder compares favorably with the current best image coders in the literature. 1
Perceptual Watermarks for Digital Images and Video
, 2007
"... The growth of new imaging technologies has created a need for techniques that can be used for copyright protection of digital images. Copyright protection involves the authentication of image content and/or ownership and can be used to identify illegal copies of a (possibly forged) image. One approa ..."
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Cited by 161 (20 self)
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The growth of new imaging technologies has created a need for techniques that can be used for copyright protection of digital images. Copyright protection involves the authentication of image content and/or ownership and can be used to identify illegal copies of a (possibly forged) image. One approach for copyright protection is to introduce an invisible signal known as a digital watermark in the image. In this paper, we describe digital image watermarking techniques, known as perceptually based watermarks, that are designed to exploit aspects of the human visual system. In the most general sense, any watermarking technique that attempts to incorporate an invisible mark into an image is perceptually based. However, in order to provide transparency (invisibility of the watermark) and robustness to attack, more sophisticated use of perceptual information in the watermarking process is required. Several techniques have been introduced that incorporate a simple visual model in the marking procedure. Such techniques usually take advantage of frequency selectivity and weighing to provide some perceptual criteria in the watermarking process. Even more elaborate visual models are used to develop schemes that not only take advantage of frequency
Spacefrequency Quantization for Wavelet Image Coding
, 1997
"... Recently, a new class of image coding algorithms coupling standard scalar quantization of frequency coefficients with treestructured quantization (related to spatial structures) has attracted wide attention because its good performance appears to confirm the promised efficiencies of hierarchical re ..."
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Cited by 160 (15 self)
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Recently, a new class of image coding algorithms coupling standard scalar quantization of frequency coefficients with treestructured quantization (related to spatial structures) has attracted wide attention because its good performance appears to confirm the promised efficiencies of hierarchical representation [1, 2]. This paper addresses the problem of how spatial quantization modes and standard scalar quantization can be applied in a jointly optimal fashion in an image coder. We consider zerotree quantization (zeroing out treestructured sets of wavelet coefficients) and the simplest form of scalar quantization (a single common uniform scalar quantizer applied to all nonzeroed coefficients), and we formalize the problem of optimizing their joint application and we develop an image coding algorithm for solving the resulting optimization problem. Despite the basic form of the two quantizers considered, the resulting algorithm demonstrates coding performance that is competitive (often...
Unconditional bases are optimal bases for data compression and for statistical estimation
 Applied and Computational Harmonic Analysis
, 1993
"... An orthogonal basis of L 2 which is also an unconditional basis of a functional space F is a kind of optimal basis for compressing, estimating, and recovering functions in F. Simple thresholding operations, applied in the unconditional basis, work essentially better for compressing, estimating, and ..."
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Cited by 156 (23 self)
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An orthogonal basis of L 2 which is also an unconditional basis of a functional space F is a kind of optimal basis for compressing, estimating, and recovering functions in F. Simple thresholding operations, applied in the unconditional basis, work essentially better for compressing, estimating, and recovering than they do in any other orthogonal basis. In fact, simple thresholding in an unconditional basis works essentially better for recovery and estimation than other methods, period. (Performance is measured in an asymptotic minimax sense.) As an application, we formalize and prove Mallat's Heuristic, which says that wavelet bases are optimal for representing functions containing singularities, when there may be an arbitrary number of singularities, arbitrarily distributed.
Image Decomposition via the Combination of Sparse Representations and a Variational Approach
 IEEE Transactions on Image Processing
, 2004
"... The separation of image content into semantic parts plays a vital role in applications such as compression, enhancement, restoration, and more. In recent years several pioneering works suggested such a separation based on variational formulation, and others using independent component analysis and s ..."
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Cited by 144 (28 self)
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The separation of image content into semantic parts plays a vital role in applications such as compression, enhancement, restoration, and more. In recent years several pioneering works suggested such a separation based on variational formulation, and others using independent component analysis and sparsity. This paper presents a novel method for separating images into texture and piecewise smooth (cartoon) parts, exploiting both the variational and the sparsity mechanisms. The method combines the Basis Pursuit Denoising (BPDN) algorithm and the TotalVariation (TV) regularization scheme. The basic idea presented in this paper is the use of two appropriate dictionaries, one for the representation of textures, and the other for the natural scene parts, assumed to be piecewisesmooth. Both dictionaries are chosen such that they lead to sparse representations over one type of imagecontent (either texture or piecewise smooth). The use of the BPDN with the two augmented dictionaries leads to the desired separation, along with noise removal as a byproduct. As the need to choose proper dictionaries is generally hard, a TV regularization is employed to better direct the separation process and reduce ringing artifacts. We present a highly e#cient numerical scheme to solve the combined optimization problem posed in our model, and show several experimental results that validate the algorithm's performance.
Interpolating Wavelet Transform
, 1992
"... We describe several "wavelet transforms" which characterize smoothness spaces and for which the coefficients are obtained by sampling rather than integration. We use them to reinterpret the empirical wavelet transform, i.e. the common practice of applying pyramid filters to samples of a f ..."
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Cited by 131 (13 self)
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We describe several "wavelet transforms" which characterize smoothness spaces and for which the coefficients are obtained by sampling rather than integration. We use them to reinterpret the empirical wavelet transform, i.e. the common practice of applying pyramid filters to samples of a function.