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Multiple Description Coding: Compression Meets the Network
, 2001
"... This article focuses on the compressed representations of the pictures ..."
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Cited by 439 (9 self)
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This article focuses on the compressed representations of the pictures
The JPEG2000 still image compression standard
 IEEE Signal Proc. Mag
, 2001
"... The development of standards (emerging and established) by the International Organization for Standardization (ISO), the International Telecommunications Union (ITU), and the International Electrotechnical Commission (IEC) for audio, image, and video, for both transmission and storage, has led to wo ..."
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Cited by 180 (11 self)
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The development of standards (emerging and established) by the International Organization for Standardization (ISO), the International Telecommunications Union (ITU), and the International Electrotechnical Commission (IEC) for audio, image, and video, for both transmission and storage, has led to worldwide activity in developing hardware and software systems and products applicable to a number of diverse disciplines [7], [22], [23], [55], [56], [73]. Although the standards implicitly address the basic encoding operations, there is freedom and flexibility in the actual design and development of devices. This is because only the syntax and semantics of the bit stream for decoding are specified by standards, their main objective being the compatibility and interoperability among the systems (hardware/software) manufactured by different companies. There is, thus, much room for innovation and ingenuity. Since the mid 1980s, members from both the ITU and the ISO have been working together to establish a joint international standard for the compression of grayscale and color still images. This effort has been known as JPEG, the Joint
Geometric approach to error correcting codes and reconstruction of signals
 INT. MATH. RES. NOT
, 2005
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Error Correction via Linear Programming
, 2005
"... Suppose we wish to transmit a vector f ∈ Rn reliably. A frequently discussed approach consists in encoding f with an m by n coding matrix A. Assume now that a fraction of the entries of Af are corrupted in a completely arbitrary fashion. We do not know which entries are affected nor do we know how t ..."
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Cited by 107 (7 self)
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Suppose we wish to transmit a vector f ∈ Rn reliably. A frequently discussed approach consists in encoding f with an m by n coding matrix A. Assume now that a fraction of the entries of Af are corrupted in a completely arbitrary fashion. We do not know which entries are affected nor do we know how they are affected. Is it possible to recover f exactly from the corrupted mdimensional vector y? This paper proves that under suitable conditions on the coding matrix A, the input f is the unique solution to the ℓ1minimization problem (�x�ℓ1: = i xi) min �y − Ag�ℓ1 g∈Rn provided that the fraction of corrupted entries is not too large, i.e. does not exceed some strictly positive constant ρ ∗ (numerical values for ρ ∗ are given). In other words, f can be recovered exactly by solving a simple convex optimization problem; in fact, a linear program. We report on numerical experiments suggesting that ℓ1minimization is amazingly effective; f is recovered exactly even in situations where a very significant fraction of the output is corrupted.
A Tutorial on Modern Lossy Wavelet Image Compression: Foundations of JPEG 2000
, 2001
"... The JPEG committee has recently released its new image coding standard, JPEG 2000, which will serve as a supplement for the original JPEG standard introduced in 1992. Rather than incrementally improving on the original standard, JPEG 2000 implements an entirely new way of compressing images based o ..."
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Cited by 97 (0 self)
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The JPEG committee has recently released its new image coding standard, JPEG 2000, which will serve as a supplement for the original JPEG standard introduced in 1992. Rather than incrementally improving on the original standard, JPEG 2000 implements an entirely new way of compressing images based on the wavelet transform, in contrast to the discrete cosine transform (DCT) used in the original JPEG standard. The significant change in coding methods between the two standards leads one to ask: What prompted the JPEG committee to adopt such a dramatic change? The answer to this question comes from considering the state of image coding at the time the original JPEG standard was being formed. At that time wavelet analysis and wavelet coding were still
The Distributed KarhunenLoève Transform
 IEEE Trans. Inform. Theory
, 2003
"... The KarhunenLoeve transform (KLT) is a key element of many signal processing tasks, including approximation, compression, and classification. Many recent applications involve distributed signal processing where it is not generally possible to apply the KLT to the signal; rather, the KLT must be ..."
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Cited by 91 (15 self)
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The KarhunenLoeve transform (KLT) is a key element of many signal processing tasks, including approximation, compression, and classification. Many recent applications involve distributed signal processing where it is not generally possible to apply the KLT to the signal; rather, the KLT must be approximated in a distributed fashion.
Ratedistortion optimized tree structured compression algorithms for piecewise smooth images
 IEEE Trans. Image Processing
, 2005
"... IEEE Transactions on Image Processing This paper presents novel coding algorithms based on tree structured segmentation, which achieve the correct asymptotic ratedistortion (RD) behavior for a simple class of signals, known as piecewise polynomials, by using an RD based prune and join scheme. Fo ..."
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Cited by 76 (16 self)
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IEEE Transactions on Image Processing This paper presents novel coding algorithms based on tree structured segmentation, which achieve the correct asymptotic ratedistortion (RD) behavior for a simple class of signals, known as piecewise polynomials, by using an RD based prune and join scheme. For the one dimensional (1D) case, our scheme is based on binary tree segmentation of the signal. This scheme approximates the signal segments using polynomial models and utilizes an RD optimal bit allocation strategy among the different signal segments. The scheme further encodes similar neighbors jointly to achieve the correct exponentially decaying RD behavior � D(R) ∼ c02 −c1R � , thus improving over classic wavelet schemes. We also prove that the computational complexity of the scheme is of O (N log N). We then show the extension of this scheme to the two dimensional (2D) case using a quadtree. This quadtree coding scheme also achieves an exponentially decaying RD behavior, for the polygonal image model composed of a white polygon shaped object against a uniform black background, with low computational cost of O (N log N). Again, the key is an RD optimized prune and join strategy. Finally, we conclude with numerical results, which show that the proposed quadtree coding scheme outperforms JPEG2000 by about 1 dB for real images, like cameraman, at low rates of around 0.15 bpp.
Wavelets, Approximation, and Compression
, 2001
"... this article is to look at recent wavelet advances from a signal processing perspective. In particular, approximation results are reviewed, and the implication on compression algorithms is discussed. New constructions and open problems are also addressed ..."
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Cited by 68 (6 self)
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this article is to look at recent wavelet advances from a signal processing perspective. In particular, approximation results are reviewed, and the implication on compression algorithms is discussed. New constructions and open problems are also addressed
Factorial coding of natural images: how effective are linear models in removing higherorder dependencies?
 JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A
, 2006
"... The performance of unsupervised learning models for natural images is evaluated quantitatively by means of information theory. We estimate the gain in statistical independence (the multiinformation reduction) achieved with independent component analysis (ICA), principal component analysis (PCA), z ..."
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Cited by 37 (12 self)
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The performance of unsupervised learning models for natural images is evaluated quantitatively by means of information theory. We estimate the gain in statistical independence (the multiinformation reduction) achieved with independent component analysis (ICA), principal component analysis (PCA), zerophase whitening, and predictive coding. Predictive coding is translated into the transform coding framework, where it can be characterized by the constraint of a triangular filter matrix. A randomly sampled whitening basis and the Haar wavelet are included into the comparison as well. The comparison of all these methods is carried out for different patch sizes, ranging from 2x2 to 16x16 pixels. In spite of large differences in the shape of the basis functions, we find only small differences in the multiinformation between all decorrelation transforms (5% or less) for all patch sizes. Among the secondorder methods, PCA is optimal for small patch sizes and predictive coding performs best for large patch sizes. The extra gain achieved with ICA is always less than 2%. In conclusion, the `edge filters&amp;amp;amp;amp;lsquo; found with ICA lead only to a surprisingly small improvement in terms of its actual objective.