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Factoring wavelet transforms into lifting steps
 J. FOURIER ANAL. APPL
, 1998
"... This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This decompositio ..."
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Cited by 575 (8 self)
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This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This decomposition corresponds to a factorization of the polyphase matrix of the wavelet or subband filters into elementary matrices. That such a factorization is possible is wellknown to algebraists (and expressed by the formula); it is also used in linear systems theory in the electrical engineering community. We present here a selfcontained derivation, building the decomposition from basic principles such as the Euclidean algorithm, with a focus on applying it to wavelet filtering. This factorization provides an alternative for the lattice factorization, with the advantage that it can also be used in the biorthogonal, i.e, nonunitary case. Like the lattice factorization, the decomposition presented here asymptotically reduces the computational complexity of the transform by a factor two. It has other applications, such as the possibility of defining a waveletlike transform that maps integers to integers.
Error Control and Concealment for Video Communication  A Review
 PROCEEDINGS OF THE IEEE
, 1998
"... The problem of error control and concealment in video communication is becoming increasingly important because of the growing interest in video delivery over unreliable channels such as wireless networks and the Internet. This paper reviews the techniques that have been developed for error control a ..."
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Cited by 437 (13 self)
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The problem of error control and concealment in video communication is becoming increasingly important because of the growing interest in video delivery over unreliable channels such as wireless networks and the Internet. This paper reviews the techniques that have been developed for error control and concealment in the past ten to fifteen years. These techniques are described in three categories according to the roles that the encoder and decoder play in the underlying approaches. Forward error concealment includes methods that add redundancy at the source end to enhance error resilience of the coded bit streams. Error concealment by postprocessing refers to operations at the decoder to recover the damaged areas based on characteristics of image and video signals. Finally, interactive error concealment covers techniques that are dependent on a dialog between the source and destination. Both current research activities and practice in international standards are covered.
Multiple Description Coding: Compression Meets the Network
, 2001
"... This article focuses on the compressed representations of the pictures ..."
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Cited by 433 (9 self)
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This article focuses on the compressed representations of the pictures
Video coding with optimal Inter/Intramode switching for packet loss resilience
 IEEE JSAC
, 2000
"... Resilience to packet loss is a critical requirement in predictive video coding for transmission over packetswitched networks, since the prediction loop propagates errors and causes substantial degradation in video quality. This work proposes an algorithm to optimally estimate the overall distortio ..."
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Cited by 192 (15 self)
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Resilience to packet loss is a critical requirement in predictive video coding for transmission over packetswitched networks, since the prediction loop propagates errors and causes substantial degradation in video quality. This work proposes an algorithm to optimally estimate the overall distortion of decoder frame reconstruction due to quantization, error propagation, and error concealment. The method recursively computes the total decoder distortion at pixel level precision to accurately account for spatial and temporal error propagation. The accuracy of the estimate is demonstrated via simulation results. The estimate is integrated into a ratedistortion (RD)based framework for optimal switching between intracoding and intercoding modes per macroblock. The cost in computational complexity is modest. The framework is further extended to optimally exploit feedback/acknowledgment information from the receiver/network. Simulation results both with and without a feedback channel demonstrate that precise distortion estimation enables the coder to achieve substantial and consistent gains in PSNR over known stateoftheart RD and nonRDbased mode switching methods.
Multiple Description Coding Using Pairwise Correlating Transforms
 IEEE Trans. Image Processing
, 1999
"... The objective of multiple description coding (MDC) is to encode a source into two (or more) bitstreams supporting two quality levels of decoding. A highquality reconstruction should be decodable from the two bitstreams together, while lower, but still acceptable, quality reconstructions should b ..."
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Cited by 93 (1 self)
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The objective of multiple description coding (MDC) is to encode a source into two (or more) bitstreams supporting two quality levels of decoding. A highquality reconstruction should be decodable from the two bitstreams together, while lower, but still acceptable, quality reconstructions should be decodable from either of the two individual bitstreams. This paper describes techniques for meeting MDC objectives in the framework of standard transformbased image coding through the design of pairwise transforms.
Multiple Description Wavelet Based Image Coding
, 1998
"... We consider the problem of coding images for transmission over errorprone channels. The impairments we target are transient channel shutdowns, as would occur in a packet network when a packet is lost, or in a wireless system during a deep fade: when data is delivered it is assumed to be errorfree, ..."
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Cited by 80 (8 self)
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We consider the problem of coding images for transmission over errorprone channels. The impairments we target are transient channel shutdowns, as would occur in a packet network when a packet is lost, or in a wireless system during a deep fade: when data is delivered it is assumed to be errorfree, but some of the data may never reach the receiver. The proposed algorithms are based on a combination of multiple description scalar quantizers with techniques successfully applied to the construction of some of the most ecient subband coders. A given image is encoded into multiple independent packets of roughly equal length. When packets are lost, the quality of the approximation computed at the receiver depends only on the number of packets received, but does not depend on exactly which packets are actually received. When compared with previously reported results on the performance of robust image coders based on multiple descriptions, on standard test images, our coders attain s...
Generalized multiple description coding with correlating transforms
 IEEE Trans. Inform. Theory
, 2001
"... Abstract—Multiple description (MD) 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 descriptio ..."
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Cited by 80 (2 self)
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Abstract—Multiple description (MD) 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 transformbased approach is developed for producing descriptions of antuple source,. The descriptions are sets of transform coefficients, and the 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 aP, aPcase 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. Index Terms—Erasure channels, integertointeger transforms, packet networks, robust source coding.
Multiple description transform coding of images
 IEEE Trans. Image Process
, 2000
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Multiple description coding for video using motion compensated prediction
 Proc. IEEE lot. Conf. Image Proc
, 1999
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Optimal multiple description transform coding of Gaussian vectors
 In Proc. IEEE Data Compr. Conf
, 1998
"... Includes minor corrections. Multiple description coding (MDC) is source coding for multiple channels such that a decoder which receives an arbitrary subset of the channels may produce a useful reconstruction. Orchard et al. [1] proposed a transform coding method for MDC of pairs of independent Gaus ..."
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Cited by 54 (12 self)
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Includes minor corrections. Multiple description coding (MDC) is source coding for multiple channels such that a decoder which receives an arbitrary subset of the channels may produce a useful reconstruction. Orchard et al. [1] proposed a transform coding method for MDC of pairs of independent Gaussian random variables. This paper provides a general framework which extends multiple description transform coding (MDTC) to any number of variables and expands the set of transforms which are considered. Analysis of the general case is provided, which can be used to numerically design optimal MDTC systems. The case of two variables sent over two channels is analytically optimized in the most general setting where channel failures need not have equal probability or be independent. It is shown that when channel failures are equally probable and independent, the transforms used in [1] are in the optimal set, but many other choices are possible. A cascade structure is presented which facilitates lowcomplexity design, coding, and decoding for a system with a large number of variables. 1