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Geoffrey M Davis - One of the best experts on this subject based on the ideXlab platform.
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a wavelet based analysis of fractal image compression
IEEE Transactions on Image Processing, 1998Co-Authors: Geoffrey M DavisAbstract:Why does fractal image compression work? What is the implicit image model underlying fractal block coding? How can we characterize the types of images for which fractal block Coders will work well? These are the central issues we address. We introduce a new wavelet-based framework for analyzing block-based fractal compression schemes. Within this framework we are able to draw upon insights from the well-established Transform Coder paradigm in order to address the issue of why fractal block Coders work. We show that fractal block Coders of the form introduced by Jacquin (1992) are Haar wavelet subtree quantization schemes. We examine a generalization of the schemes to smooth wavelets with additional vanishing moments. The performance of our generalized Coder is comparable to the best results in the literature for a Jacquin-style coding scheme. Our wavelet framework gives new insight into the convergence properties of fractal block Coders, and it leads us to develop an unconditionally convergent scheme with a fast decoding algorithm. Our experiments with this new algorithm indicate that fractal Coders derive much of their effectiveness from their ability to efficiently represent wavelet zero trees. Finally, our framework reveals some of the fundamental limitations of current fractal compression schemes.
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adaptive self quantization of wavelet subtrees a wavelet based theory of fractal image compression
SPIE's 1995 International Symposium on Optical Science Engineering and Instrumentation, 1995Co-Authors: Geoffrey M DavisAbstract:Fractal image compression was one of the earliest compression schemes to take advantage of image redundancy in scale. The theory of iterated function systems motivates a broad class of fractal schemes but does not give much guidance for implementation. Fractal compression schemes do not fit into the standard Transform Coder paradigm and have proven difficult to analyze. We introduce a wavelet-based framework for analyzing fractal block Coders which simplifies these schemes considerably. Using this framework we find that fractal block Coders are Haar wavelet subtree quantization schemes, and we thereby place fractal schemes in the context of conventional Transform Coders. We show that the central mechanism of fractal schemes is an extrapolation of fine-scale Haar wavelet coefficients from coarse-scale coefficients. We use this insight to derive a wavelet-based analog of fractal compression, the self-quantization of subtrees (SQS) scheme. We obtain a simple SQS deCoder convergence proof and a fast SQS decoding algorithm which simplify and generalize existing fractal compression results. We describe an adaptive SQS compression scheme which outperforms the best fractal schemes in the literature by roughly 1 dB in PSNR across a broad range of compression ratios and which has performance comparable to some of the best conventional wavelet subtree quantization schemes.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
Tiago Alves Da ,fonseca - One of the best experts on this subject based on the ideXlab platform.
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Redução de complexidade na compressão de vídeo de alta resolução
2011Co-Authors: Tiago Alves Da ,fonsecaAbstract:O H.264/AVC é o mais novo padrão de compressão de vídeo e é tomado como estado da arte. Ele proporciona melhorias consideráveis de desempenho quando comparado a outros padrões existentes. Entretanto, como outros padrões, ele é um codificador híbrido composto por módulo preditivo e de Transformada. No presente trabalho, propomos duas abordagens diferentes para implementação do estágio preditivo. A primeira idéia é usar dados originais em vez de dados reconstruídos para realizar os testes de predição na escolha do melhor modo de predição. O resíduo, todavia, continua sendo calculado usando dados anteriormente decodificados de forma a evitar drifting; essa técnica permite a paralelização do estágio de predição Inter-quadros, a operação mais demorada no H.264/AVC. A segunda contribuição reduz a complexidade da codificação pela supressão dos testes de predição de modos menos frequentes. Resultados mostram que, para seqüências de alta resolução, as metodologias propostas implicam pouca perda de qualidade no sinal aliada a uma grande economia de recursos. ____________________________________________________________________________ ABSTRACTH.264/AVC is the newest, state-of-art, video compression standard. It leads to substantial performance improvement compared to other existing standards. However, like other video standards, it is a hybrid predictive-Transform Coder. In this work, we propose two different approaches to implement the prediction stage. The first idea is to employ original data rather than reconstructed ones to perform prediction tests before choosing the best mode. The residue, however, is evaluated using previously decoded data in order to avoid drifting. The technique allows parallelization of the inter-prediction stage, which is the most time consuming operation in H.264/AVC. The second contribution reduces the overall enCoder complexity by avoiding less frequent prediction mode tests. Results show that, for high definition sequences, the proposed metodogies introduced very small quality losses associated with large reduction of computational burden
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Redução de complexidade na compressão de vídeo de alta resolução
2008Co-Authors: Tiago Alves Da ,fonsecaAbstract:Dissertação (mestrado)—Universidade de Brasília, Departamento de Engenharia Elétrica, 2008.O H.264/AVC é o mais novo padrão de compressão de vídeo e é tomado como estado da arte. Ele proporciona melhorias consideráveis de desempenho quando comparado a outros padrões existentes. Entretanto, como outros padrões, ele é um codificador híbrido composto por módulo preditivo e de Transformada. No presente trabalho, propomos duas abordagens diferentes para implementação do estágio preditivo. A primeira idéia é usar dados originais em vez de dados reconstruídos para realizar os testes de predição na escolha do melhor modo de predição. O resíduo, todavia, continua sendo calculado usando dados anteriormente decodificados de forma a evitar drifting; essa técnica permite a paralelização do estágio de predição Inter-quadros, a operação mais demorada no H.264/AVC. A segunda contribuição reduz a complexidade da codificação pela supressão dos testes de predição de modos menos frequentes. Resultados mostram que, para seqüências de alta resolução, as metodologias propostas implicam pouca perda de qualidade no sinal aliada a uma grande economia de recursos. ____________________________________________________________________________ ABSTRACTH.264/AVC is the newest, state-of-art, video compression standard. It leads to substantial performance improvement compared to other existing standards. However, like other video standards, it is a hybrid predictive-Transform Coder. In this work, we propose two different approaches to implement the prediction stage. The first idea is to employ original data rather than reconstructed ones to perform prediction tests before choosing the best mode. The residue, however, is evaluated using previously decoded data in order to avoid drifting. The technique allows parallelization of the inter-prediction stage, which is the most time consuming operation in H.264/AVC. The second contribution reduces the overall enCoder complexity by avoiding less frequent prediction mode tests. Results show that, for high definition sequences, the proposed metodogies introduced very small quality losses associated with large reduction of computational burden
Florin Ghido - One of the best experts on this subject based on the ideXlab platform.
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spectral envelope reconstruction via igf for audio Transform coding
International Conference on Acoustics Speech and Signal Processing, 2015Co-Authors: Christian R Helmrich, Andreas Niedermeier, Sascha Disch, Florin GhidoAbstract:In low-bitrate audio coding, modern Coders often rely on efficient parametric techniques to enhance the performance of the waveform preserving Transform Coder core. While the latter features well-known perceptually adapted quantization of spectral coefficients, parametric techniques reconstruct the signal parts that have been quantized to zero by the enCoder to meet the low-bitrate constraint. Large numbers of zeroed spectral values and especially consecutive zeros constituting gaps often lead to audible artifacts at the deCoder. To avoid such artifacts the new 3GPP Enhanced Voice Services (EVS) coding standard utilizes noise filling and intelligent gap filling (IGF) techniques, guided by spectral envelope information. In this paper the underlying considerations of the parametric energy adjustment and transmission in EVS and its relation to noise filling, IGF, and tonality preservation are presented. It is further shown that complex-valued IGF envelope calculation in the enCoder improves the temporal energy stability of some signals while retaining real-valued deCoder-side processing.
P P Vaidyanathan - One of the best experts on this subject based on the ideXlab platform.
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the roles of majorization and generalized triangular decomposition in communication and signal processing
2011Co-Authors: P P Vaidyanathan, Ching-chih WengAbstract:The main contribution of this thesis is toward the use of majorization and generalized triangular decomposition (GTD) to the theory and many applications of signal processing. In particular, the focus is on developing new signal processing methods based on these mathematical tools for digital communication, data compression, and filter bank design. The first part of the thesis focuses on transceiver design for multiple-input multiple-output (MIMO) communications. The first problem considered is the joint optimization of transceivers with linear preCoders, decision feedback equalizers (DFEs), and bit allocation schemes for frequency flat MIMO channels. We show that the generalized triangular decomposition offers an optimal family of solutions to this problem. This general framework incorporates many existing designs, such as the optimal linear transceiver, the ZF-VBLAST system, and the geometric mean decomposition (GMD) transceiver, as special cases. It also predicts many novel optimal solutions that have not been observed before. We also discuss the use of each of these theoretical solutions under practical considerations. In addition to total power constraints, we also consider the transceiver optimization under individual power constraints and other linear constraints on the transmitting covariance matrix, which includes a more realistic individual power constraint on each antenna. We show the use of semidefinite programming (SDP), and the theory of majorization again provides a general framework for optimizing the linear transceivers as well as the DFE transceivers. The transceiver design for frequency selective MIMO channels is then considered. Block diagonal GMD (BD-GMD), which is a special instance of GTD with block diagonal structure in one of the semi-unitary matrices, is used to design transceivers that have many desirable properties in both performance and computation. The second part of the thesis focuses on signal processing algorithms for data compressions and filter bank designs. We revisit the classical Transform coding problem (for optimizing the theoretical coding gain in the high bit rate regime) from the view point of GTD and majorization theory. A general family of optimal Transform Coders is introduced based on GTD. This family includes the Karhunen-Loeve Transform (KLT), and the prediction-based lower triangular Transform (PLT) as special cases. The coding gain of the entire family, with optimal bit allocation, is maximized and equal to those of the KLT and the PLT. Other special cases of the GTD-TC are the GMD (geometric mean decomposition) and the BID (bidiagonal Transform). The GMD in particular has the property that the optimum bit allocation is a uniform allocation. We also propose using dither quantization in the GMD Transform Coder. Under the uniform bit loading scheme, it is shown that the proposed dithered GMD Transform Coders perform significantly better than the original GMD Coder in the low rate regime. Another important signal processing problem, namely the filter bank optimization based on the knowledge of input signal statistics, is then considered. GTD and the theory of majorization are again used to give a new look to this classical problem. We propose GTD filter banks as subband Coders for optimizing the theoretical coding gain. The orthonormal GTD filter bank and the biorthogonal GTD filter bank are discussed in detail. We show that in both cases there are two fundamental properties in the optimal solutions, namely, total decorrelation and spectrum equalization. The optimal solutions can be obtained by performing the frequency dependent GTD on the Cholesky factor of the input power spectrum density matrices. We also show that in both theory and numerical simulations, the optimal GTD subband Coders have superior performance than optimal traditional subband Coders. In addition, the uniform bit loading scheme can be used in the optimal biorthogonal GTD Coders with no loss of optimality. This solves the granularity problem in the conventional optimum bit loading formula. The use of the GTD filter banks in frequency selective MIMO communication systems is also discussed. Finally, the connection between the GTD filter bank and the traditional filter bank is clearly indicated. (Abstract shortened by UMI.)
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results on principal component filter banks colored noise suppression and existence issues
IEEE Transactions on Information Theory, 2001Co-Authors: S Akkarakaran, P P VaidyanathanAbstract:We have made explicit the precise connection between the optimization of orthonormal filter banks (FBs) and the principal component property: the principal component filter bank (PCFB) is optimal whenever the minimization objective is a concave function of the subband variances of the FB. This explains PCFB optimality for compression, progressive transmission, and various hitherto unnoticed white-noise, suppression applications such as subband Wiener filtering. The present work examines the nature of the FB optimization problems for such schemes when PCFBs do not exist. Using the geometry of the optimization search spaces, we explain exactly why these problems are usually analytically intractable. We show the relation between compaction filter design (i.e., variance maximization) and optimum FBs. A sequential maximization of subband variances produces a PCFB if one exists, but is otherwise suboptimal for several concave objectives. We then study PCFB optimality for colored noise suppression. Unlike the case when the noise is white, here the minimization objective is a function of both the signal and the noise subband variances. We show that for the Transform Coder class, if a common signal and noise PCFB (KLT) exists, it is, optimal for a large class of concave objectives. Common PCFBs for general FB classes have a considerably more restricted optimality, as we show using the class of unconstrained orthonormal FBs. For this class, we also show how to find an optimum FB when the signal and noise spectra are both piecewise constant with all discontinuities at rational multiples of /spl pi/.
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principal component filter banks existence issues and application to modulated filter banks
International Symposium on Circuits and Systems, 2000Co-Authors: S Akkarakaran, P P VaidyanathanAbstract:Principal component filter banks (PCFBs) sequentially compress most of the input signal energy into the first few subbands, and are mathematically defined using the notion of majorization. In a series of recent works, we have exploited connections between majorization and convexity theory to provide a unified explanation of PCFB optimality for numerous signal processing problems, involving compression, noise suppression and progressive transmission, However PCFBs are known to exist for all input spectra only for three special classes of orthonormal filter banks (FBs): any class of two channel FBs, the Transform Coder class and the unconstrained class. This paper uses the developed theory to describe techniques to examine existence of PCFBs. We prove that the classes of DFT and cosine-modulated FBs do not have PCFBs for large families of input spectra. This result is new and quite different from most known facts on nonexistence of PCFBs, which usually involve very specific examples and proofs with numerical optimizations.
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theory of optimal orthonormal subband Coders
IEEE Transactions on Signal Processing, 1998Co-Authors: P P VaidyanathanAbstract:The theory of the orthogonal Transform Coder and methods for its optimal design have been known for a long time. We derive a set of necessary and sufficient conditions for the coding-gain optimality of an orthonormal subband Coder for given input statistics. We also show how these conditions can be satisfied by the construction of a sequence of optimal compaction filters one at a time. Several theoretical properties of optimal compaction filters and optimal subband Coders are then derived, especially pertaining to behavior as the number of subbands increases. Significant theoretical differences between optimum subband Coders, Transform Coders, and predictive Coders are summarized. Finally, conditions are presented under which optimal orthonormal subband Coders yield as much coding gain as biorthogonal ones for a fixed number of subbands.
Christian R Helmrich - One of the best experts on this subject based on the ideXlab platform.
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spectral envelope reconstruction via igf for audio Transform coding
International Conference on Acoustics Speech and Signal Processing, 2015Co-Authors: Christian R Helmrich, Andreas Niedermeier, Sascha Disch, Florin GhidoAbstract:In low-bitrate audio coding, modern Coders often rely on efficient parametric techniques to enhance the performance of the waveform preserving Transform Coder core. While the latter features well-known perceptually adapted quantization of spectral coefficients, parametric techniques reconstruct the signal parts that have been quantized to zero by the enCoder to meet the low-bitrate constraint. Large numbers of zeroed spectral values and especially consecutive zeros constituting gaps often lead to audible artifacts at the deCoder. To avoid such artifacts the new 3GPP Enhanced Voice Services (EVS) coding standard utilizes noise filling and intelligent gap filling (IGF) techniques, guided by spectral envelope information. In this paper the underlying considerations of the parametric energy adjustment and transmission in EVS and its relation to noise filling, IGF, and tonality preservation are presented. It is further shown that complex-valued IGF envelope calculation in the enCoder improves the temporal energy stability of some signals while retaining real-valued deCoder-side processing.
