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A Class of low-complexity DCT-Like transforms for Image and Video Coding

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY 2022年第7期32卷 4364-4375页

作者： da Silveira, Thiago L. T. Canterle, Diego Ramos Coelho, Diego F. G. Coutinho, Vitor A. Bayer, Fabio M. Cintra, Renato J. Univ Fed Rio Grande do Sul UFRGS Inst Inform & X00E1 Tica BR-90040060 Porto Alegre RS Brazil Univ Sao Paulo Inst Math & Stat BR-05508090 Sao Paulo Brazil Recife Ctr Adv Studies & Syst CESAR BR-50030390 Recife PE Brazil Univ Fed Santa Maria UFSM Dept Estat BR-97105900 Santa Maria RS Brazil Univ Fed Santa Maria UFSM LACESM BR-97105900 Santa Maria RS Brazil Univ Fed Pernambuco UFPE Dept Estat Signal Proc Grp BR-50670901 Recife PE Brazil

The discrete cosine transform (DCT) is a relevant tool in signal processing applications, mainly known for its good decorrelation properties. Current image and video coding standards-such as JPEG and HEVC-adopt the DCT as a fundamental building block for compression. Recent works have introduced low-complexity approximations for the DCT, which become paramount in applications demanding real-time computation and low-power consumption. The design of DCT approximations involves a trade-off between computational complexity and performance. This paper introduces a new multiparametric transform class encompassing the round-off DCT (RDCT) and the modified RDCT (MRDCT), two relevant multiplierless 8-point approximate DCTs. The associated fast algorithm is provided. Four novel orthogonal low-complexity 8-point DCT approximations are obtained by solving a multicriteria optimization problem. The optimal 8-point transforms are scaled to lengths 16 and 32 while keeping the arithmetic complexity low. The proposed methods are assessed by proximity and coding measures with respect to the exact DCT. Image and video coding experiments and hardware realization are performed. The novel transforms perform close to or outperform the current state-of-the-art DCT approximations.

关键词： transforms Discrete cosine transforms complexity theory Video coding Arithmetic Hardware Encoding DCT approximation low-complexity transforms image and video coding

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An Integer Approximation Method for Discrete Sinusoidal transforms

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2011年第6期30卷 1481-1501页

作者： Cintra, R. J. Univ Fed Pernambuco Dept Estat Recife PE Brazil

Approximate methods have been considered as a means to the evaluation of discrete transforms. In this work, we propose and analyze a class of integer transforms for the discrete Fourier, Hartley, and cosine transforms (DFT, DHT, and DCT), based on simple dyadic rational approximation methods. The introduced method is general, applicable to several blocklengths, whereas existing approaches are usually dedicated to specific transform sizes. The suggested approximate transforms enjoy low multiplicative complexity and the orthogonality property is achievable via matrix polar decomposition. We show that the obtained transforms are competitive with archived methods in literature. New 8-point square wave approximate transforms for the DFT, DHT, and DCT are also introduced as particular cases of the introduced methodology.

关键词： Approximate transforms discrete sinusoidal transforms low-complexity transforms Nonorthogonal transforms Orthogonalization

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low-complexity rounded KLT approximation for image compression

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JOURNAL OF REAL-TIME IMAGE PROCESSING 2022年第1期19卷 173-183页

作者： Radunz, Anabeth P. Bayer, Fabio M. Cintra, Renato J. Univ Fed Pernambuco Programa Posgrad Estat Recife PE Brazil Univ Fed Santa Maria Dept Estat Santa Maria RS Brazil Univ Fed Santa Maria LACESM Santa Maria RS Brazil Univ Fed Pernambuco Dept Estat Signal Proc Grp Recife PE Brazil Univ Calgary Dept Elect & Comp Engn Calgary AB Canada Florida Int Univ Miami FL 33199 USA

The Karhunen-Loeve transform (KLT) is often used for data decorrelation and dimensionality reduction. Because its computation depends on the matrix of covariances of the input signal, the use of the KLT in real-time applications is severely constrained by the difficulty in developing fast algorithms to implement it. In this context, this paper proposes a new class of low-complexity transforms that are obtained through the application of the round function to the elements of the KLT matrix. The proposed transforms are evaluated considering figures of merit that measure the coding power and distance of the proposed approximations to the exact KLT and are also explored in image compression experiments. Fast algorithms are introduced for the proposed approximate transforms. It was shown that the proposed transforms perform well in image compression and require a low implementation cost.

关键词： Approximate KLT Image compression Karhunen-Loeve transform low-complexity transforms

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Comments on 'Area and power efficient DCT architecture for image compression' by Dhandapani and Ramachandran

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EURASIP JOURNAL ON ADVANCES IN SIGNAL PROCESSING 2017年第1期2017卷 1页

作者： Cintra, Renato J. Bayer, Fabio M. Univ Fed Pernambuco Dept Estat Recife PE Brazil Univ Fed Santa Maria Dept Estat Santa Maria RS Brazil Univ Fed Santa Maria LACESM Santa Maria RS Brazil

In [Dhandapani and Ramachandran, "Area and power efficient DCT architecture for image compression", EURASIP Journal on Advances in Signal Processing 2014, 2014: 180] the authors claim to have introduced an approximation for the discrete cosine transform capable of outperforming several well-known approximations in literature in terms of additive complexity. We could not verify the above results and we offer corrections for their work.

关键词： DCT approximations low-complexity transforms

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Fast data-independent KLT approximations based on integer functions

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MULTIMEDIA TOOLS AND APPLICATIONS 2024年第26期83卷 67303-67325页

作者： Radunz, A. P. Coelho, D. F. G. Bayer, F. M. Cintra, R. J. Madanayake, A. Univ Fed Pernambuco Dept Estat BR-50670901 Recife Brazil Univ Fed Pernambuco Dept Tecnol Signal Proc Grp BR-55014900 Caruaru Brazil Univ Fed Santa Maria Dept Estat LACESM BR-97105900 Santa Maria Brazil Florida Int Univ Dept Elect & Comp Engn Miami FL 33174 USA

The Karhunen-Loeve transform (KLT) stands as a well-established discrete transform, demonstrating optimal characteristics in data decorrelation and dimensionality reduction. Its ability to condense energy compression into a select few main components has rendered it instrumental in various applications within image compression frameworks. However, computing the KLT depends on the covariance matrix of the input data, which makes it difficult to develop fast algorithms for its implementation. Approximations for the KLT, utilizing specific rounding functions, have been introduced to reduce its computational complexity. Therefore, our paper introduces a category of low-complexity, data-independent KLT approximations, employing a range of round-off functions. The design methodology of the approximate transform is defined for any block-length N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{N}$$\end{document}, but emphasis is given to transforms of N=8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{N} = 8$$\end{document} due to its wide use in image and video compression. The proposed transforms perform well when compared to the exact KLT and approximations considering classical performance measures. For particular scenarios, our proposed transforms demonstrated superior performance when compared to KLT approximations documented in the literature. We also developed fast algorithms for the proposed transforms, further reducing the arithmetic cost associated with their implementation. Evaluation of field programmable gate array (FPGA) hardware implementation metrics was conducted. Practical applicatio

关键词： Approximate transforms Fast algorithms Image compression Karhunen-Loeve transform low-complexity transforms

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A class of DCT approximations based on the Feig-Winograd algorithm

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SIGNAL PROCESSING 2015年 113卷 38-51页

作者： Tablada, C. J. Bayer, F. M. Cintra, R. J. Univ Fed Pernambuco Dept Estat Signal Proc Grp Recife PE Brazil Univ Fed Santa Maria Dept Estat Santa Maria RS Brazil Univ Fed Santa Maria LACESM Santa Maria RS Brazil Inst Natl Sci Appl LIRIS Lyon France

A new class of matrices based on a parametrization of the Feig-Winograd factorization of 8-point DcT is proposed. such parametrization induces a matrix subspace, which unifies a number of existing methods for DCT approximation. By solving a comprehensive multicriteria optimization problem, we identified several new DCT approximations. Obtained solutions were sought to possess the following properties: (i) low multiplierless computational complexity, (ii) orthogonality or near orthogonality, (iii) low complexity invertibility, and (iv) close proximity and performance to the exact DCT. Proposed approximations were submitted to assessment in terms of proximity to the DCT, coding performance, and suitability for image compression. Considering Pareto efficiency, particular new proposed approximations could outperform various existing methods archived in literature. (C) 2015 Elsevier B.V. All rights reserved.

关键词： DCT approximation Feig-Winograd algorithm low-complexity transforms Image compression

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An orthogonal 16-point approximate DCT for image and video compression

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MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING 2016年第1期27卷 87-104页

作者： da Silveira, Thiago L. T. Bayer, Fabio M. Cintra, Renato J. Kulasekera, Sunera Madanayake, Arjuna Kozakevicius, Alice J. Univ Fed Santa Maria Programa Posgrad Informat BR-97119900 Santa Maria RS Brazil Univ Fed Santa Maria Dept Estat BR-97119900 Santa Maria RS Brazil Univ Fed Santa Maria LACESM BR-97119900 Santa Maria RS Brazil Univ Fed Pernambuco Dept Estat Signal Proc Grp Recife PE Brazil Univ Akron Dept Elect & Comp Engn Akron OH 44325 USA Univ Fed Santa Maria Dept Matemat BR-97119900 Santa Maria RS Brazil

A low-complexity orthogonal multiplierless approximation for the 16-point discrete cosine transform (DCT) was introduced. The proposed method was designed to possess a very low computational cost. A fast algorithm based on matrix factorization was proposed requiring only 60 additions. The proposed architecture outperforms classical and state-of-the-art algorithms when assessed as a tool for image and video compression. Digital VLSI hardware implementations were also proposed being physically realized in field programmable gate array technology and implemented in 45 nm up to synthesis and place-route levels. Additionally, the proposed method was embedded into a high efficiency video coding (HEVC) reference software for actual proof-of-concept. Obtained results show negligible video degradation when compared to Chen DCT algorithm in HEVC.

关键词： 16-Point DCT approximation low-complexity transforms Image compression Video coding

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DCT approximations based on Chen's factorization

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SIGNAL PROCESSING-IMAGE COMMUNICATION 2017年 58卷 14-23页

作者： Tablada, C. J. da Silveira, T. L. T. Cintra, R. J. Bayer, F. M. Univ Fed Pernambuco Dept Estat Signal Proc Grp Recife PE Brazil Univ Fed Paraiba Dept Estat Joao Pessoa Paraiba Brazil Univ Fed Rio Grande do Sul Programa Posgrad Comp Porto Alegre RS Brazil Univ Calgary ECE Calgary AB Canada Univ Fed Santa Maria Dept Estat Santa Maria RS Brazil Univ Fed Santa Maria LACESM Santa Maria RS Brazil

In this paper, two 8-point multiplication-free DCT approximations based on the Chen's factorization are proposed and their fast algorithms are also derived. Both transformations are assessed in terms of computational cost, error energy, and coding gain. Experiments with a JPEG-like image compression scheme are performed and results are compared with competing methods. The proposed low-complexity transforms are scaled according to Jridi-Alfalou-Meher algorithm to effect 16- and 32-point approximations. The new sets of transformations are embedded into an HEVC reference software to provide a fully HEVC-compliant video coding scheme. We show that approximate transforms can outperform traditional transforms and state-of-the-art methods at a very low complexity cost. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Approximate DCT Chen's factorization Fast algorithms Image and video compression low-complexity transforms

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Evaluation and Comparison of DCT Approximations on FPGA for Hardware Reduction

Evaluation and Comparison of DCT Approximations on FPGA for ...

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22nd IEEE International Autumn Meeting on Power, Electronics and Computing (ROPEC)

作者： Escobar, R. Villagernez Patino, A. Mendez Moreno, I. Molina Ramirez, M. Garcia Archundia, E. Reyes Gnecchi, J. A. Gutierrez Tecnol Nacl Mexico Div Estudios Posgrad & Invest DEPI IT Morelia Morelia Michoacan Mexico

ISBN: (纸本)9781728199535

Discrete cosine transform (DCT) is commonly used in image and video compression. DCT approximations are excellent alternatives to reduce the computational complexity of exact DCT with good coding *** this article we review and compare some of the most interesting multiplication-free approximations in the literature and their hardware cost.

关键词： DCT approximation discrete cosine transform (DCT) FPGA Image compression low-complexity transforms

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Data-independent low-complexity KLT approximations for image and video coding

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SIGNAL PROCESSING-IMAGE COMMUNICATION 2022年第0期101卷 116585-116585页

作者： Radunz, Anabeth P. da Silveira, Thiago L. T. Bayer, Fabio M. Cintra, Renato J. Univ Fed Pernambuco Programa Posgrad Estat Recife PE Brazil Univ Fed Rio Grande do Sul Inst Informat Porto Alegre RS Brazil Univ Fed Santa Maria Dept Estat Santa Maria RS Brazil Univ Fed Santa Maria LACESM Santa Maria RS Brazil Univ Fed Pernambuco Dept Estat Signal Proc Grp Recife PE Brazil

The Karhunen-Loeve transform (KLT) is often used for data decorrelation and dimensionality reduction. The KLT is able to optimally retain the signal energy in only few transform components, being mathematically suitable for image and video compression. However, in practice, because of its high computational cost and dependence on the input signal, its application in real-time scenarios is precluded. This work proposes low-computational cost approximations for the KLT. We focus on the blocklengths N is an element of{4,8, 16, 32} because they are widely employed in image and video coding standards such as JPEG and high efficiency video coding (HEVC). Extensive computational experiments demonstrate the suitability of the proposed low-complexity transforms for image and video compression.

关键词： Approximate transform Image compression Karhunen-Loeve transform low-complexity transforms Signed KLT

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