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A global method for invertible integer DCT and integer wavelet algorithms

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 2004年第2期16卷 90-110页

作者： Plonka, G Univ Duisburg Gesamthsch Inst Math D-47048 Duisburg Germany

In this paper we present a new global method to derive invertible integer-to-integer mappings from given linear mappings F : R-n --> R-n. If F is given by F(x) = H(n)x and H-n is an invertible matrix, then one can always find a suitable factor a such that the condition [-1/2, 1/2)(n) subset of or equal to alphaH(n) ((- 1/2, 1/2](n)) is satisfied. An invertible mapping F: Z(n) --> Z(n) can now simply be defined by F(x) = rd(alphaH(n)x), and obviously, this nonlinear integer mapping is close to the linear mapping alphaF. We apply this idea in order to derive a new invertible integer DCT-II transform of radix-2 length and new integer wavelet algorithms. It turns out, that the expansion factors a can be chosen very small. (C) 2003 Elsevier Inc. All rights reserved.

关键词： invertible integer to integer transforms discrete cosine transform lossless coding expansion factors rounding-off reversible integer DCT integer wavelet transform

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The error exponent and minimum achievable rates for the fixed-length coding of general sources

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2001年第10期E84A卷 2466-2473页

作者： Iriyama, K Ihara, S Nagoya Univ Grad Sch Human Informat Nagoya Aichi 4648601 Japan Nagoya Univ Sch Informat & Sci Nagoya Aichi 4648601 Japan

We study the reliability functions or the minimum r-achievable rates of the lossless coding for the general sources in the sense of Han-Verdu, where r means the exponent of the error probability. Han has obtained formulas for the minimum r-achievable rates of the general sources. Our aim is to give alternative expressions for the minimum r-achievable rates. Our result seems to be a natural extension of the known results for the stationary memoryless sources and Markov sources.

关键词： error exponent general source lossless coding minimum achievable rate reliability function

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Piecewise DC prediction in HEVC

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SIGNAL PROCESSING-IMAGE COMMUNICATION 2014年第9期29卷 945-950页

作者： Kim, Kibaek Jeon, Gwanggil Jeong, Jechang Hanyang Univ Dept Elect & Comp Engn Seoul 133791 South Korea Incheon Natl Univ Dept Embedded Syst Engn Inchon 406772 South Korea

In this paper, we propose an improved DC prediction method for high-efficiency video coding (HEVC) intra coding. The technique involves the application of pixel-wise predictors rather than block-based predictor in the DC mode. In HEVC, the pixels of neighboring reconstructed blocks are used to support multiple directional spatial prediction modes and reduce spatial redundancy. For lossless coding, pixel-by-pixel differential pulse code modulation (DPCM) is applied to directional predictions. Consequently, residuals are reduced and coding efficiency is improved. Since DC prediction still employs block-based coding, pixel-wise DC prediction is needed for better coding efficiency. When compared to HEVC lossless intra coding, the proposed algorithm reduces the bit rate by 5.95%. Furthermore, with pixel-by-pixel DPCM, the average bit rate reduction is 10.64% when compared to HEVC lossless intra coding. (C) 2014 Elsevier B.V. All rights reserved.

关键词： HEVC Intra prediction lossless coding Differential pulse code modulation Pixel-wise predictor

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Multilevel Split Regression Wavelet Analysis for lossless Compression of Remote Sensing Data

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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS 2018年第10期15卷 1540-1544页

作者： Alvarez-Cortes, Sara Bartrina-Rapesta, Joan Serra-Sagrista, Joan Univ Autonoma Barcelona Dept Informat & Commun Engn E-08193 Barcelona Spain

Spectral redundancy is a key element to be exploited in compression of remote sensing data. Combined with an entropy encoder, it can achieve competitive lossless coding performance. One of the latest techniques to decorrelate the spectral signal is the regression wavelet analysis (RWA). RWA applies a wavelet transform in the spectral domain and estimates the detail coefficients through the approximation coefficients using linear regression. RWA was originally coupled with JPEG 2000. This letter introduces a novel coding approach, where RWA is coupled with the predictor of CCSDS-123.0-B-1 standard and a lightweight contextual arithmetic coder. In addition, we also propose a smart strategy to select the number of RWA decomposition levels that maximize the coding performance. Experimental results indicate that, on average, the obtained coding gains vary between 0.1 and 1.35 bits-per-pixel-per-component compared with the other state-of-the-art coding techniques.

关键词： lossless coding predictive coding spectral decorrelation

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Silhouette 4D With Context Selection: lossless Geometry Compression of Dynamic Point Clouds

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IEEE SIGNAL PROCESSING LETTERS 2021年 28卷 1660-1664页

作者： Ramalho, Evaristo Peixoto, Eduardo Medeiros, Edil Univ Brasilia Dept Elect Engn BR-70910900 Brasilia DF Brazil

Recently we have proposed a coding algorithm of point cloud geometry based on a rather different approach from the popular octree representation. In our algorithm, the point cloud is decomposed in silhouettes, hence the name Silhouette Coder, and context adaptive arithmetic coding is used to exploit redundancies within the point cloud (intra frame coding), and also using a reference point cloud (inter frame coding). In this letter we build on our previous work and propose a context selection algorithm as a pre-processing stage. With this algorithm, the point cloud is first parsed testing a large number of candidate context locations. The algorithm selects a small number of these contexts that better reflect the current point cloud, and then encode it with this choice. The proposed method further improves the results of our previous coder, Silhouette 4D, by 10%, on average, on a dynamic point cloud dataset of the JPEG Pleno, and achieves bitrates competitive with some high quality lossy coders such as the MPEG G-PCC.

关键词： Three-dimensional displays Image coding Encoding Transform coding Signal processing algorithms Codecs Geometry Point clouds inter coder lossless coding arithmetic coding

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Existence of optimal prefix codes for infinite source alphabets

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IEEE TRANSACTIONS ON INFORMATION THEORY 1997年第6期43卷 2026-2028页

作者： Linder, T Tarokh, V Zeger, K AT&T BELL LABS FLORHAM PKNJ 07932

It Is proven that for every random variable with a countably infinite set of outcomes and finite entropy there exists an optimal prefix code which can be constructed from Huffman codes for truncated versions of the random variable, and that the average lengths of any sequence of Huffman codes for the truncated versions converge to that of the optimal code. Also, it is shown that every optimal Infinite code achieves Kraft's inequality with equality.

关键词： Huffman lossless coding prefix codes

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Complexity Reduction Method for BSAC Decoder

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ETRI JOURNAL 2009年第3期31卷 336-338页

作者： Jeong, Gyuhyeok Ahn, Yeonguk Lee, Insung Chungbuk Natl Univ Sch Elect & Comp Engn Cheongju South Korea

This letter proposes a complexity reduction method to speed up the noiseless decoding of a bit-sliced arithmetic coding (BSAC) decoder This scheme fully utilizes the group of consecutive arithmetic-coded symbols known as the decoding band and the significance tree structure sorted in order of significance at every decoding band With the same audio quality, the proposed method reduces the number of calculations that are performed during the noiseless decoding in BSAC to about 22% of the amount of calculations with the conventional full-search method.

关键词： MPEG-4 BSAC lossless coding complexity reduction algorithm

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Invertible integer DCT algorithms

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APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 2003年第1期15卷 70-88页

作者： Plonka, G Tasche, M Univ Duisburg Gesamthsch Math Inst D-47048 Duisburg Germany Univ Rostock Dept Math D-18051 Rostock Germany

Integer DCTs have important applications in lossless coding. In this paper, an integer DCT of radix-2 length n is understood to be a nonlinear, (left-)invertible mapping which acts on Z(n) and approximates the classical discrete cosine transform (DCT) of length n. In image compression, the DCT of type I (DCT-II) is of special interest. In this paper we present a new approach to invertible integer DCT-II and integer DCT-IV. Our method is based on a factorization of the cosine matrices of types II and IV into products of sparse, orthogonal matrices. Up to some permutations, each matrix factor is a block-diagonal matrix with blocks being orthogonal matrices of order 2. Hence one has to construct only integer transforms of length 2. We factorize an orthogonal matrix of order 2 into three lifting matrices and work with lifting steps and rounding-off. This allows the construction of new integer DCT algorithms. We give uniform bounds for the worst case difference between the results of exact DCT and the corresponding integer DCT. Finally, we present some numerical experiments for the integer DCT-II of length 8 and for the 2-dimensional integer DCT-II of size 8 x 8. (C) 2003 Elsevier Inc. All rights reserved.

关键词： discrete cosine transform lossless coding data compression factorization of cosine matrix lifting matrix rounding-off integer DCT invertible integer DCT worst case error error estimate

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Compact and Computationally Efficient Representation of Deep Neural Networks

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2020年第3期31卷 772-785页

作者： Wiedemann, Simon Mueller, Klaus-Robert Samek, Wojciech Fraunhofer Heinrich Hertz Inst D-10587 Berlin Germany Tech Univ Berlin D-10587 Berlin Germany Max Planck Inst Informat D-66123 Saarbrucken Germany Korea Univ Dept Brain & Cognit Engn Seoul 136713 South Korea

At the core of any inference procedure, deep neural networks are dot product operations, which are the component that requires the highest computational resources. For instance, deep neural networks, such as VGG-16, require up to 15-G operations in order to perform the dot products present in a single forward pass, which results in significant energy consumption and thus limits their use in resource-limited environments, e.g., on embedded devices or smartphones. One common approach to reduce the complexity of the inference is to prune and quantize the weight matrices of the neural network. Usually, this results in matrices whose entropy values are low, as measured relative to the empirical probability mass distribution of its elements. In order to efficiently exploit such matrices, one usually relies on, inter alia, sparse matrix representations. However, most of these common matrix storage formats make strong statistical assumptions about the distribution of the elements;therefore, cannot efficiently represent the entire set of matrices that exhibit low-entropy statistics (thus, the entire set of compressed neural network weight matrices). In this paper, we address this issue and present new efficient representations for matrices with low-entropy statistics. Alike sparse matrix data structures, these formats exploit the statistical properties of the data in order to reduce the size and execution complexity. Moreover, we show that the proposed data structures can not only be regarded as a generalization of sparse formats but are also more energy and time efficient under practically relevant assumptions. Finally, we test the storage requirements and execution performance of the proposed formats on compressed neural networks and compare them to dense and sparse representations. We experimentally show that we are able to attain up to x42 compression ratios, x5 speed ups, and x 90 energy savings when we lossless convert the state-of-the-art networks, such as AlexNet, VG

关键词： Computationally efficient deep learning data structures lossless coding neural network compression sparse matrices

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United coding method for compound image compression

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MULTIMEDIA TOOLS AND APPLICATIONS 2014年第3期71卷 1263-1282页

作者： Wang, Shuhui Lin, Tao Tongji Univ VLSI Lab Shanghai 200092 Peoples R China

This paper proposes a compound image coding method named united coding (UC). In UC, several lossless coding tools such as dictionary-entropy coders, run-length encoding (RLE), Hextile, and a few filters used in portable network graphics (PNG) format are united into H.264 like intraframe hybrid video coding. The basic coding unit (BCU) has a size typically between 16 x 16 pixels to 64 x 64 pixels. All coders in UC are used to code each BCU. Then, the lossless coder that generates minimum bit-rate (R) is chosen as the optimal lossless coder. Finally, the final optimal coder is chosen from the lossy intraframe hybrid coder and the optimal lossless coder using R-D cost based optimization criterion. Moreover, the data coded by one lossless coder can be used as the dictionary of other lossless coders. Experimental results demonstrate that compared with H.264, UC achieves up to 20 dB PSNR improvement and better visual picture quality for compound images with mixed text, graphics and natural picture. Compared with lossless coders such as gzip and PNG, UC can achieve 2-5 times higher compression ratio with just a minor loss and keep partial-lossless picture quality. The partial-lossless nature of UC is indispensable for some typical applications, such as cloud computing and rendering, cloudlet-screen computing and remote desktop, where lossless coding of partial image regions is demanded. On the other hand, the implementation complexity and cost increment of UC is moderate, typically less than 25 % of a traditional hybrid coder such as H.264.

关键词： Compound image and video United coding Hybrid coding lossless coding Dictionary-entropy coding

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