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Compressing Sets and Multisets of Sequences

IEEE TRANSACTIONS ON INFORMATION THEORY 2015年第3期61卷 1485-1490页

作者： Steinruecken, Christian Univ Cambridge Dept Engn Cambridge CB2 1PZ England

This paper describes lossless compression algorithms for multisets of sequences, taking advantage of the multiset's unordered structure. Multisets are a generalization of sets, where members are allowed to occur multiple times. A multiset can be encoded naively by simply storing its elements in some sequential order, but then information is wasted on the ordering. We propose a technique that transforms the multiset into an order-invariant tree representation, and derive an arithmetic code that optimally compresses the tree. Our method achieves compression even if the sequences in the multiset are individually incompressible (such as cryptographic hash sums). The algorithm is demonstrated practically by compressing collections of SHA-1 hash sums, and multisets of arbitrary, individually encodable objects.

关键词： arithmetic coding Bayesian methods data compression hash sums multisets tree data structures

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Progressive space frequency quantization for SAR data compression

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 2002年第1期40卷 3-10页

作者： Gleich, D Planinsic, P Gergic, B Cucej, Z Univ Maribor Fac Elect Engn & Comp Sci Signal Proc Lab SLO-2000 Maribor Slovenia

In this paper, we propose a new wavelet image coding technique for synthetic aperture radar (SAR) data compression called a progressive space-frequency quantization (PSFQ). PSFQ performs spatial quantization via rate distortion-optimized zerotree pruning of wavelet coefficients that are coded using a progressive subband coding technique. We compared the performances of zerotree-based methods: EZW, SPIRT, SFQ, and PSFQ with the classical wavelet-based method (CWM), which uses uniform scalar quantization of subbands followed by recency rank coding. The performances of the methods based on zerotree quantization were better than the CWM in the rate distortion sense. The embedded coding techniques perform better SNR results than the methods using scalar quantization. However, the probability density function (PDF) of the reconstructed amplitude SAR data compressed using CWM, better corresponded to the PDF of the original data than the PDF of the reconstructed data compressed using the zerotree based methods. The amplitude PDF of the reconstructed data obtained using PSFQ compression algorithm better corresponded to the original PDF than the amplitude PDF of the data obtained using the multilook method.

关键词： arithmetic coding compression radar synthetic aperture radar (SAR) wavelet transform zerotree coding

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Advances in the data compression of digital elevation models

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COMPUTERS & GEOSCIENCES 2003年第8期29卷 985-1002页

作者： Kidner, DB Smith, DH Univ Glamorgan Sch Comp Pontypridd CF37 1DL Rhonodda Cyon T Wales Univ Glamorgan Div Math Pontypridd CF37 1DL Rhonodda Cyon T Wales

The maintenance and dissemination of spatial databases requires efficient strategies for handling the large volumes of data that are now publicly available. It particular, satellite and aerial imagery, radar, LiDAR, and digital elevation models (DEMs) are being utilised by a sizeable user-base, for predominantly environmental applications. The efficient dissemination of such datasets has become a key issue in the development of web-based and distributed computing environments. However, the physical size of these datasets is a major bottleneck in their storage and transmission. The problem is often exaggerated when the data is supplied in less efficient, proprietary or national data formats. This paper presents a methodology for the lossless compression of DEMs, based on the statistical correlation of terrain data in local neighbourhoods. Most data and image compression algorithms fail to capitalise fully on the inherent redundancy in spatial data. At the same time, users often prefer a uniform solution to all their data compression requirements, but these solutions may be far from optimal. The approach presented here can be thought of as a simple pre-processing of the elevation data before the use of traditional data compression software frequently applied to spatial data sets, such as GZIP. Identification and removal of the spatial redundancy in terrain data, with the use of optimal predictors for DEMs and optimal statistical encoders such as arithmetic coding, gives even higher Huffman coding are shown to be far from optimal in identifying and removing the spatial redundancy in DEMs. The new approaches presented here typically calve the file sizes of our earlier approach, and give a 40-62% improvement on GZIP-compressed DEMs. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： DEMs linear prediction Lagrange multipliers entropy arithmetic coding

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Lossless chaos-based crypto-compression scheme for image protection

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IET IMAGE PROCESSING 2014年第12期8卷 671-686页

作者： Masmoudi, Atef Puech, William Univ Sfax Sfax Preparatory Engn Inst Dept Math & Comp Sci Sfax 3018 Tunisia Univ Montpellier 2 CNRS UMR 5506 LIRMM F-34392 Montpellier 05 France

In this study, the authors proposed a new scheme which performs both lossless compression and encryption of images. Lossless compression is done by arithmetic coding (AC) while encryption is based on a chaos-based pseudorandom bit generator. Hence, they proposed to incorporate recent results of chaos theory into AC in order to shuffle the cumulative frequency vector of input symbols chaotically to make AC secure and the decoding process completely key-dependent. Many other techniques based on varying the statistical model used by AC have been proposed in literature, however, these techniques suffer from losses in compression efficiency that result from changes in entropy model statistics and are weak against known attacks. The proposed compression-encryption techniques were developed and discussed. The numerical simulation analysis indicates that the proposed scheme is highly satisfactory for image encryption without any AC compression efficiency loss. In addition, it can be incorporated into any image compression standard or algorithm employing AC as entropy coding stage, including static, adaptive and context-based adaptive models, and at any level, including bit, pixel and predictive error pixel levels.

关键词： CHAOS theory DATA protection IMAGE processing DATA encryption (Computer science) arithmetic coding PIXELS

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Quality controlled ECG compression using essentially non-oscillatory point-value decomposition (ENOPV) technique

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DIGITAL SIGNAL PROCESSING 2012年第6期22卷 878-884页

作者： Aggarwal, Vibha Patterh, Manjeet Singh Punjabi Univ COEM Rampura Phul Punjab India Punjabi Univ UCOE Patiala Punjab India

This paper presents an essentially non-oscillatory point-value (ENOPV) scheme based ECG compression. ENOPV scheme is a combination of multiresolution scheme (analysis) and interpolation scheme (synthesis). Advantage of using ENOPV scheme is that it avoids the discontinuities and therefore large numbers of coefficient do not appear at edges. It also provides better compression capabilities. The results are presented in tabular and graphical form for the different ECG signals of varying characteristics. Results are also compared with the results reported in the literature. It has been observed that there is significant increase in compression ratio (CR) at a given quality. For example, at percentage of root mean square difference (PRO) 2.65, the CR in case of ENOPV based scheme is 28.22, which is higher than 10.84, the best reported result. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Electrocardiogram (ECG) Compression Essentially non-oscillatory point-value decomposition (ENOPV) PRD Sequential Huffman coding arithmetic coding

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A Novel Assessment of Baroreflex Activity Through the Similarity of Ternary Codes of Oscillations Between Arterial Blood Pressure and R-R Intervals

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JOURNAL OF MEDICAL AND BIOLOGICAL ENGINEERING 2020年第5期40卷 727-734页

作者： Chen, Po-Wei Lin, Chun-Keng Liu, Wei-Min Chen, Yu-Chen Tsai, Sheng-Tzung Liu, An-Bang Buddhist Tzu Chi Med Fdn Hualien Tzu Chi Hosp Dept Med Educ Hualien Taiwan Natl Dong Hwa Univ Dept Elect Engn Hualien Taiwan Natl Chung Cheng Univ Dept Comp Sci & Informat Engn Chiayi Taiwan Tzu Chi Univ Inst Med Sci Hualien Taiwan Buddhist Tzu Chi Med Fdn Hualien Tzu Chi Hosp Dept Neurosurg Hualien Taiwan Tzu Chi Univ 707Sec 3Chung Yang Rd Hualien 970 Taiwan Buddhist Tzu Chi Med Fdn Hualien Tzu Chi Hosp Dept Neurol 707Sec 3Chung Yang Rd Hualien 970 Taiwan

Purpose Arterial baroreflex plays a crucial role in the homeostasis of blood pressure. Elevated blood pressure stimulates baroreceptors and slows the heart rate consequently. Baroreflex activity has been quantified as the relationship between systolic blood pressure (SBP) and ECG R-R intervals (RRI), which is called baroreflex sensitivity (BRS). The purpose of this study is to define a new parameter of BRS and verify the reproducibility and validity of this indicator as compared with a popular BRS estimated by sequence method and a traditional BRS evaluated by pharmacological intervention. Methods At first, the spontaneous oscillations of SBP and RRI were defined by ternary arithmetic codes: decrease as 0, unchanged as 1 and increase as 2. The new BRS was quantified as the similarity between these two ternary coded series after decimalization with different digits from 3 to 5. The validity and reproducibility of this method were verified in vivo in 10 adult male Wistar Kyoto rats. Results This new parameter correlated well with the BRS estimated by the sequence method and pharmacological intervention. The reproducibility of this novel method was good according to the Bland-Altman plot. Conclusions This study offered a simple and reliable algorithm to estimate BRS, which can be embed in current instruments for clinical research.

关键词： Baroreflex sensitivity R-R intervals arithmetic coding Spontaneous oscillation

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A new data structure for cumulative probability tables: An improved frequency-to-symbol algorithm

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SOFTWARE-PRACTICE & EXPERIENCE 1996年第4期26卷 489-490页

作者： Fenwick, PM Department of Computer Science The University of Auckland Private Bag 92019 Auckland New Zealand

A recent paper presented a new efficient data structure, the 'binary indexed tree', for maintaining the cumulative frequencies for arithmetic data compression. Although algorithms were presented for all of the necessary operations, significant problems remained with the method for determining the symbol corresponding to a known frequency. This communication corrects that deficiency.

关键词： binary indexed tree arithmetic coding cumulative probabilities

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A new, fast, and efficient image codec based on set partitioning in hierarchical trees

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY 1996年第3期6卷 243-250页

作者： Said, A Pearlman, WA RENSSELAER POLYTECH INST DEPT ELECT COMP & SYST ENGNTROYNY 12180

Embedded zerotree wavelet (EZW) coding, introduced by J. M. Shapiro, is a very effective and computationally simple technique for image compression, Here we offer an alternative explanation of the principles of its operation, so that the reasons for its excellent performance can be better understood, These principles are partial ordering by magnitude with a set partitioning sorting algorithm, ordered bit plane transmission, and exploitation of self-similarity across different scales of an image wavelet transform, Moreover, we present a new and different implementation based on set partitioning in hierarchical trees (SPIHT), which provides even better performance than our previously reported extension of EZW that surpassed the performance of the original EZW, The image coding results, calculated from actual file sizes and images reconstructed by the decoding algorithm, are either comparable to or surpass previous results obtained through much more sophisticated and computationally complex methods, In addition, the new coding and decoding procedures are extremely fast, and they can be made even faster, with only small loss in performance, by omitting entropy coding of the bit stream by arithmetic code.

关键词： set partitioning Partial ordering Image compression decoding algorithm Data compression Entropy coding Hierarchical arithmetic coding codecs bit stream

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Universal lossless data compression with side information by using a conditional MPM grammar transform

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IEEE TRANSACTIONS ON INFORMATION THEORY 2001年第6期47卷 2130-2150页

作者： Yang, EH Kaltchenko, A Kieffer, JC Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada Univ Minnesota Dept Elect & Comp Engn Minneapolis MN 55455 USA

A grammar transform is a transformation that converts any data sequence to be compressed into a grammar from which the original data sequence can be fully reconstructed. In a grammar-based code, a data sequence is first converted into a grammar by a grammar transform and then losslessly encoded. Among several recently proposed grammar transforms is the multilevel pattern matching (MPM) grammar transform. In this paper, the MPM grammar transform is first extended to the case of side information known to both the encoder and decoder, yielding a conditional MPM (CMPM) grammar transform. A new simple linear-time and space complexity algorithm is then proposed to implement the MPM and CMPM grammar transforms. Based on the CMPM grammar transform, a universal lossless data compression algorithm with side information is developed, which can achieve asymptotically the conditional entropy rate of any stationary, ergodic source pair. It is shown that the algorithm's worst case redundancy/sample against the k-context conditional empirical entropy among all individual sequences of length n is upper-bounded by c (1/ log n), where c is a constant. The proposed algorithm with side information is the first in the coming family of conditional grammar-based codes, whose expected high efficiency is due to the efficiency of the corresponding unconditional codes.

关键词： arithmetic coding coding with side information entropy grammar-based source codes multilevel pattern matching (MPM) redundancy string matching universal data compression

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Variable-rate trellis source encoding

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IEEE TRANSACTIONS ON INFORMATION THEORY 1999年第2期45卷 586-608页

作者： Yang, EH Zhang, Z Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada Univ So Calif Dept Elect Engn Syst Inst Commun Sci Los Angeles CA 90089 USA

The fixed slope lossy algorithm derived from the kth-order adaptive arithmetic codeword length function is extended to the case of finite-state decoders or trellis-structured decoders. It is shown that when this algorithm is used to encode a stationary, ergodic source with a continuous alphabet, the Lagrangian performance (i.e., the resulting compression rate plus lambda times the resulting distortion) converges with probability one to a quantity computable as the infimum of an information-theoretic functional over a set of auxiliary random variables and reproduction levels, where lambda > 0 and -lambda is designated to be the slope of the rate-distortion function R(D) of the source at some D;the quantity is close to R(D) + lambda D when the order k used in the arithmetic coding or the number of states in the decoders is large enough, An alternating minimization algorithm for computing the quantity is presented;this algorithm is based on a training sequence and in turn gives rise to a design algorithm for variable-rate trellis source codes, The resulting variable-rate trellis source codes are very efficient in low-rate regions (below 0.8 bits/sample), With k = 8, the mean-squared error encoding performance at the rate 1/2 bits/sample for memoryless Gaussian sources is comparable to that afforded by trellis-coded quantizers;with k = 8 and the number of states in the decoder = 32, the mean-squared error encoding performance at the rate 1/2 bits/sample for memoryless Laplacian sources is about 1 dB better than that afforded by the trellis-coded quantizers with 256 states, With k = 8 and the number of states in the decoder = 256, the mean-squared error encoding performance at the rates of a fraction of 1 bit/sample for highly dependent Gauss-Markov sources with correlation coefficient 0.9 is within about 0.6 dB of the distortion-rate function. Note that at such low rates, predictive coders usually perform poorly.

关键词： arithmetic coding data compression quantization rate-distortion function stationary and ergodic sources variable-rate trellis source encoding

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