Post BWT stages of the Burrows–Wheeler compression algorithm

The lossless Burrows–Wheeler compression algorithm has received considerable attention over recent years for both its simplicity and effectiveness. It is based on a permutation of the input sequence—the Burrows–Wheeler transformation (BWT)—which groups symbols with a similar context close together. In the original version, this permutation was followed by a Move‐To‐Front transformation and a final entropy coding stage. Later versions used different algorithms, placed after the BWT, since the following stages have a significant influence on the compression rate. This paper describes different algorithms and improvements for these post BWT stages including a new context‐based approach. The results for compression rates are presented together with compression and decompression times on the Calgary corpus, the Canterbury corpus, the large Canterbury corpus and the Lukas 2D 16‐bit medical image corpus. Copyright © 2010 John Wiley & Sons, Ltd.     

Second step algorithms in the Burrows–Wheeler compression algorithm

In this paper we focus our attention on the second step algorithms of the Burrows–Wheeler compression algorithm, which in the original version is the Move To Front transform. We discuss many of its replacements presented so far, and compare compression results obtained using these replacements. Then we propose a new algorithm that yields a better compression ratio than the previous algorithms. Copyright © 2001 John Wiley & Sons, Ltd.     

Investigation of block-sorting of multiset permutations

A recent development in data compression area is Burrows–Wheeler Compression algorithm (BWCA). Introduced by Burrows and Wheeler, the BWCA achieves compression ratio closer to the best compression techniques, such as partial pattern matching (PPM) techniques, but with a faster execution speed. In this paper, we analyze the combinatorial properties of the Burrows–Wheeler transformation (BWT), which is a block-sorting transformation and an essential part of the BWCA, introduce a new transformation, and delineate the new transformation with the BWT based on the multiset permutations.     

Burrows–Wheeler compression with variable length integer codes

The final coder in Burrows–Wheeler compression is usually either an adaptive Huffman coder (for speed) or a complex of arithmetic coders for better compression. This article describes the use of conventional pre‐defined variable length codes or universal codes and shows that they too can give excellent compression. The paper also describes a ‘sticky Move‐to‐Front’ modification which gives a useful improvement in compression for most files. Copyright © 2002 John Wiley & Sons, Ltd.     

Improvements to Burrows–Wheeler compression algorithm

In 1994 Burrows and Wheeler presented a new algorithm for lossless data compression. The compression ratio that can be achieved using their algorithm is comparable with the best known other algorithms, whilst its complexity is relatively small. In this paper we explain the internals of this algorithm and discuss its various modifications that have been presented so far. Then we propose new improvements for its effectiveness. They allow us to obtain a compression ratio equal to 2.271 bpc for the Calgary Corpus files, which is the best result in the class of Burrows–Wheeler transform based algorithms. Copyright © 2000 John Wiley & Sons, Ltd.     

Developing a Dynamic Cluster Quantization based Lossless Audio Compression (DCQLAC)

In this paper, an approach has been made to produce a compressed audio without losing any information. The proposed scheme is fabricated with the help of dynamic cluster quantization followed by Burrows Wheeler Transform (BWT) and Huffman coding. The encoding algorithm has been designed in two phases, i.e., dynamic cluster selection (of sampled audio) followed by dynamic bit selection for determining quantization level of individual cluster. Quantization level of each cluster is selected dynamically based on mean square quantization error (MSQE). Bit stream is further compressed by applying Burrows Wheeler Transform (BWT) and Huffman code respectively. Experimental results are supported with current state-of-the-art in audio quality analysis (like statistical parameters (compression ratio, space savings, SNR, PSNR) along with other parameters (encoding time, decoding time, Mean Opinion Score (MOS) and entropy) and compared with other existing techniques.

     

A simpler analysis of Burrows–Wheeler-based compression

In this paper, we present a new technique for worst-case analysis of compression algorithms which are based on the Burrows–Wheeler Transform. We mainly deal with the algorithm proposed by Burrows and Wheeler in their first paper on the subject [M. Burrows, D.J. Wheeler, A block sorting lossless data compression algorithm, Technical Report 124, Digital Equipment Corporation, Palo Alto, California, 1994], called bw0. This algorithm consists of the following three essential steps: (1) Obtain the Burrows–Wheeler Transform of the text, (2) Convert the transform into a sequence of integers using the move-to-front algorithm, (3) Encode the integers using Arithmetic code or any order-0 encoding (possibly with run-length encoding).     

Lossless image compression: application of Bi-level Burrows Wheeler Compression Algorithm (BBWCA) to 2-D data

This research paper demonstrates the robustness of Bi-level Burrows Wheeler Compression Algorithm (BBWCA) in terms of the compression efficiency for different types of image data. The scheme was designed to take advantage of the increased inter-pixel redundancies resulting from a two pass Burrows Wheeler Transformation (BWT) stage and the use of Reversible Colour Transform (RCT). In this research work, BBWCA was evaluated for raster map images, Colour Filter Array (CFA) images as well as 2-D ElectroEncephaloGraphy (EEG) data and compared against benchmark schemes. Validation has been carried out on various examples and they show that BBWCA is capable of compressing 2-D data effectively. The proposed method achieves marked improvement over the existing methods in terms of compression size. BBWCA is 18.8 % better at compressing images as compared to High Efficiency Video Codec (HEVC) and 21.2 % more effective than LZ4X compressor for CFA images. For the EEG data, BBWCA is 17 % better at compressing images as compared to WINRK and 25.2 % more effective than NANOZIP compressor. However, for the Raster images PAQ8 supersedes BBWCA by 11 %. Among the different schemes compared, the proposed scheme achieves overall best performance and is well suited to small and large size image data compression. The parallelization process reduces the execution time particularly for large size images. The parallelized BBWCA scheme reduces the execution time by 31.92 % on average as compared to the non-parallelized BBWCA.     

From first principles to the Burrows and Wheeler transform and beyond,via combinatorial optimization

We introduce a combinatorial optimization framework that naturally induces a class of optimal word permutations with respect to a suitably defined cost function taking into account various measures of relatedness between words. The Burrows and Wheeler transform (bwt) (cf. [M. Burrows, D. Wheeler, A block sorting lossless data compression algorithm, Technical Report 124, Digital Equipment Corporation, 1994]), and its analog for labelled trees (cf. [P. Ferragina, F. Luccio, G. Manzini, S. Muthukrishnan, Structuring labeled trees for optimal succinctness, and beyond, in: Proc. of the 45th Annual IEEE Symposium on Foundations of Computer Science, 2005, pp. 198–207]), are special cases in the class. We also show that the class of optimal word permutations defined here is identical to the one identified by Ferragina et al. for compression boosting [P. Ferragina, R. Giancarlo, G. Manzini, M. Sciortino, Boosting textual compression in optimal linear time, Journal of the ACM 52 (2005) 688–713]. Therefore, they are all highly compressible. We also provide, by using techniques from Combinatorics on Words, a fast method to compute bwt without using any end-of-string symbol. We also investigate more general classes of optimal word permutations, where relatedness of symbols may be measured by functions more complex than context length. For this general problem we provide an instance that is MAX-SNP hard, and therefore unlikely to be solved or approximated efficiently. The results presented here indicate that a key feature of the Burrows and Wheeler transform seems to be, besides compressibility, the existence of efficient algorithms for its computation and inversion.     

一种基于LFU置换的BWT压缩算法的改进

BWT算法是目前广泛关注的一种基于块压缩的无损压缩算法。由BWT变换,MTF变换和熵编码三部分组成。本文对其做了具体介绍和分析并在此基础上提出了一种基于LFU缓冲区置换策略的MTF变换的改进方法,实验结果表明改进后的算法使压缩比有所提高。     

Revisiting bounded context block‐sorting transformations

The Burrows–Wheeler Transform (BWT ) produces a permutation of a string X, denoted X^?, by sorting the n cyclic rotations of X into full lexicographical order and taking the last column of the resulting n×n matrix to be X^?. The transformation is reversible in time. In this paper, we consider an alteration to the process, called k‐BWT , where rotations are only sorted to a depth k. We propose new approaches to the forward and reverse transform, and show that the methods are efficient in practice. More than a decade ago, two algorithms were independently discovered for reversing k‐BWT , both of which run in time. Two recent algorithms have lowered the bounds for the reverse transformation to and, respectively. We examine the practical performance for these reversal algorithms. We find that the original approach is most efficient in practice, and investigates new approaches, aimed at further speeding reversal, which store precomputed context boundaries in the compressed file. By explicitly encoding the context boundaries, we present an reversal technique that is both efficient and effective. Finally, our study elucidates an inherently cache‐friendly – and hitherto unobserved – behavior in the reverse k‐BWT , which could lead to new applications of the k‐BWT transform. In contrast to previous empirical studies, we show that the partial transform can be reversed significantly faster than the full transform, without significantly affecting compression effectiveness. Copyright © 2011 John Wiley & Sons, Ltd.     

Context-based embedded image compression using binary wavelet transform

Binary wavelet transform (BWT) has several distinct advantages over the real wavelet transform (RWT), such as the conservation of alphabet size of wavelet coefficients, no quantization introduced during the transform and the simple Boolean operations involved. Thus, less coding passes are engaged and no sign bits are required in the compression of transformed coefficients. However, the use of BWT for the embedded grayscale image compression is not well established. This paper proposes a novel Context-based Binary Wavelet Transform Coding approach (CBWTC) that combines the BWT with a high-order context-based arithmetic coding scheme to embedded compression of grayscale images. In our CBWTC algorithm, BWT is applied to decorrelate the linear correlations among image coefficients without expansion of the alphabet size of symbols. In order to match up with the CBWTC algorithm, we employ the gray code representation (GCR) to remove the statistical dependencies among bi-level bitplane images and develop a combined arithmetic coding scheme. In the proposed combined arithmetic coding scheme, three highpass BWT coefficients at the same location are combined to form an octave symbol and then encoded with a ternary arithmetic coder. In this way, the compression performance of our CBWTC algorithm is improved in that it not only alleviate the degradation of predictability caused by the BWT, but also eliminate the correlation of BWT coefficients in the same level subbands. The conditional context of the CBWTC is properly modeled by exploiting the characteristics of the BWT as well as taking advantages of non-causal adaptive context modeling. Experimental results show that the average coding performance of the CBWTC is superior to that of the state-of-the-art grayscale image coders, and always outperforms the JBIG2 algorithm and other BWT-based binary coding technique for a set of test images with different characteristics and resolutions.     

On the combinatorics of suffix arrays

We present a bijective characterization of suffix array permutations obtained from a characterization of Burrows–Wheeler arrays given in [1]. We show that previous characterizations [2], [3], [4], or their analogs, can be obtained in a simple and elegant way using this relationship. To demonstrate the usefulness of our approach, we obtain simpler proofs for some known enumeration results about suffix arrays [3]. Our characterization of suffix arrays is the first based on their relationship with Burrows–Wheeler permutations.     

基于子带谱熵的仿生小波语音增强

前端噪声处理直接关系着语音识别的准确性和稳定性,针对小波去噪算法所分离出的信号不是原始信号的最佳估计,提出一种基于子带谱熵的仿生小波变换(BWT)去噪算法。充分利用子带谱熵端点检测的精确性,区分含噪语音部分和噪声部分,实时更新仿生小波变换中的阈值,精确地区分出噪声信号小波系数,达到语音增强目的。实验结果表明,提出的基于子带谱熵的仿生小波语音增强方法与维纳滤波方法相比,信噪比(SNR)平均提高约8%,所提方法对噪声环境下语音信号有显著的增强效果。     

Compression of small text files

This paper suggests a novel compression scheme for small text files. The proposed scheme depends on Boolean minimization of binary data accompanied with the adoption of Burrows-Wheeler transformation (BWT) algorithm. Compression of small text files must fulfil special requirements since they have small context. The use of Boolean minimization and Burrows-Wheeler transformation generate better context information for compression with standard algorithms. We tested the suggested scheme on collections of small and medium-sized files. The testing results showed that proposed scheme improve the compression ratio over other existing methods.     

An optimal high capacity reversible data hiding scheme using move to front coding for LZW codes

Reversible Data hiding techniques reduce transmission cost as secret data is embedded into a cover image without increasing its size in such a way that at the receiving end, both secret data and the cover image can be extracted and recovered, respectively, to their original form. To further reduce the transmission cost, the secret data can be embedded in the compression codes by some popular reversible data hiding schemes. One of the popular and important reversible data hiding method is high- performance data-hiding Lempel–Ziv–Welch (HPDH-LZW) scheme which hides the secret data in LZW codes. In this paper, the HPDH-LZW scheme is modified in order to increase its hiding capacity and compression ratio. First, the proposed work modifies the Move to Front (MTF) encoding technique to hide the secret data and also to increase the similarity among the element of the cover media. Then, LZW encoding technique is applied on the resultant cover data to obtain LZW codes, which are used to hide further secret data. Experimental results show that the proposed scheme has significantly increased the data hiding capacity and have good embedding and extraction speed in comparison to other state of the art schemes.

     

Context exhumation after the Burrows-Wheeler transform

The essence of compression algorithms based on the Burrows-Wheeler transform is their first stage. In this stage, the information about the symbol contexts in the original sequence is lost and cannot be used in the rest of the algorithm. We show how to obtain some knowledge of the symbol contexts after the BWT. Using this information makes the prediction of symbol occurrence in further stages more accurate, which is confirmed by experiments.     

Rank and select revisited and extended

The deep connection between the Burrows–Wheeler transform (BWT) and the so-called rank and select data structures for symbol sequences is the basis of most successful approaches to compressed text indexing. Rank of a symbol at a given position equals the number of times the symbol appears in the corresponding prefix of the sequence. Select is the inverse, retrieving the positions of the symbol occurrences. It has been shown that improvements to rank/select algorithms, in combination with the BWT, turn into improved compressed text indexes.     

交易数据库的加权关联规则增量更新算法

针对文献犤1犦提出的加权关联规则挖掘算法,文章提出了交易数据库的加权关联规则增量更新算法(DWARIUA算法)。该算法充分利用已存在的频繁项目集,因此,算法是有效而可行的。