A Reference-Free Lossless Compression Algorithm for DNA Sequences Using a Competitive Prediction of Two Classes of Weighted Models

The development of efficient data compressors for DNA sequences is crucial not only for reducing the storage and the bandwidth for transmission, but also for analysis purposes. In particular, the development of improved compression models directly influences the outcome of anthropological and biomedical compression-based methods. In this paper, we describe a new lossless compressor with improved compression capabilities for DNA sequences representing different domains and kingdoms. The reference-free method uses a competitive prediction model to estimate, for each symbol, the best class of models to be used before applying arithmetic encoding. There are two classes of models: weighted context models (including substitutional tolerant context models) and weighted stochastic repeat models. Both classes of models use specific sub-programs to handle inverted repeats efficiently. The results show that the proposed method attains a higher compression ratio than state-of-the-art approaches, on a balanced and diverse benchmark, using a competitive level of computational resources. An efficient implementation of the method is publicly available, under the GPLv3 license.Peer reviewe

A General Model for the Design of Efficient Sign-Coding Tools for Wavelet-Based Encoders

[EN] Traditionally, it has been assumed that the compression of the sign of wavelet coefficients is not worth the effort because they form a zero-mean process. However, several image encoders such as JPEG 2000 include sign-coding capabilities. In this paper, we analyze the convenience of including sign-coding techniques into wavelet-based image encoders and propose a methodology that allows the design of sign-prediction tools for whatever kind of wavelet-based encoder. The proposed methodology is based on the use of metaheuristic algorithms to find the best sign prediction with the most appropriate context distribution that maximizes the resulting sign-compression rate of a particular wavelet encoder. Following our proposal, we have designed and implemented a sign-coding module for the LTW wavelet encoder, to evaluate the benefits of the sign-coding tool provided by our proposed methodology. The experimental results show that sign compression can save up to 18.91% of bit-rate when enabling sign-coding capabilities. Also, we have observed two general behaviors when coding the sign of wavelet coefficients: (a) the best results are provided from moderate to high compression rates; and (b) the sign redundancy may be better exploited when working with high-textured images.This research was supported by the Spanish Ministry of Economy and Competitiveness under Grant RTI2018-098156-B-C54, co-financed by FEDER funds (MINECO/FEDER/UE).López-Granado, OM.; Martínez-Rach, MO.; Martí-Campoy, A.; Cruz-Chávez, MA.; Pérez Malumbres, M. (2020). A General Model for the Design of Efficient Sign-Coding Tools for Wavelet-Based Encoders. Electronics. 9(11):1-17. https://doi.org/10.3390/electronics9111899S117911Said, A., & Pearlman, W. A. (1996). A new, fast, and efficient image codec based on set partitioning in hierarchical trees. IEEE Transactions on Circuits and Systems for Video Technology, 6(3), 243-250. doi:10.1109/76.499834ISO/IEC 15444-1:2019. Information technology—JPEG 2000 Image Coding System—Part 1: Core Coding Systemhttps://www.iso.org/standard/78321.htmlTaubman, D. (2000). High performance scalable image compression with EBCOT. IEEE Transactions on Image Processing, 9(7), 1158-1170. doi:10.1109/83.847830Bilgin, A., Sementilli, P. J., & Marcellin, M. W. (1999). Progressive image coding using trellis coded quantization. IEEE Transactions on Image Processing, 8(11), 1638-1643. doi:10.1109/83.799891Oliver, J., & Malumbres, M. P. (2006). Low-Complexity Multiresolution Image Compression Using Wavelet Lower Trees. IEEE Transactions on Circuits and Systems for Video Technology, 16(11), 1437-1444. doi:10.1109/tcsvt.2006.883505Cho, Y., & Pearlman, W. A. (2007). Hierarchical Dynamic Range Coding of Wavelet Subbands for Fast and Efficient Image Decompression. IEEE Transactions on Image Processing, 16(8), 2005-2015. doi:10.1109/tip.2007.901247Deever, A. T., & Hemami, S. S. (2003). Efficient sign coding and estimation of zero-quantized coefficients in embedded wavelet image codecs. IEEE Transactions on Image Processing, 12(4), 420-430. doi:10.1109/tip.2003.811499Mallat, S., & Zhong, S. (1992). Characterization of signals from multiscale edges. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(7), 710-732. doi:10.1109/34.142909López-Granado, O., Galiano, V., Martí, A., Migallón, H., Martínez-Rach, M., Piñol, P., & Malumbres, M. P. (2013). Improving image compression through the use of evolutionary computing algorithms. Data Management and Security. doi:10.2495/data130041Kodak Lossless True Color Image Suitehttp://r0k.us/graphics/kodak/Rawzor—Lossless Compression Software for Camera Raw Imageshttp://imagecompression.info/test_images

Optimal LZ-End Parsing Is Hard

LZ-End is a variant of the well-known Lempel-Ziv parsing family such that each phrase of the parsing has a previous occurrence, with the additional constraint that the previous occurrence must end at the end of a previous phrase. LZ-End was initially proposed as a greedy parsing, where each phrase is determined greedily from left to right, as the longest factor that satisfies the above constraint [Kreft & Navarro, 2010]. In this work, we consider an optimal LZ-End parsing that has the minimum number of phrases in such parsings. We show that a decision version of computing the optimal LZ-End parsing is NP-complete by showing a reduction from the vertex cover problem. Moreover, we give a MAX-SAT formulation for the optimal LZ-End parsing adapting an approach for computing various NP-hard repetitiveness measures recently presented by [Bannai et al., 2022]. We also consider the approximation ratio of the size of greedy LZ-End parsing to the size of the optimal LZ-End parsing, and give a lower bound of the ratio which asymptotically approaches 2

Fixed Block Compression Boosting in FM-Indexes : Theory and Practice

The FM index (Ferragina and Manzini in J ACM 52(4):552-581, 2005) is a widely-used compressed data structure that stores a string T in a compressed form and also supports fast pattern matching queries. In this paper, we describe new FM-index variants that combine nice theoretical properties, simple implementation and improved practical performance. Our main theoretical result is a new technique called fixed block compression boosting, which is a simpler and faster alternative to optimal compression boosting and implicit compression boosting used in previous FM-indexes. We also describe several new techniques for implementing fixed-block boosting efficiently, including a new, fast, and space-efficient implementation of wavelet trees. Our extensive experiments show the new indexes to be consistently fast and small relative to the state-of-the-art, and thus they make a good off-the-shelf choice for many applications.Peer reviewe

Quantization and Compressive Sensing

Quantization is an essential step in digitizing signals, and, therefore, an indispensable component of any modern acquisition system. This book chapter explores the interaction of quantization and compressive sensing and examines practical quantization strategies for compressive acquisition systems. Specifically, we first provide a brief overview of quantization and examine fundamental performance bounds applicable to any quantization approach. Next, we consider several forms of scalar quantizers, namely uniform, non-uniform, and 1-bit. We provide performance bounds and fundamental analysis, as well as practical quantizer designs and reconstruction algorithms that account for quantization. Furthermore, we provide an overview of Sigma-Delta ($\Sigma\Delta$) quantization in the compressed sensing context, and also discuss implementation issues, recovery algorithms and performance bounds. As we demonstrate, proper accounting for quantization and careful quantizer design has significant impact in the performance of a compressive acquisition system.Comment: 35 pages, 20 figures, to appear in Springer book "Compressed Sensing and Its Applications", 201

Multiband and Lossless Compression of Hyperspectral Images

Hyperspectral images are widely used in several real-life applications. In this paper, we investigate on the compression of hyperspectral images by considering different aspects, including the optimization of the computational complexity in order to allow implementations on limited hardware (i.e., hyperspectral sensors, etc.). We present an approach that relies on a three-dimensional predictive structure. Our predictive structure, 3D-MBLP, uses one or more previous bands as references to exploit the redundancies among the third dimension. The achieved results are comparable, and often better, with respect to the other state-of-art lossless compression techniques for hyperspectral images