Compression-Based Compressed Sensing

Modern compression algorithms exploit complex structures that are present in signals to describe them very efficiently. On the other hand, the field of compressed sensing is built upon the observation that "structured" signals can be recovered from their under-determined set of linear projections. Currently, there is a large gap between the complexity of the structures studied in the area of compressed sensing and those employed by the state-of-the-art compression codes. Recent results in the literature on deterministic signals aim at bridging this gap through devising compressed sensing decoders that employ compression codes. This paper focuses on structured stochastic processes and studies the application of rate-distortion codes to compressed sensing of such signals. The performance of the formerly-proposed compressible signal pursuit (CSP) algorithm is studied in this stochastic setting. It is proved that in the very low distortion regime, as the blocklength grows to infinity, the CSP algorithm reliably and robustly recovers $n$ instances of a stationary process from random linear projections as long as their count is slightly more than $n$ times the rate-distortion dimension (RDD) of the source. It is also shown that under some regularity conditions, the RDD of a stationary process is equal to its information dimension (ID). This connection establishes the optimality of the CSP algorithm at least for memoryless stationary sources, for which the fundamental limits are known. Finally, it is shown that the CSP algorithm combined by a family of universal variable-length fixed-distortion compression codes yields a family of universal compressed sensing recovery algorithms

Feasibility and performances of compressed-sensing and sparse map-making with Herschel/PACS data

The Herschel Space Observatory of ESA was launched in May 2009 and is in operation since. From its distant orbit around L2 it needs to transmit a huge quantity of information through a very limited bandwidth. This is especially true for the PACS imaging camera which needs to compress its data far more than what can be achieved with lossless compression. This is currently solved by including lossy averaging and rounding steps on board. Recently, a new theory called compressed-sensing emerged from the statistics community. This theory makes use of the sparsity of natural (or astrophysical) images to optimize the acquisition scheme of the data needed to estimate those images. Thus, it can lead to high compression factors. A previous article by Bobin et al. (2008) showed how the new theory could be applied to simulated Herschel/PACS data to solve the compression requirement of the instrument. In this article, we show that compressed-sensing theory can indeed be successfully applied to actual Herschel/PACS data and give significant improvements over the standard pipeline. In order to fully use the redundancy present in the data, we perform full sky map estimation and decompression at the same time, which cannot be done in most other compression methods. We also demonstrate that the various artifacts affecting the data (pink noise, glitches, whose behavior is a priori not well compatible with compressed-sensing) can be handled as well in this new framework. Finally, we make a comparison between the methods from the compressed-sensing scheme and data acquired with the standard compression scheme. We discuss improvements that can be made on ground for the creation of sky maps from the data.Comment: 11 pages, 6 figures, 5 tables, peer-reviewed articl

Robust transmission techniques for block compressed sensing

[[abstract]]Compressed sensing is famous for its compression performances over existing schemes in this field. Conventional researches aim at reaching the larger compression ratio at the encoder, with acceptable quality of reconstructed images at the decoder. This implies the error-free transmission between the encoder and the decoder. Unlike existing researches which look for compression performances, we apply compressed sensing to digital images for robust transmission in this paper. For transmitting compressed sensing signals over lossy channels, error propagation would be expected, and the ways to apply some means of protection for compressed sensing signals would be much required for guaranteed quality of reconstructed images. We propose to transmit compressed sensing signals over multiple independent channels for robust transmission. By introducing the correlations between the compressed sensing signals from different channels, induced errors from the lossy channels can be effectively alleviated. Simulation results have presented the reconstructed image qualities, which depict the effectiveness for the protection of compressed sensing signals.[[notice]]補正完

Data Compression in Multi-Hop Large-Scale Wireless Sensor Networks

Data collection from a multi-hop large-scale outdoor WSN deployment for environmental monitoring is full of challenges due to the severe resource constraints on small battery-operated motes (e.g., bandwidth, memory, power, and computing capacity) and the highly dynamic wireless link conditions in an outdoor communication environment. We present a compressed sensing approach which can recover the sensing data at the sink with good accuracy when very few packets are collected, thus leading to a significant reduction of the network traffic and an extension of the WSN lifetime. Interplaying with the dynamic WSN routing topology, the proposed approach is efficient and simple to implement on the resource-constrained motes without motes storing of a part of random measurement matrix, as opposed to other existing compressed sensing based schemes. We provide a systematic method via machine learning to find a suitable representation basis, for the given WSN deployment and data field, which is both sparse and incoherent with the measurement matrix in the compressed sensing. We validate our approach and evaluate its performance using our real-world multi-hop WSN testbed deployment in situ in collecting the humidity and soil moisture data. The results show that our approach significantly outperforms three other compressed sensing based algorithms regarding the data recovery accuracy for the entire WSN observation field under drastically reduced communication costs. For some WSN scenarios, compressed sensing may not be applicable. Therefore we also design a generalized predictive coding framework for unified lossless and lossy data compression. In addition, we devise a novel algorithm for lossless compression to significantly improve data compression performance for variouSs data collections and applications in WSNs. Rigorous simulations show our proposed framework and compression algorithm outperform several recent popular compression algorithms for wireless sensor networks such as LEC, S-LZW and LTC using various real-world sensor data sets, demonstrating the merit of the proposed framework for unified temporal lossless and lossy data compression in WSNs