Graded quantization for multiple description coding of compressive measurements

Compressed sensing (CS) is an emerging paradigm for acquisition of compressed representations of a sparse signal. Its low complexity is appealing for resource-constrained scenarios like sensor networks. However, such scenarios are often coupled with unreliable communication channels and providing robust transmission of the acquired data to a receiver is an issue. Multiple description coding (MDC) effectively combats channel losses for systems without feedback, thus raising the interest in developing MDC methods explicitly designed for the CS framework, and exploiting its properties. We propose a method called Graded Quantization (CS-GQ) that leverages the democratic property of compressive measurements to effectively implement MDC, and we provide methods to optimize its performance. A novel decoding algorithm based on the alternating directions method of multipliers is derived to reconstruct signals from a limited number of received descriptions. Simulations are performed to assess the performance of CS-GQ against other methods in presence of packet losses. The proposed method is successful at providing robust coding of CS measurements and outperforms other schemes for the considered test metrics

Distributed Representation of Geometrically Correlated Images with Compressed Linear Measurements

This paper addresses the problem of distributed coding of images whose correlation is driven by the motion of objects or positioning of the vision sensors. It concentrates on the problem where images are encoded with compressed linear measurements. We propose a geometry-based correlation model in order to describe the common information in pairs of images. We assume that the constitutive components of natural images can be captured by visual features that undergo local transformations (e.g., translation) in different images. We first identify prominent visual features by computing a sparse approximation of a reference image with a dictionary of geometric basis functions. We then pose a regularized optimization problem to estimate the corresponding features in correlated images given by quantized linear measurements. The estimated features have to comply with the compressed information and to represent consistent transformation between images. The correlation model is given by the relative geometric transformations between corresponding features. We then propose an efficient joint decoding algorithm that estimates the compressed images such that they stay consistent with both the quantized measurements and the correlation model. Experimental results show that the proposed algorithm effectively estimates the correlation between images in multi-view datasets. In addition, the proposed algorithm provides effective decoding performance that compares advantageously to independent coding solutions as well as state-of-the-art distributed coding schemes based on disparity learning

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

Compressed Sensing based Low-Power Multi-View Video Coding and Transmission in Wireless Multi-Path Multi-Hop Networks

Wireless Multimedia Sensor Network (WMSN) is increasingly being deployed for surveillance, monitoring and Internet-of-Things (IoT) sensing applications where a set of cameras capture and compress local images and then transmit the data to a remote controller. Such captured local images may also be compressed in a multi-view fashion to reduce the redundancy among overlapping views. In this paper, we present a novel paradigm for compressed-sensing-enabled multi-view coding and streaming in WMSN. We first propose a new encoding and decoding architecture for multi-view video systems based on Compressed Sensing (CS) principles, composed of cooperative sparsity-aware block-level rate-adaptive encoders, feedback channels and independent decoders. The proposed architecture leverages the properties of CS to overcome many limitations of traditional encoding techniques, specifically massive storage requirements and high computational complexity. Then, we present a modeling framework that exploits the aforementioned coding architecture. The proposed mathematical problem minimizes the power consumption by jointly determining the encoding rate and multi-path rate allocation subject to distortion and energy constraints. Extensive performance evaluation results show that the proposed framework is able to transmit multi-view streams with guaranteed video quality at lower power consumption

Operational Rate-Distortion Performance of Single-source and Distributed Compressed Sensing

We consider correlated and distributed sources without cooperation at the encoder. For these sources, we derive the best achievable performance in the rate-distortion sense of any distributed compressed sensing scheme, under the constraint of high--rate quantization. Moreover, under this model we derive a closed--form expression of the rate gain achieved by taking into account the correlation of the sources at the receiver and a closed--form expression of the average performance of the oracle receiver for independent and joint reconstruction. Finally, we show experimentally that the exploitation of the correlation between the sources performs close to optimal and that the only penalty is due to the missing knowledge of the sparsity support as in (non distributed) compressed sensing. Even if the derivation is performed in the large system regime, where signal and system parameters tend to infinity, numerical results show that the equations match simulations for parameter values of practical interest.Comment: To appear in IEEE Transactions on Communication

Graded quantization for multiple description coding of compressive measurements

Compressed sensing (CS) is an emerging paradigm for acquisition of compressed representations of a sparse signal. Its low complexity is appealing for resource-constrained scenarios like sensor networks. However, such scenarios are often coupled with unreliable communication channels and providing robust transmission of the acquired data to a receiver is an issue. Multiple description coding (MDC) effectively combats channel losses for systems without feedback, thus raising the interest in developing MDC methods explicitly designed for the CS framework, and exploiting its properties. We propose a method called Graded Quantization (CS-GQ) that leverages the democratic property of compressive measurements to effectively implement MDC, and we provide methods to optimize its performance. A novel decoding algorithm based on the alternating directions method of multipliers is derived to reconstruct signals from a limited number of received descriptions. Simulations are performed to assess the performance of CS-GQ against other methods in presence of packet losses. The proposed method is successful at providing robust coding of CS measurements and outperforms other schemes for the considered test metrics

Detection and identification of sparse audio tampering using distributed source coding and compressive sensing techniques

In most practical applications, for the sake of information integrity not only it is useful to detect whether a multimedia content has been modified or not, but also to identify which kind of attack has been carried out. In the case of audio streams, for example, it may be useful to localize the tamper in the time and/or frequency domain. In this paper we devise a hash-based tampering detection and localization system exploiting compressive sensing principles. The multimedia content provider produces a small hash signature using a limited number of random projections of a time-frequency representation of the original audio stream. At the content user side, the hash signature is used to estimate the distortion between the original and the received stream and, provided that the tamper is sufficiently sparse or sparsifiable in some orthonormal basis expansion or redundant dictionary (e.g. DCT or wavelet), to identify the time-frequency portion of the stream that has been manipulated. In order to keep the hash length small, the algorithm exploits distributed source coding techniques