Compressive Sensing Based Image Compression and Transmission for Noisy Channels

This paper presents the design of an optimized Compressive Sensing image compression technique for data transmission over noisy mobile wireless channel. The proposed technique is more robust to channel noise. It uses individual measurement driven coding scheme, which facilitates simpler encoder design. The shift of computational burden from encoder to decoder is more suitable for mobile devices applications where computational power and battery life are limited. This paper also presents a novel quantizer which allows the encoder to dynamically adapt to the channel conditions and provides optimum performance

Channel-Optimized Vector Quantizer Design for Compressed Sensing Measurements

We consider vector-quantized (VQ) transmission of compressed sensing (CS) measurements over noisy channels. Adopting mean-square error (MSE) criterion to measure the distortion between a sparse vector and its reconstruction, we derive channel-optimized quantization principles for encoding CS measurement vector and reconstructing sparse source vector. The resulting necessary optimal conditions are used to develop an algorithm for training channel-optimized vector quantization (COVQ) of CS measurements by taking the end-to-end distortion measure into account.Comment: Published in ICASSP 201

Distributed Quantization for Compressed Sensing

We study distributed coding of compressed sensing (CS) measurements using vector quantizer (VQ). We develop a distributed framework for realizing optimized quantizer that enables encoding CS measurements of correlated sparse sources followed by joint decoding at a fusion center. The optimality of VQ encoder-decoder pairs is addressed by minimizing the sum of mean-square errors between the sparse sources and their reconstruction vectors at the fusion center. We derive a lower-bound on the end-to-end performance of the studied distributed system, and propose a practical encoder-decoder design through an iterative algorithm.Comment: 5 Pages, Accepted for presentation in ICASSP 201

Nonasymptotic noisy lossy source coding

This paper shows new general nonasymptotic achievability and converse bounds and performs their dispersion analysis for the lossy compression problem in which the compressor observes the source through a noisy channel. While this problem is asymptotically equivalent to a noiseless lossy source coding problem with a modified distortion function, nonasymptotically there is a noticeable gap in how fast their minimum achievable coding rates approach the common rate-distortion function, as evidenced both by the refined asymptotic analysis (dispersion) and the numerical results. The size of the gap between the dispersions of the noisy problem and the asymptotically equivalent noiseless problem depends on the stochastic variability of the channel through which the compressor observes the source.Comment: IEEE Transactions on Information Theory, 201

Optimized Compressed Sensing Matrix Design for Noisy Communication Channels

We investigate a power-constrained sensing matrix design problem for a compressed sensing framework. We adopt a mean square error (MSE) performance criterion for sparse source reconstruction in a system where the source-to-sensor channel and the sensor-to-decoder communication channel are noisy. Our proposed sensing matrix design procedure relies upon minimizing a lower-bound on the MSE. Under certain conditions, we derive closed-form solutions to the optimization problem. Through numerical experiments, by applying practical sparse reconstruction algorithms, we show the strength of the proposed scheme by comparing it with other relevant methods. We discuss the computational complexity of our design method, and develop an equivalent stochastic optimization method to the problem of interest that can be solved approximately with a significantly less computational burden. We illustrate that the low-complexity method still outperforms the popular competing methods.Comment: Submitted to IEEE ICC 2015 (EXTENDED VERSION

Power-Constrained Sparse Gaussian Linear Dimensionality Reduction over Noisy Channels

In this paper, we investigate power-constrained sensing matrix design in a sparse Gaussian linear dimensionality reduction framework. Our study is carried out in a single--terminal setup as well as in a multi--terminal setup consisting of orthogonal or coherent multiple access channels (MAC). We adopt the mean square error (MSE) performance criterion for sparse source reconstruction in a system where source-to-sensor channel(s) and sensor-to-decoder communication channel(s) are noisy. Our proposed sensing matrix design procedure relies upon minimizing a lower-bound on the MSE in single-- and multiple--terminal setups. We propose a three-stage sensing matrix optimization scheme that combines semi-definite relaxation (SDR) programming, a low-rank approximation problem and power-rescaling. Under certain conditions, we derive closed-form solutions to the proposed optimization procedure. Through numerical experiments, by applying practical sparse reconstruction algorithms, we show the superiority of the proposed scheme by comparing it with other relevant methods. This performance improvement is achieved at the price of higher computational complexity. Hence, in order to address the complexity burden, we present an equivalent stochastic optimization method to the problem of interest that can be solved approximately, while still providing a superior performance over the popular methods.Comment: Accepted for publication in IEEE Transactions on Signal Processing (16 pages

One-bit Distributed Sensing and Coding for Field Estimation in Sensor Networks

This paper formulates and studies a general distributed field reconstruction problem using a dense network of noisy one-bit randomized scalar quantizers in the presence of additive observation noise of unknown distribution. A constructive quantization, coding, and field reconstruction scheme is developed and an upper-bound to the associated mean squared error (MSE) at any point and any snapshot is derived in terms of the local spatio-temporal smoothness properties of the underlying field. It is shown that when the noise, sensor placement pattern, and the sensor schedule satisfy certain weak technical requirements, it is possible to drive the MSE to zero with increasing sensor density at points of field continuity while ensuring that the per-sensor bitrate and sensing-related network overhead rate simultaneously go to zero. The proposed scheme achieves the order-optimal MSE versus sensor density scaling behavior for the class of spatially constant spatio-temporal fields.Comment: Fixed typos, otherwise same as V2. 27 pages (in one column review format), 4 figures. Submitted to IEEE Transactions on Signal Processing. Current version is updated for journal submission: revised author list, modified formulation and framework. Previous version appeared in Proceedings of Allerton Conference On Communication, Control, and Computing 200