Doctorate thesis defense of Ines Elleuch

Doctorate thesis defense on November 29^th 2017 at 15H30 ,in Amphi I, Sup’Com .

Committee

Abstract

This thesis aims to develop novel sparsity-aware approaches and practical algorithms in the context of two signal processing applications, where minimizing the sensing requirements is crucial.

The first application is quantized compressed sensing, for which we propose two sparse reconstruction approaches, where distortion of the underdetermined linear measurements, introduced by the quantization step, is taken into account. The first approach is an extension to standard convex-optimization based and greedy based methods, where a two-component noise model is integrated to properly model the quantization and the saturation errors arising from scalar quantization. The second approach is based on the graduated-non-convexity methodology, invokes advanced optimization-techniques, requires a great care for effective algorithm implementation, and provides substantial performance gain.

The second application is concerned with spectrum sensing in cognitive radio networks. To decide whether a primary user occupies a frequency of interest, we capitalize on the inherent sparsity of the primary signal in different domains, which avoids the need for additional prior knowledge that could not be available, and relax the sensing requirement in terms of the number of observations. Moreover, we resort to the construction of multiple measurement vectors that share a joint sparsity pattern to improve the detection reliability. We propose a first approach that exploits the angular sparsity of the primary signal to estimate the energy received from different directions-of-arrival. The second approach capitalizes on the sparsity of the second-order cyclic features of the primary signal exhibiting a cyclostationary induced by its symbol period. It relies on a simple autocorrelation test based on the position of the most significant peak of the cyclic autocorrelation function computed via a standard greedy algorithm for sparse recovery. The results presented in the thesis demonstrate the performance gain of the proposed approaches with respect to state-of-the-art methods.

Keywords

Sparsity, Quantized Compressed Sensing, Graduated-Non-Convexity, Spectrum Sensing, Angular Sparsity, Cyclostationarity