A robust approach for optimization of the measurement matrix in Compressed Sensing

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Abstract
In this paper we address the problem of measurement matrix optimization in Compressed Sensing (CS) framework. Although the measurement matrix is generally selected randomly, some methods have been recently proposed to optimize it. It is shown that the optimized matrices can improve the quality of reconstruction and satisfy the required conditions for an efficient sampling. We propose a new optimization method with the aim of decreasing the “Mutual Coherence”. Defining a new cost function, we suggest to use a Gradient descent algorithm for this optimization problem. The advantages are less computational complexity, which makes the method suitable for large-scale problems, more robustness, and higher incoherence between the measurement matrix and sparsifying matrix (dictionary). By conducting several experiments, we obtained promising results which confirm a considerable improvement compared to those achieved by other methods.

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