On optimization of the measurement matrix for compressive sensing

In this paper the problem of Compressive Sensing (CS) is addressed. The focus is on estimating a proper measurement matrix for compressive sampling of signals. The fact that a small mutual coherence between the measurement matrix and the representing matrix is a requirement for achieving a successful CS is now well known. Therefore, designing measurement matrices with smaller coherence is desired. In this paper a gradient descent method is proposed to optimize the measurement matrix. The proposed algorithm is designed to minimize the mutual coherence which is described as absolute off-diagonal elements of the corresponding Gram matrix. The optimization is mainly applied to random Gaussian matrices which is common in CS. An extended approach is also presented for sparse signals with respect to redundant dictionaries. Our experiments yield promising results and show higher reconstruction quality of the proposed method compared to those of both unoptimized case and previous methods. © EURASIP, 2010