Sensing Matrix Design via Capacity Maximization for Block Compressive Sensing Applications

It is well-established in the compressive sensing (CS) literature that sensing matrices whose elements are drawn from independent random distributions exhibit enhanced reconstruction capabilities. In many CS applications, such as electromagnetic imaging, practical limitations on the measurement system prevent one from generating sensing matrices in this fashion. Although one can usually randomize the measurements to some degree, these sensing matrices do not achieve the same reconstruction performance as the aforementioned truly random sensing matrices. This paper presents a novel method, based upon capacity maximization, for designing sensing matrices with enhanced block-sparse signal reconstruction capabilities. Additionally, several numerical examples are also included to show how the proposed method enhances reconstruction performance.