Application of compressive sampling to passive sonar signals

Recently the compressive sampling (CS) paradigm has generated considerable interest in the signal processing community because it offers the potential to fully characterize signals without satisfying the Nyquist requirement (sampling frequency must be more than twice the highest frequency in the signal). Signal compression itself is not new; it is used in all file compression algorithms. However, it generally requires that all coefficients be generated, many or most of which are discarded and only a few are transmitted. The theoretical basis for CS has been presented in a number of signal processing and statistics journal articles [e.g., Candès and Wakin, IEEE SP (March 2008)]. CS is fixed (non-adaptive) and is efficient in that only the coefficients required for signal characterization are calculated. The key requirement of CS is to find a basis in which the signal representation is sparse and thus can be represented with a minimum number of coefficients. Here we explore possible benefits of applying CS to sonar signals, including signal compression, bandwidth reduction, and exploitation of sparse sampling geometries. [Work sponsored by ONR Undersea Signal Processing.]