Adaptive measurement matrix design oriented toward low signal-to-noise ratio scene

As an alternative paradigm to the Shannon-Nyquist sampling theorem, compressive sensing (CS) enables sparse signal to be acquired by sub-Nyquist analog-to-digital converters (ADC). The open literature on CS has focused almost entirely on settings with noiseless or low signal noise environment, which is contrary to many practical applications. In this paper, the authors present an adaptive measurement matrix design scheme (AMMDS) oriented toward high signal noise levels. The impact of white Gaussian signal noise on recovery performance is analyzed, so as to provide the theoretical basis for the reasonable design of measurement matrix. The multiple measurement vectors (MMV) model based measurement matrix design scheme is proposed, which enables the measurement matrix update adaptively according to the noise level. Extended numerical experiments show that the proposed AMMDS improves the support recovery for sparse signals.