In this paper, we consider a general form of noisy compressive sensing (CS) where the sensing matrix is not precisely known. Such cases exist when there are imperfections or unknown calibration parameters during the measurement process. Particularly, the sensing matrix may have some structure, which makes the perturbation follow a fixed pattern. While previous work has focused on extending the approximate message passing (AMP) and LASSO algorithm to deal with the independent and identically distributed (i.i.d.) perturbation, we propose the robust variant vector approximate message passing (VAMP) algorithm with the perturbation being structured, based on the recent VAMP algorithm. The performance of the robust version of VAMP is demonstrated numerically.
A recently paper considers the signal recovery from compressive sensing using the vector approximate message passing (VAMP) algorithm when the perturbation of the measurement matrix is more structured REF .
Vector Approximate Message Passing Algorithm for Structured Perturbed Sensing Matrix
arXiv: Signal Processing
Computer Science Engineering