بازسازی سیگنال پراکنده از طریق برنامه ریزی خطی تکهای مستمر مقعر☆

Compressed sensing (CS) is a new paradigm for acquiring sparse and compressible signals which can be approximated using much less information than their nominal dimension would suggest. In order to recover a signal from its compressive measurements, the conventional CS theory seeks the sparsest signal that agrees with the measurements via a great many algorithms, which usually solve merely an approximation of the l0l0 norm minimization. In this paper, CS has been considered from a new perspective. We equivalently transform the l0l0 norm minimization into a concave continuous piecewise linear programming based on the prior knowledge of sparsity, and propose a novel global optimization algorithm for it based on a sophisticated detour strategy and the γ valid cut theory. Numerical experiments demonstrate that our algorithm improves the best known number of measurements in the literature, relaxes the restrictions of the sensing matrix to some extent, and performs robustly in the noisy scenarios.