compressed sensing, continuous piecewise linear programming, interior point method
In order to recover a signal from its compressive measurements, the compressed sensing theory seeks the sparsest signal that agrees with the measurements, which is actually an l0 norm minimization problem. In this paper, we equivalently transform the l0 norm minimization into a concave continuous piecewise linear programming, and propose an optimization algorithm based on a modified interior point method. Numerical experiments demonstrate that our algorithm improves the sufficient number of measurements, relaxes the restrictions of the sensing matrix to some extent, and performs robustly in the noisy scenarios.
Tsinghua University Press
Kuangyu Liu, Xiangming Xi, Zhiming Xu et al. A Piecewise Linear Programming Algorithm for Sparse Signal Reconstruction. Tsinghua Science and Technology 2017, 22(1): 29-41.