A Robust Approach to Compressive Sensing by Shortest-Solution Decimation

Compressed sensing is an important problem in many fields of science and engineering, including computational physics. It reconstructs signals by finding sparse solutions to underdetermined linear equations. We propose a deterministic and non-parametric algorithm, shortest-solution guided decimation (SSD), to construct support of the sparse solution under the guidance of the dense least-squares solution of the recursively decimated linear equation. The most significant feature of SSD is its insensitivity to correlations in the sampling matrix. Using extensive numerical experiments, we show that SSD greatly outperforms L₁ -norm based methods, orthogonal least squares, orthogonal matching pursuit, and approximate message passing when the sampling matrix contains strong correlations. This nice property of correlation tolerance makes SSD a versatile and robust tool for different types of real-world signal acquisition tasks.