Compressed Sensing by Shortest-Solution Guided Decimation

Compressed sensing is an important problem in many fields of science and engineering. It reconstructs signals by finding sparse solutions to underdetermined linear equations. In this work we propose a deterministic and non-parametric algorithm SSD (Shortest-Solution guided Decimation) 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.