An approach of regularization parameter estimation for sparse signal recovery

In this paper, we focus on how to obtain a proper regularization parameter that should be properly selected for a reasonable compromise between finding a sparse solution and restricting the recovery error. An enlarged the square of the Frobenius norm of noise can be employed to select a proper regularization parameter. In this methodology, we exploit the inverse of noise cumulative distribution function (CDF) to achieve this ideal. The simulations demonstrate that the proposed method of selecting the regularization parameter has a large dynamic range and therefore can effectively suppress spurious peaks.