Smoothing Modified Newton Algorithm Based on LpNorm Regularization for Signal Recovery

Although the compressed sensing model has a good effect on signal recovery, it is quite difficult to design reconstruction algorithms for compressive sensing. The challenge is that the sampling rate is low, the sparsity is high, which makes it difficult to recover the original signal. In this paper, a new Smoothing Modified Newton algorithm based on ℓ
_p
norm regularization (SMN-lp) is proposed to recover the original sparse signal, where p is 10
^-9
. Our algorithm is different from the modified Newton algorithm, for which the Hessian matrix of the objective function is modified. The strategy of synchronously updating smoothing parameter μ and regularizing parameter λ are also applied to the proposed SMN-lp algorithm. Comparison experiments with the state-of-the-art algorithms show that SMN-lp algorithm has good performance for signal recovery with high sparsity and low sampling rate interference. Meanwhile, it also shows that SMN-lp algorithm has high adaptability with the highest precision.