A Fast Sparse Recovery Algorithm for Compressed Sensing Using Approximate l(0) Norm and Modified Newton Method

In this paper, we propose a fast sparse recovery algorithm based on the approximate l(0) norm (FAL0), which is helpful in improving the practicability of the compressed sensing theory. We adopt a simple function that is continuous and differentiable to approximate the l(0) norm. With the aim of minimizing the l(0) norm, we derive a sparse recovery algorithm using the modified Newton method. In addition, we neglect the zero elements in the process of computing, which greatly reduces the amount of computation. In a computer simulation experiment, we test the image denoising and signal recovery performance of the different sparse recovery algorithms. The results show that the convergence rate of this method is faster, and it achieves nearly the same accuracy as other algorithms, improving the signal recovery efficiency under the same conditions.