An Alternative Robust SL0 Based on Recursive Huber Stochastic Estimation Technique in Frequency Domain

In this paper, we propose a novel robust algorithm based on Huber norm estimation to recover the signal under several noise models by using only a few components. The proposed algorithm is used with a matrix that the number of row is obviously fewer than the column. It is stated that if the signal or the image is sufficiently sparse, we can recover it from a small number of linear measurements by solving a convex program of the measurement vector. For most of the image, the signal information tends to be concentrated in the low frequency components of the frequency domain. The performance of the proposed algorithm is compared with other classical algorithms such as L1 and SL0 norm estimations. Finally, the experimental results are presented on both synthesis and real image under various kinds of noises (AWGN, Salt & Pepper Noise and Speckle Noise) with different powers. The effects of different noise models are compared in order to show the improvement of Huber over SL0 Norm estimation.