Performance Evaluation of L1, L2 and SL0 on Compressive Sensing based on stochastic estimation technique

In this paper, we proposed 2 algorithms based on L1 and L2 norm estimator to recover the signal by using just few components. Moreover we comprehensively present the recovery algorithm based on L1, L2 and SL0 for digital signal or image under some several noise models from their incomplete observation. The proposed algorithm is used with a matrix that the number of row is much fewer than the column. The algorithm states that if signal or image is sufficient sparse, we can recover it from small number of linear measurement by solving convex program of observation vector. Base on the very important properties of the image which most of the signal information tends to be concentrated in few low frequency components of the DCT. Finally experiments results are presented on both synthesis and real image under various kind of noise (AWGN, Salt & Pepper Noise and Speckle Noise) with different noise power. The effects of different noise models will be compared in order to show the improvement of L1 norm over SL0 and L2 norm under heavy noise or some noise that doesn´t have Gaussian form.