A novel frequency domain image reconstruction based on the Tikhonov regularization and robust estimation technique for Compressive Sensing

Recently, a lot of attention has been paid to image reconstructionalgorithms based on Smoothed L0 (SL0) under the frequency domain. SL0 is fast and accurate under the noise free environment however it is unstable with the additional noise.According to ill-posed condition; without any prior information of the original image, the reconstruction procedure of SL0 is much affected by the noise. The frequency domain Tikhonov reduces and constrains the gap of restored image due to the ill-posed situation. Therefore, image restoration algorithm is better and immutable under the noise which can eliminate the image´s properties. Moreover, in this paper we propose an l1 norm estimation, it is conceived less sensitivity to the outlier than an l2 norm. Thereforethe quality of reconstructed image under noise with high power is improved. Furthermore, the advancedrobust regularization algorithmcan be effectively applied under difference type of noise models (such as Speckle noise,AWGN, Salt & Pepper noise and Poisson noise) and at different noise powers.