The Novel Frequency Domain Tikhonov Regularization for an Image Reconstruction Based on Compressive Sensing with SL0 Algorithm

In this recent year, an image reconstruction based on small number of measured components is a useful application of Compressive Sensing (CS). In the field of CS, SL0 algorithm is known as one of the fastest and most accurate algorithm but this algorithm is very unreliable under the noisy environment. Unfortunately, there are no researches for solving this SL0 ill-posed condition therefore the SL0 algorithm can only apply on limited applications. To solve the SL0 ill-posed condition, this paper proposes a novel regularization technique for the image reconstruction algorithm based on the SL0 technique to estimate the reconstructed image in the frequency domain for CS implementations. The novel frequency domain Tikhonov regularization technique is cooperated in this SL0 algorithm for reducing and constraining the space of possible reconstructed image due to this ill-posed problem. By cooperating the proposed regularization technique, the solution of the image reconstruction algorithm has better performance and more stable under the noise which contaminates the properties of the image. The experimental result shows that the proposed Tikhonov regularization technique can be well effectively applied on noisy images such as Lena, Resolution_Chat and Cameraman under both Gaussian and Non-Gaussian noise models (such as AWGN, Poisson noise, Salt & Pepper noise and Speckle noise) at different noise powers.