Combined First-and Second-Order Variational Model for Image Compressive Sensing

Ahybrid variationalmodel combined first-and second-order total variation for image reconstruction fromits finite number of noisy compressive samples is proposed in this paper. Inspired by majorization-minimization scheme, we develop an efficient algorithmto seek the optimal solution of the proposed model by successively minimizing a sequence of quadratic surrogate penalties. Both the nature andmagnetic resonance (MR) images are used to compare its numerical performance with four state-of-the-art algorithms. Experimental results demonstrate that the proposed algorithm obtained a significant improvement over related state-of-the-art algorithms in terms of the reconstruction relative error (RE) and peak signal to noise ratio (PSNR).