Sparse MRI reconstruction via different norms based on total variation

In a wide variety of imaging applications (especially medical imaging), the theory of compressed sensing has shown it is surprisingly possible to reconstruct the entire original image from a partial set or subset of the Fourier transform of an image, if the image has a sparse or nearly sparse representation in some transform domain. Recently many fast and efficient algorithms have been proposed by solving a convex lscr₁-minimization problem, which is often used as a scheme of the image recovery. In our work, we will introduce other methods in which the lscr₁ norm is replaced by the lscr_p norm for p isin (0,1) and the log-sum penalty function, and then perform numerical experiments to compare their performance.