Sparse Reconstruction via Gradient Restoration for Magnetic Resonance Images

Abstract

Sparse Reconstruction based on the theory of compressed sensing is one of hot topics in image processing, especially for the magnetic resonance image because of its inherent features of sparsity and compressibility. A novel reconstruction method via the gradient restoration for magnetic resonance images is proposed in this paper. The restoration of image gradient is firstly handled by the convex optimization. Then the resulting image gradient is used to convert the image reconstruction into the Poisson equation, which is solved by the matrix calculation using the discrete cosine transform. The experimental results show that the proposed method obtains better subjective effects as well as higher peak signal noise rate in terms of objective evaluation, which is compared to the method of nonlinear conjugate gradient for the 1 l -TV regularization.