Magnetic resonance image reconstruction by nullspace based finite rate of innovation framework

Abstract

The finite rate of innovation (FRI) framework has proved that it is possible to reconstruct the analog signals which have a finite number of parameters. FRI framework is used to reconstruct the images from undersampled magnetic resonance (MR) data. The reconstruction of the MR image from the MR data is a estimation problem, which can be solved by utilizing Prony's method. However, Prony's method involves solving the polynomial roots of the annihilating filter and this fact leads to an unstable reconstruction in the high noise scenario. In this paper, we introduce a novel reconstruction approach is also based on the annihilating filter. However, it involves the use of solutions of an underdetermined linear system. The simulation results of the proposed reconstruction approach show that the peak signal to noise ratio (PSNR) and the structural similarity index measure (SSIM) are higher magnitude than that of conventional FRI methods in the high noise scenario.1