Improving Image Quality and Convergence Rate of Perona–Malik Diffusion Based Compressed Sensing MR Image Reconstruction by Gradient Correction

Abstract

A memory-based reconstruction algorithm is developed for optimizing image quality and convergence rate of Compressed Sensing-Magnetic Resonance Image (CS-MRI) reconstruction using Perona–Malik (PM) diffusion. The PM diffusion works by estimating the underlying structure of an image and diffusing the image in a nonlinear fashion to preserve the sharpness of edge information. The edges due to undersampling artifacts are generally characterized as weak edges (false edges) identified by the comparatively smaller gradient magnitude associated with it. The convergence rate for CS-MRI reconstruction based on PM diffusion, therefore, depends on the extent by which the gradients attributed to false edges are diffused off per iteration. However, if the undersampling interference in high, gradient magnitudes of false edges can become comparable to that of true edges (boundaries of actual anatomical features). This might either lead to preservation of false edges or diffusion of true edges. This reduces the quality of reconstructed images. In such scenarios, we assume that the gradient information in past iterations contains useful structural information of the image which is lost while diffusing the image. Hence, we propose to overcome this problem by correcting the estimate of the underlying structure of the image using a combination of gradient information from a number of past iterations. This reduces the diffusion of weak edges by restoring the otherwise lost weak structural information at every iteration.