Using graph signal processing in model-based compressive sensing of MRI brain image

MRI acquisition time is often long, and subjecting patients to multiple breath holds usually becomes unfeasible. Compressive Sensing (CS) is a new paradigm that allows lower sampling rate as well as shorter acquisition time. In this paper, a graph-based signal model is introduced for CS-MRI brain images, which provides more precise information about these types of images and thus improves the recovery process. This model is constructed from the general template of brain MRI image and captures interdependencies between signal elements through a graph model. We limit the CS MRI image recovery search space by using graph-based parameters. In addition to image template, node value sparsity and graph total variation are incorporated in our investigation to build a convex optimization problem. This problem is formulated by a system of Lagrange equations that is solved by employing the ADMM method. The graph model parameters are used in recovery of the CS-MRI image in a system of Lagrange equations. Numerical simulation shows that the recovery can attain a higher quality at considerably fewer sampling rate.