Image reconstruction in low-field MRI: A super-resolution approach

Abstract

The quality of magnetic resonance images produced by conventional MRI scanners is guaranteed by the strength and homogeneity of the magnetic field. However, the superconducting magnets required to produce such a field make MRI scanners large and expensive and hence inaccessible to a large number of people in developing countries. Our partners are developing low-cost, portable MRI scanners that do not depend on superconducting magnets. In these scanners, the signal-to-noise ratio will be significantly lower due to the lower magnetic field strength. Additionally, inhomogeneities will be present, which means that the traditional way of obtaining the image, by inverse Fourier Transform, is no longer feasible. In this research, image reconstruction is done using an ill-posed system of equations of the form Ax = y, where A is the reconstruction matrix and x and y are vectors containing the image pixel values and the measured signals, respectively. Three different regularization techniques are considered, with total variation yielding the best results. Two methods for solving the regularized least-squares problem are considered: CGLS and CGNE. For the types of problems we are dealing with, CGNE is outperformed by CGLS: CGLS requires a lower number of iterations to converge and the computational cost per iteration is lower. The main focus of this research is on super-resolution: reconstructing a high resolution image from one or several low resolution images. Due to the low signal-to-noise ratios that are expected in the low-field MRI prototypes, it might be better to reconstruct images of a low resolution, and using these, create high resolution images, instead of opting for a direct high resolution reconstruction. In order to test this, the signal generation in a Halbach array based MRI scanner is simulated. Our simulations show that for very low (<1.5-2) signal-to-noise ratios, super-resolution can yield better results than direct high resolution reconstruction. Data obtained in a 7 T MRI scanner is used to validate our reconstruction model. Due to the type of gradient used and the low number of measurements in this experiment, the amount of available information is very limited. This makes it challenging to produce an image of good quality. However, in our final image, out of the four water bottles in the phantom, the three largest ones are clearly visible.Electrical Engineering, Mathematics and Computer ScienceDelft Institute of Applied Mathematic