<title>Reconstruction of MR spectroscopic images using finite elements and spatial domain priors</title>

Abstract

This paper describes a method for reconstructing images in magnetic resonance spectroscopic imaging (MRSI) using finite element methods and incorporating a priori information into the image reconstruction using a model. The reconstructed image is modeled as a projection of the desired metabolic intensity function onto a set of basis functions. For a general set of basis functions that span the reconstruction space, this problem is shown to result in a set of linear equations. For non- orthogonal basis functions, a singular value decomposition (SVD) technique can be used to obtain a least-squares estimate of the unknown coefficients. Polynomial basis functions with a large rectangular support region were tested and shown to lack the local control necessary to sufficiently resolve some important clinical features of interest (e.g., transmural myocardial infarction). Bilinear finite elements were selected for this problem because they are a basis set with very local support. Various sized finite elements were tested with simulated and phantom myocardium data similar to those that might be obtained from a gated phosphocreatine MRSI patient study. The conclusions of this investigation were: a) finite elements can give the desired local control to resolve clinically relevant lesions such as (simulated) transmural myocardial infarction, b) finite elements are robust in the presence of k-space additive Gaussian noise, and c)editing of the singular values was shown to be important to achieve optimum results. Remaining difficulties with the method include (a) O(N3) SVD computational complexity as the finite elements are made smaller, and (b) 'blockiness' in the reconstructed image due to the regular rectangular nature of elements.