High-Resolution Spectroscopic Imaging with Statistical Reconstruction

INTRODUCTION MRSI has been recognized for a long time as a powerful tool for biochemical imaging. However, its practical utility is still rather limited due to poor spatial resolution, low signal-to-noise ratio, and long data acquisition times. To address the sensitivity limitations of MRSI, several constrained reconstruction approaches have been proposed [1-5]. The constraints used by these approaches are derived from coregistered high-resolution anatomical datasets, and include boundary locations and regions of support. Previous approaches all have the same goal, which is to elicit highresolution information from limited data with high SNR through the use of these anatomical constraints. The proposed method addresses the limitations of Fourier reconstruction from a completely new angle. We advocate the collection of higher k-space information at the expense of correspondingly lower SNR. From this noisy high-resolution data, we use anatomical constraints to reduce the noise contamination, while preserving the high-resolution anatomical structure. THEORY The MRSI imaging equation can be modeled in vector form as d=Fρ+η, where d is the data, ρ is the desired spatial-spectral function, η is noise samples, and F is the encoding matrix. The optimal solution for ρ using a penalized maximum-likelihood (PML) functional [6] is given by