Non-uniformly under-sampled multi-dimensional spectroscopic imaging in vivo: maximum entropy versus compressed sensing reconstruction.

The four-dimensional (4D) echo-planar correlated spectroscopic imaging (EP-COSI) sequence allows for the simultaneous acquisition of two spatial (ky, kx) and two spectral (t2, t1) dimensions in vivo in a single recording. However, its scan time is directly proportional to the number of increments in the ky and t1 dimensions, and a single scan can take 20–40 min using typical parameters, which is too long to be used for a routine clinical protocol. The present work describes efforts to accelerate EP-COSI data acquisition by application of non-uniform under-sampling (NUS) to the ky–t1 plane of simulated and in vivo EP-COSI datasets then reconstructing missing samples using maximum entropy (MaxEnt) and compressed sensing (CS). Both reconstruction problems were solved using the Cambridge algorithm, which offers many workflow improvements over other l1-norm solvers. Reconstructions of retrospectively under-sampled simulated data demonstrate that the MaxEnt and CS reconstructions successfully restore data fidelity at signal-to-noise ratios (SNRs) from 4 to 20 and 5× to 1.25× NUS. Retrospectively and prospectively 4× under-sampled 4D EP-COSI in vivo datasets show that both reconstruction methods successfully remove NUS artifacts; however, MaxEnt provides reconstructions equal to or better than CS. Our results show that NUS combined with iterative reconstruction can reduce 4D EP-COSI scan times by 75% to a clinically viable 5 min in vivo, with MaxEnt being the preferred method