Compressed sensing effects on quantitative analysis of undersampled human brain sodium MRI

Abstract

Purpose: The clinical application of sodium MRI is hampered due to relatively low image quality and associated long acquisition times. Compressed sensing (CS) aims at a reduction of measurement time, but has been found to encompass quantitative estimation bias when used in low SNR x-Nuclei imaging. This work analyses CS in quantitative human brain sodium MRI from undersampled acquisitions and provides recommendations for tissue sodium concentration (TSC) estimation.

Methods: CS reconstructions from 3D radial acquisitions of 5 healthy volunteers were investigated over varying undersampling factors (USFs) and CS penalty weights on different sparsity domains, Wavelet, Discrete Cosine Transform (DCT), and Identity. Resulting images were compared with highly sampled and undersampled NUFFT-based images and evaluated for image quality (i.e. structural similarity), image intensity bias, and its effect on TSC estimates in gray and white matter.

Results: Wavelet-based CS reconstructions show highest image quality with stable TSC estimates for most USFs. Up to an USF of 4, images showed good structural detail. DCT and Identity-based CS enable good image quality, however show a bias in TSC with a reduction in estimates across USFs.

Conclusions: The image intensity bias is lowest in Wavelet-based reconstructions and enables an up to fourfold acquisition speed up while maintaining good structural detail. The associated acquisition time reduction can facilitate a translation of sodium MRI into clinical routine.

Keywords: compressed sensing; iterative reconstruction; quantitative imaging; sodium (${}^{23}$ Na) MRI; x-Nuclei.