Spatiotemporal denoising of MR spectroscopic imaging data by low-rank approximations

This paper addresses the denoising problem associated with magnetic resonance spectroscopic imaging (MRSI), where low signal-to-noise ratio (SNR) has been a critical problem. A new scheme is proposed, which exploits two low-rank structures that exist in MRSI data, one due to partial separability and the other is due to linear predictability. Experimental results from practical data demonstrate that the proposed method provides an effective way to denoise MRSI data while preserving spatial-spectral features in a wide range of SNR values.

1. INTRODUCTION

The acquired MRSI signal is conventionally modeled as

$${\mbi s}({\mbi k}, t)=\int \int\rho({\mbi r}, f)e^{-i2\pi {\mmb k}\cdot {\mmb r}}e^{-i2\pi ft}d{\mbi r}df+\xi({\mbi k}, t), \eqno{\hbox{(1)}}$$ where denotes the desired spatial-spectral function and represents the measurement noise often modeled as a complex white Gaussian process. The function contains valuable information on the spatial-spectral distribution of metabolites, and is useful for noninvasive metabolite imaging of living systems. For example, MRSI can be used to study glucose metabolism [1]; MRSI can map out the spatial distributions of N-Acetyl aspartate (NAA), creatine, choline, and lactate metabolites that are useful for the investigation of neurological disorders [2]. However, considerable practical challenges remain in obtaining in both high spatial-spectral resolution and high SNR. These difficulties are due to acquisition time limitations and low concentrations of metabolites (typically thousands-fold below that of tissue water [3]). This paper addresses the low SNR problem.