Denoising MR Spectroscopic Imaging Data With Low-Rank Approximations

This paper addresses the denoising problem associated with magnetic resonance spectroscopic imaging (MRSI), where 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 due to linear predictability. Denoising is performed by arranging the measured data in appropriate matrix forms (i.e., Casorati and Hankel) and applying low-rank approximations by singular value decomposition (SVD). The proposed method has been validated using simulated and experimental data, producing encouraging results. Specifically, the method can effectively denoise MRSI data in a wide range of SNR values while preserving spatial-spectral features. The method could prove useful for denoising MRSI data and other spatial-spectral and spatial-temporal imaging data as well.

I. Introduction

The acquired magnetic resonance spectroscopic (MRS) signal in -space can be expressed as

$$s({\bm k},t) = \int\!\!\!\!\int \rho ({\bm r},f) e^{-i 2 \pi {\bm k} \cdot {\bm r}} e^{-i 2 \pi ft} d {\bm r} df + \xi ({\bm k},t) \eqno{\hbox{(1)}}$$ where denotes the desired spatial-spectral function and is the measurement noise often modeled as a complex white Gaussian process. The function provides valuable information on the spatial-spectral distribution of metabolites, and is useful for noninvasive metabolite imaging of living systems. For example, ¹³C magnetic resonance spectroscopic imaging (MRSI) can be used to study glucose metabolism [1]; ³¹P MRSI is capable of detecting metabolites participating in tissue energy metabolism [1]; ¹H MRSI can map out the spatial distributions of N-Acetylaspartate (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 signal-to-noise ratio (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.