Application of low‐rank approximation using truncated singular value decomposition for noise reduction in hyperpolarized ¹³C NMR spectroscopy

Abstract

Dissolution dynamic nuclear polarization allows in vivo studies of metabolic flux using 13 C-hyperpolarized tracers by enhancing signal intensity by up to four orders of magnitude. The T 1 for in vivo applications is typically in the range of 10-50 s for the different 13 C-enriched metabolic substrates; the exponential loss of polarization due to various relaxation mechanisms leads to a strong reduction of the signal-to-noise ratio (SNR). A common solution to the problem of low SNR is the accumulation/averaging of consecutive spectra. However, some limitations related to long delays between consecutive scans occur: in particular, following biochemical kinetics and estimate apparent enzymatic constants becomes time critical when measurement scans are repeated with the typical delay of about 3 T 1 . Here we propose a method to dramatically reduce the noise, and therefore also the acquisition times, by computing, via truncated singular value decomposition, a low-rank approximation to the individual complex time-domain signals. Moreover, this approach has the additional advantage that the phase correction can be applied to the spectra already denoised, thus greatly reducing phase correction errors. We have tested the method on (1) simulated data;(2) performing dissolution of hyperpolarized 1-13 C-pyruvate in standard conditions and (3) in vivo data sets, using a porcine model injected with hyperpolarized Na-1-13 C-acetate. It was shown that the presented method reduces the noise level in all the experimental data sets, allowing the retrieval of signals from highly noisy data without any prior phase correction pre-processing. The effects of the proposed approach on the quantification of metabolic kinetics parameters have to be shown by full quantification studies.

In vivo phosphorus magnetic resonance spectroscopic imaging of the whole human liver at 7 T using a phosphorus whole‐body transmit coil and 16‐channel receive array: Repeatability and effects of principal component analysis‐based denoising

“…One commonly used class of denoising methods consists of low-rank denoising methods such as principal component analysis (PCA)-based denoising, with applications in, for example, diffusion imaging 25 and functional MRI, 26 as well as MRS and MRSI. 24,[27][28][29] A requirement for PCA-based denoising is that data can be transformed to a large signal matrix, which has homogeneous noise and high similarity of information, as expected for 3D MRSI of large organs such as the liver. It has been shown that PCAbased denoising yields an approximate SNR gain of 5 when applied to simulated 31 P MRSI data and an SNR gain of 3 for in vivo measured 31 P MRSI data of the upper legs.…”

Uncertainty in denoising of MRSI using low‐rank methods

“…High levels of apparent denoising are consistently achieved by denoising algorithms in MRS with additional encoding dimensions, 7 , 8 or MRSI. 1 , 9 , 10 However, it is not clear whether there is an overall reduction in uncertainty of final dynamic model parameters, 11 or metabolite concentrations (the typical output of MRSI).…”

Uncertainty in denoising of MRSI using low-rank methods

“…High levels of apparent denoising are consistently achieved by denoising algorithms in MRS with additional encoding dimensions (7,8), or MRSI (1,9,10). However, it is not clear whether there is an overall reduction in uncertainty of final dynamic model parameters (11), or metabolite concentrations (the typical output of MRSI).…”