# Assessment of reconstruction accuracy for under-sampled 31P-MRS data using compressed sensing and a low rank Hankel matrix completion approach

## TL;DR

This paper evaluates how undersampling patterns affect the accuracy of 31P-MRS data reconstruction using compressed sensing and low rank Hankel matrix completion.

## Contribution

The study introduces a novel evaluation of how specific sampling patterns influence reconstruction accuracy in 31P-MRS.

## Key findings

- Reconstruction accuracy is heavily influenced by the selection of specific samples rather than the undersampling factor.
- Noise levels in the signal have a more pronounced impact on reconstruction quality.
- Early sampling time density significantly correlates with reconstruction accuracy.

## Abstract

Phosphorus magnetic resonance spectroscopy and spectroscopic imaging (31P-MRS/MRSI) are techniques to evaluate energy metabolism in vivo, they are capable of measuring metabolites such as phosphocreatine and inorganic phosphate in muscle and brain tissue. Despite their capability, these techniques are not very often used in clinical settings due to the long acquisition times required. In recent years, compressed sensing has been widely used as an acceleration method for MRI signal acquisition and translated to MRS. In order to use it, one of the main criteria states that the aliasing resulting from the undersampling scheme must be incoherent, which is achieved using a pseudo-random sampling strategy. However, when a set of pseudo-random sampling patterns are applied for the same acceleration factor, there is significant variability in the quality of the reconstructed signal. We present an evaluation of the influence of the undersampling pattern in the quality of the signal reconstruction through a series of experiments in 31P-MRS data using the low rank Hankel matrix completion as the reconstruction method. Our results demonstrate that the reconstruction accuracy is heavily influenced by the selection of specific samples rather than the undersampling factor. Furthermore, the noise level in the signal has a more pronounced impact on reconstruction quality. Additionally, reconstruction accuracy is significantly correlated with the density of samples collected at early sampling times, making it possible to set large time values to zero without producing any statistical difference in the error distribution means for some cases.