Tensor denoising of high-dimensional MRI data

TL;DR

This paper introduces tensor MPPCA (tMPPCA), a novel denoising method for high-dimensional MRI data that leverages tensor structures to improve noise removal, especially in small data patches with spatially varying noise.

Contribution

tMPPCA extends matrix-based MPPCA to multidimensional tensor data, enhancing denoising performance without additional assumptions, particularly for small patches and complex MRI datasets.

Findings

tMPPCA outperforms traditional MPPCA in numerical phantom tests.

tMPPCA significantly improves denoising in multi-contrast MRI data.

Method effectively handles small data patches with spatially varying noise.

Abstract

The signal to noise ratio (SNR) fundamentally limits the information accessible by magnetic resonance imaging (MRI). This limitation has been addressed by a host of denoising techniques, recently including so-called MPPCA: Principal component analysis (PCA) of the signal followed by automated rank estimation, exploiting the Marchenko-Pastur (MP) distribution of noise singular values. Operating on matrices comprised by data-patches, this popular approach objectively identifies noise components and, ideally, allows noise to be removed without introducing artifacts such as image blurring or non-local averaging. The MPPCA rank estimation, however, relies on a large number of noise singular values relative to the number of signal components to avoid such ill effects. This condition is unlikely to be met when data-patches and therefore matrices are small, for example due to spatially varying noise. Here, we introduce tensor MPPCA (tMPPCA) for the purpose of denoising multidimensional data, for example from multi-contrast acquisitions. Rather than combining dimensions in matrices, tMPPCA utilizes each dimension of the multidimensional data's inherent tensor-structure to better characterize noise, and to recursively estimate signal components. Relative to matrix-based MPPCA, tMPPCA requires no additional assumptions, and comparing the two in a numerical phantom and a multi-TE diffusion MRI dataset, tMPPCA dramatically improves denoising performance. This is particularly true for small data-patches, which we believe will improve denoising in cases of spatially varying noise.