Jonas Lynge Olesen^{1,2}, Andrada Ianus^{3}, Noam Shemesh^{3}, and Sune Nørhøj Jespersen^{1,2}

^{1}Center of Functionally Integrative Neuroscience (CFIN) and MINDLab, Aarhus University, Aarhus, Denmark, ^{2}Department of Physics and Astronomy, Aarhus University, Aarhus, Denmark, ^{3}Champalimaud Research, Champalimaud Centre for the Unknown, Lisbon, Portugal

A popular SNR-boosting method in MRI is denoising based on principal component analysis with automated rank estimation by exploiting the Marchenko-Pastur distribution of noise singular values (MP-PCA). MP-PCA operates by reshaping data-patches into matrices to discriminate signal from noise using random matrix theory. Here, we generalize MP-PCA to exploit tensor-structured data arising in, e.g., multi-contrast or multicoil acquisitions, without introducing new assumptions. As proof of concept, we demonstrate a substantial increase in denoising performance in a multi-TE DKI dataset, in particular for small sliding windows. This is beneficial especially in cases of rapidly varying contrast or spatially varying noise.

Information redundancy in MRI acquisitions (e.g. in directions in DTI or TE in T2 mapping) make typical MRI data well described by a low-rank approximation suitable for MP-PCA denoising. However, in many cases, multiple dimensions with redundancy exist, which opens opportunities for improved denoising. Here, we generalize matrix MP-PCA to tensor-structured data (tensor MP-PCA) and exploit the redundancy in multiple dimensions by applying MP rank-reduction to the higher-order singular value decomposition (HOSVD) recursively, without introducing new assumptions. Tensor MP-PCA performs as well or better than matrix MP-PCA in general, and we demonstrate substantial improvements in tensor-structure scenarios. Through objective rank estimation, recursivity, and shrinkage

For proof of concept, we employ a mouse brain dMRI dataset recorded at 16.4T using a microimaging probe with a multi-spin-echo sequence (FOV 10x8mm

Fig. 2 compares performance on multi-TE phantom data for various sliding window sizes. Tensor MP-PCA outperforms matrix MP-PCA for any window size, consistent with containing matrix PCA as a special case. Tensor MP-PCA reaches optimal performance at smaller patches, making it better suited for spatially varying noise or rapidly varying contrast. Additionally, the smaller patches reduces computation time.

Fig. 3 compares performance on single-TE phantom data. Comparing Fig. 2 and 3 it is apparent that the tensor-structure from multiple TEs benefits tensor MP-PCA substantially. This opens several perspectives on particularly favorable applications such as multicoil

The authors thank Martin Mikkelsen for support with the design and creation of illustrations.

SJ and JO are supported by the Danish National Research Foundation (CFIN), and the Danish Ministry of Science, Innovation, and Education (MINDLab). Additionally, JO are supported by the VELUX Foundation (ARCADIA, grant no. 00015963). NS was supported in part by the European Research Council (ERC) (agreement No. 679058). AI is supported by ”la Caixa” Foundation (ID 100010434) and European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 847648, fellowship code CF/BQ/PI20/11760029. The authors acknowledge the vivarium of the Champalimaud Centre for the Unknown, a facility of CONGENTO which is a research infrastructure co-financed by Lisboa Regional Operational Programme (Lisboa 2020), under the PORTUGAL 2020 Partnership Agreement through the European Regional Development Fund (ERDF) and Fundação para a Ciência e Tecnologia (Portugal), project LISBOA-01-0145-FEDER-022170.

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DOI: https://doi.org/10.58530/2022/2905