Discrete Shearlets as a Sparsifying Transform in Low-Rank Plus Sparse Decomposition for Undersampled (k, t)-Space MR Data.

Nicholas E Protonotarios,George A Kastis,Nikolaos Dikaios,Evangelia Tzampazidou

doi:10.3390/jimaging8020029

Nicholas E Protonotarios, George A Kastis + Show 2 more

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https://doi.org/10.3390/jimaging8020029

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Abstract

The discrete shearlet transformation accurately represents the discontinuities and edges occurring in magnetic resonance imaging, providing an excellent option of a sparsifying transform. In the present paper, we examine the use of discrete shearlets over other sparsifying transforms in a low-rank plus sparse decomposition problem, denoted by . The proposed algorithm is evaluated on simulated dynamic contrast enhanced (DCE) and small bowel data. For the small bowel, eight subjects were scanned; the sequence was run first on breath-holding and subsequently on free-breathing, without changing the anatomical position of the subject. The reconstruction performance of the proposed algorithm was evaluated against k-t FOCUSS. decomposition, using discrete shearlets as sparsifying transforms, successfully separated the low-rank (background and periodic motion) from the sparse component (enhancement or bowel motility) for both DCE and small bowel data. Motion estimated from low-rank of DCE data is closer to ground truth deformations than motion estimated from L and S. Motility metrics derived from the S component of free-breathing data were not significantly different from the ones from breath-holding data up to four-fold undersampling, indicating that bowel (rapid/random) motility is isolated in S. Our work strongly supports the use of discrete shearlets as a sparsifying transform in a decomposition for undersampled MR data.

Highlights

Robust principal component analysis (RPCA) techniques [1,2] have been proposed to decompose dynamic MR images to a low-rank and a sparse component
Previous studies involving RPCArelated medical imaging analysis were performed in order to isolate (i) noise from the signal [6], (ii) enhancement in dynamic contrast enhanced (DCE) imaging from the background respiratory motion [4,5,8], and (iii) bowel motility from respiratory motion [9]
RPCA is well-poised for small bowel data, since breathing is periodic and bowel motility is comparatively unperiodic, and the estimated bowel motility from the sparse component, isolated from respiratory motion, has the potential to serve as a useful biomarker in a range of gastrointestinal disorders [8]

Summary

Introduction

Robust principal component analysis (RPCA) techniques [1,2] have been proposed to decompose dynamic MR images to a low-rank and a sparse component. The low-rank should ideally contain the background and periodic motion, whereas the sparse component should include rapid intensity changes including noise, signal enhancement, non-periodic deformations, etc. Previous studies involving RPCArelated medical imaging analysis were performed in order to isolate (i) noise from the signal [6], (ii) enhancement in DCE imaging from the background respiratory motion [4,5,8], and (iii) bowel motility from respiratory motion [9]. A potential benefit in DCE image registration involves the fact that motion will be estimated from the low-rank, where intensity changes due to enhancement are not present, leading to more accurate image registration [8]. Volumetric acquisitions may prove helpful for the improvement of physiological coherence [14]

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