Optshrink LR + S: accelerated fMRI reconstruction using non-convex optimal singular value shrinkage

Abstract

This paper presents a new accelerated fMRI reconstruction method, namely, OptShrink LR + S method that reconstructs undersampled fMRI data using a linear combination of low-rank and sparse components. The low-rank component has been estimated using non-convex optimal singular value shrinkage algorithm, while the sparse component has been estimated using convex l ¹ minimization. The performance of the proposed method is compared with the existing state-of-the-art algorithms on real fMRI dataset. The proposed OptShrink LR + S method yields good qualitative and quantitative results.

Keywords: Accelerated functional MRI; Compressed sensing; Low-rank recovery; Sparse recovery; Undersampling; k–t acceleration.

Fig. 1

Radial sampling pattern on one slice: a 6 radial lines (12.856 acceleration factor); b 12 radial lines (6.065 acceleration factor); c 24 radial lines (3.495 acceleration factor)

Fig. 2

Objective function value versus number of iterations

Fig. 3

Task-based fMRI data–original and reconstructed slice no. 18 [left to right Original; LR + S; Optshrink LR + S (rank = 1); Optshrink LR + S (rank = 2); Optshrink LR + S (rank = 3)]: a 6 radial lines (time point 100); b 12 radial lines (time point 100); c 24 radial lines (time point 100)

Fig. 4

Resting-state fMRI data—original and reconstructed slice no. 24 [left to right Original; LR + S; Optshrink LR + S (rank = 1); Optshrink LR + S (rank = 2); Optshrink LR + S (rank = 3)]: a 6 radial lines (time point 100); b 12 radial lines (time point 100); c 24 radial lines (time point 100)

Fig. 5

Normalized mean square error versus time points on task-based fMRI dataset (slice no. 18): a 6 radial lines (12.856 acceleration factor); b 12 radial lines (6.065 acceleration factor); c 24 radial lines (3.495 acceleration factor)

Fig. 6

Normalized mean square error versus time points on resting-state fMRI dataset (slice no. 24): a 6 radial lines (12.856 acceleration factor); b 12 radial lines (6.065 acceleration factor); c 24 radial lines (3.495 acceleration factor)

Fig. 7

Task-based fMRI dataset, slice no. 18, time point 100: NMSE versus rank of the proposed Optshrink LR + S method using 6 radial lines

Fig. 8

Resting-state fMRI dataset—slice no. 24, time point 100: NMSE versus rank of the proposed Optshrink LR + S method using 6 radial lines

Fig. 9

Task-based fMRI dataset—slice no. 18: NMSE versus subject number with the proposed Optshrink LR + S method (rank = 1) using 6 radial lines

Fig. 10

Resting-state fMRI dataset—slice no. 24: NMSE versus subject number with the proposed Optshrink LR + S method (rank = 1) using 6 radial lines

Fig. 11

Design matrix of task-based fMRI dataset (false belief task)

Fig. 12

False belief fMRI data shown on sagittal, coronal, and axial planes: a fully sampled fMRI data; b smoothed fully sampled fMRI data; c reconstructed fMRI data using LR + S (6 radial lines) (without smoothing); d reconstructed fMRI data using LR + S (6 radial lines) (with smoothing); e reconstructed fMRI data using proposed Optshrink LR + S method (rank = 1) (6 radial lines) (without smoothing); f reconstructed fMRI data using proposed Optshrink LR + S method (rank = 1) (6 radial lines) (with smoothing)

Fig. 13

False belief fMRI data shown on sagittal, coronal, and axial planes: a fully sampled fMRI data; b smoothed fully sampled fMRI data; c reconstructed fMRI data using LR + S (12 radial lines) (without smoothing); d reconstructed fMRI data using LR + S (12 radial lines) (with smoothing); e reconstructed fMRI data using proposed Optshrink LR + S method (rank = 1) (12 radial lines) (without smoothing); (f) reconstructed fMRI data using proposed Optshrink LR + S method (rank = 1) (12 radial lines) (with smoothing)

Fig. 14

False belief fMRI data shown on sagittal, coronal, and axial planes: a fully sampled fMRI data; b smoothed fully sampled fMRI data; c reconstructed fMRI data using LR + S (24 radial lines) (without smoothing); d reconstructed fMRI data using LR + S (24 radial lines) (with smoothing); e reconstructed fMRI data using proposed Optshrink LR + S method (rank = 1) (24 radial lines) (without smoothing); f reconstructed fMRI data using proposed Optshrink LR + S method (rank = 1) (24 radial lines) (with smoothing)

Fig. 15

Axial view of spatial maps of various RSNs where left part of each figure is from the original fully available dataset and right part is from the Optshrink LR + S reconstructed data

Fig. 16

Axial view of spatial maps of various RSNs where left part of each figure is from the original fully available dataset and right part is from the Optshrink LR + S reconstructed data