Accelerated fMRI Reconstruction using Matrix Completion with Sparse Recovery via Split Bregman

Accelerated fMRI reconstruction, nuclear norm, l1 minimization, sparse recovery, compressed sensing

In this work, we propose a new method of accelerated functional MRI recon-
struction, namely, Matrix Completion with Sparse Recovery (MCwSR). The
proposed method combines low rank condition with transform domain spar-
sity for fMRI reconstruction and is solved using state-of-the-art Split Bregman
algorithm as described in the paper:
P. Aggarwal and A. Gupta, "Accelerated fMRI reconstruction using Matrix Completion
with Sparse Recovery via Split Bregman", Neurocomputing, Available online 8 August 2016,
ISSN 0925-2312, http://dx.doi.org/10.1016/j.neucom.2016.08.016.
The proposed method exploits both sparsity and low-rank to improve fMRI reconstruction
accuracy and is named as Matrix completion with Sparse Recovery (MCwSR). We formulate a
reconstruction problem as follows (equ.2 in above paper):

\hat{X}=argmin ||Y-\Phi FX||_{F}^{2} + \mu _{1}||X||_{\ast } + \mu _{2}||\Psi X||_{1},

where Y is an undersampled fMRI data and \Psi is sparsifying transform. In this toolbox,
you are required to input fully sampled 4-D fMRI data. Afterwards, undersampled data
Y is simulated by computing Fourier transform followed by undersampling using radial
sampling pattern \Phi. Please note that this work is general and can be used with any
sampling patterns. You are free to input under-sampled k-t space data (captured inside scanner)
as well, if available with you.

This toolbox contains the following files.

README
Main_MCwSR.m (main file of MCwSR)
rec_codes folder (containing supporting codes to run Main_MCwSR.m (main file)).

Main_MCwSR.m is a main file with input and output as described below:

==============================================================
%%%%%% FMRI Reconstruction using MCwSR %%%%%
==============================================================

% Input: brainimageseq is 4D fully sampled fMRI data where x and y
% coordinates represents dimensions of a slice. z coordinates
% represents no. of slices and last coordinate represents no.
% of time points.

% Output: brainimageseq_rec is a 4D reconstructed fMRI data
==============================================================

This is the first time above formulation is proposed for an application of offline reconstruction
of fMRI data. This toolbox will help you to simulate larger bigger size matrices in fMRI, where
operators are designed to deal with bigger matrices in an application of 4-D fMRI data. Furthermore,
we have compared with various other existing offline reconstruction methods so far in fMRI literature
in our above paper. Please feel free to contact us in case you need help of simulating other methods.