This repository contains MATLAB code for B-spline-based compressed sensing (SPLICS) method presented in the paper J F P J Abascal, P Montesinos, E Marinetto, J Pascau, M Desco. Comparison of total variation with a motion estimation based compressed sensing approach for self-gated cardiac cine MRI in small animal studies. PLOS ONE 9(10): e110594, 2014. DOI: http://dx.doi.org/10.1371/journal.pone.0110594
SPLICS generalizes spatiotemporal total variation (ST-TV) by modelling the motion between consecutive frames into the reconstruction framework. Motion is estimated using a nonrigid registration method based on hierarchical B-splines. SPLICS solves the following problem
where the first term corresponds to TV, T is the temporal sparsity operator, F is the Fourier transform, u is the reconstrcuted image and f is undersampled data. The optimization problem is efficiently solved using the Split Bregman formulation.
This demo compares TV, spatiotemporal TV and SPLICS on cardiac cine MRI data.
This version of the SPLICS comprises two steps: i) motion is estimated from a previous reconstruction (image given by TV in this example) to build a sparse temporal operator encoding motion, ii) image reconstruction taking into account the previously estimated motion operator. This process could be iterated for further improvement. We found that if the previous reconstruction had good quality, motion could be accurately estimated. A demo that iterates these two steps will be added to the toolbox soon.
To run SPLICS method you need the following MATLAB toolbox:
- FFD-based registration package. Dirk-Jan Kroon; B-spline grid, image and point based registration; 2012, retrieved from http://www.mathworks.com/matlabcentral/fileexchange/20057-b-spline-grid-image-and-point-based-registration
The repository contains the following files: Data and MATLAB functions
- Demo_MotionEstimationCompressedSensingMRI_Sim.m: Demo that loads data and shows how to use TV, ST-TV and SPLICS methods
- SpatialTVSB.m: TV method. Solved efficiently in the Fourier domain
- SpatioTemporalTVSB.m: Spatiotemporal TV method. Solved efficiently in the Fourier domain
- SPLICS.m: SPLICS method. Solved in the Image domain
- ComputeSplineRegTwoDirectionsPoolDouble.m: Function to compute the registration between consecutive gates
- dataCine8fr.mat: Absolute image of retrospective cardiac cine small-animal data (8 frames, healthy rat) (Acquired data can be found at http://biig.uc3m.es/cardiac-cine-data)
- TParameters_x5,x7,x10.mat: Registration results needed for SPLICS method for different acceleration factors, precomputed with ComputeSplineRegTwoDirectionsPoolDouble.m
- genPDF.m: Function to generate a pdf with polynomial variable density sampling, by Michael Lustig 2007, downloaded from (SparseMRI V0.2), http://web.stanford.edu/~mlustig/SparseMRI.html, see M. Lustig, D.L
- genSampling_LIM.m: Monte-carlo algorithm to generate a sampling pattern. Modified from the original function by Michael Lustig 2007
- maxSidePeakRatio.m: Computes the maximum sidelobe to peak ratio of point spread function for undersampled data. Used within genSampling_LIM.m
If you use this code, please reference the paper JFPJ Abascal et al. Comparison of total variation with a motion estimation based compressed sensing approach for self-gated cardiac cine MRI in small animal studies. PLOS ONE 9(10): e110594, 2014. DOI: http://dx.doi.org/10.1371/journal.pone.0110594. If you need to contact the author, please do so at juanabascal78@gmail.com, paumsdv@gmail.com, desco@hggm.es