Speedup of Geometric Decomposition Coil Compression

This is a demo of the Geometric-decomposition Coil Compression (GCC) based on Zhang et. al MRM 2013;69(2):571-82. The demo shows how to use the compression and in addition it shows the use of alignment of the compression matrices. The example is on 2D data, but can also be applied on 3D as well. GCC removes correlations between channels along a fully sampled readout dimension. This allows for significant reduction in data, so parallel imaging and other multi-channel algorithms are much more computationally efficient. This demo demonstrate effective compression from 32->5 virtual channels.

This demo aims to show speedup of computation for parallel imaging

Set parameters:

load brain_32ch.mat
im = ifft2c(DATA);
DATA = DATA/max(abs(im(:)));

% number of compressed virtual coils
ncc = 5;
dim = 2;
ncalib = 20; % use 24 calibration lines to compute compression
[sx,sy,Nc] = size(DATA);
slwin = 5; % sliding window length for GCC

mask = zpad(ones(ncalib,sy,Nc),[sx,sy,Nc]);
mask(1:2:end,:,:) = 1;
dens = -zpad(ones(ncalib,sy,Nc),[sx,sy,Nc]) + 2;
DATAc = DATA.*mask;
% crop calibration data
calib = crop(DATAc,[ncalib,sy,Nc]);

disp('Performing GCC')
tic
gccmtx = calcGCCMtx(calib,dim,slwin);
gccmtx_aligned = alignCCMtx(gccmtx(:,1:ncc,:));
DATAcc = CC(DATAc,gccmtx_aligned,dim);
calibcc = CC(calib,gccmtx_aligned,dim);
gcct = toc;

disp('perfomring GRAPPA on GCC coils');
tic; resGRAPPAcc = GRAPPA(DATAcc,calibcc,[5,5],0.01);grappacct = toc;
disp('performing GRAPPA on physical coils');
tic; resGRAPPA = GRAPPA(DATAc,calib,[5,5],0.01);grappat = toc;

errGcc = unCC(resGRAPPAcc,dim,gccmtx_aligned)-DATA;
errG = resGRAPPA - DATA;

Performing GCC
perfomring GRAPPA on GCC coils
reconstructing coil 1
reconstructing coil 2
reconstructing coil 3
reconstructing coil 4
reconstructing coil 5
performing GRAPPA on physical coils
reconstructing coil 1
reconstructing coil 2
reconstructing coil 3
reconstructing coil 4
reconstructing coil 5
reconstructing coil 6
reconstructing coil 7
reconstructing coil 8
reconstructing coil 9
reconstructing coil 10
reconstructing coil 11
reconstructing coil 12
reconstructing coil 13
reconstructing coil 14
reconstructing coil 15
reconstructing coil 16
reconstructing coil 17
reconstructing coil 18
reconstructing coil 19
reconstructing coil 20
reconstructing coil 21
reconstructing coil 22
reconstructing coil 23
reconstructing coil 24
reconstructing coil 25
reconstructing coil 26
reconstructing coil 27
reconstructing coil 28
reconstructing coil 29
reconstructing coil 30
reconstructing coil 31
reconstructing coil 32

GCC has many order of magnitude improvement in recon time. Note thst the error image does not have any aliasing patterns in it and is coming from the compression error, rather than the parallel imaging recon

figure, imshow(cat(2, sos(ifft2c(resGRAPPAcc)), sos(ifft2c(resGRAPPA)), sos(ifft2c(DATAc.*dens))),[]);
title('Left: GRAPPA with GCC, middle GRAPPA, right: Zero-filling');

figure, imshow(cat(2, sos(ifft2c(errGcc)), sos(ifft2c(errG))),[]);
title('Reconstruction error in %. Left: GRAPPA with GCC, right GRAPPA');
colorbar

disp(sprintf('Speedup is: %f times!', grappat/(grappacct + gcct)));

Speedup is: 46.173861 times!

Published with MATLAB® R2013a