Monday Morning Algorithm 11: Sparse Measurement Matrix using Scrambled Block Hadamard Ensemble

In a previous entry, we discovered the paper by Lu Gan, Thong Do and Trac Tran that provides us with a compact measurement matrix as described in Fast compressive imaging using scrambled block Hadamard ensemble. We are going to implement this sparse measurement matrix as we have previously done with a similar entry in the Monday Morning Algorithm series. This measurement matrix is a cornerstone in the field of Compressed Sensing. If you don't know about Compressed Sensing, you may want to check this out. As usual all errors are mine and if you find a mistake in the implementation, please let me know. If you also know how to quietly do evals with matlab I am also a taker.

function [wfinal]=sbhe(k,hd,mt)
%
% Function implementing measurement matrix as given in
% "Fast compressive imaging using scrambled block Hadamard ensemble."
% by Lu Gan, Thong Do and Trac Tran
%
% Written by Igor Carron.
%
% Input:
% k : number of hadamard matrix blocks
% hd: size of Hadamard matrix (needs to be divisible by 2)
% mt: number of columns of wfinal
% Output:
% wfinal: matrix with k*nd columns and mt rows
%
% k=10;
% hd = 32;
% mt = 30;
ntotal = hd * k;
wh = hadamard(hd);
st1='';
for i=1:k-1
st1 = strcat(st1,'wh,');
end
st1= strcat(st1,'wh');
eval(['w = blkdiag(' st1 ')']);
u = randperm(ntotal);
for ii=1:ntotal
wnew(:,ii)=w(:,u(ii));
end
%figure(1)
%spy(w)
%figure(2)
%spy(wnew)
vv = [];
while size(vv,1)~=mt
v2 = cat(2,vv,round(1+rand(mt,1)*(ntotal-1)));
vv = unique(v2);
end
m = size(vv,1);
for j=1:m
wfinal(j,:) = wnew(vv(j),:);
end
%spy(wfinal)

The m file can be downloaded from here or here.

Credit Photo: ESA/ MPS/DLR/IDA, Venus’s atmosphere, taken by the Venus Monitoring Camera (VMC) during Venus Express orbit number 458 on 23 July 2007.