A brief talk on compression perception (vii): MATLAB implementation of common measurement matrices

1. Random Gaussian measurement matrix

function [Phi] = gaussmtx (m,n) This function goeshere%      M-- Rownumbe R%   N-- columnnumber%   Phi--The Gauss matrixpercent Generate Gauss matrix        = Randn (m,n);     %phi = phi/sqrt (M); end

2. Random beta-effort measurement matrix

function [Phi] =bernoullimtx (m,n)%BERNOULLIMTX Summary of Thisfunction goes here%Generate Bernoulli Matrix% M--RowNumber% N--ColumnNumber% Phi--The Bernoulli matrix%% (1) Generate Bernoulli matrix (the first kind)%1--p=0.5-1--p=0.5Phi= Randi ([0,1],M,N);%I F Your MATLAB version istoo low,please use Randint instead Phi (Phi==0) = -1; %phi = phi/sqrt (M);% %% (2) Generate Bernoulli matrix (the second kind)% %1--p=1/6-1--p=1/6  0--2/3% Phi = Randi ([-1,4],M,N);%I F Your MATLAB version istoo low,please use Randint instead% Phi (phi==2) =0;%p=1/6% Phi (phi==3) =0;%p=1/6% Phi (phi==4) =0;%p=1/6%%phi = PHI*SQRT (3/M); end

3. Partial Hada Measurement matrix

function [Phi] =parthadamardmtx (m,n)%PARTHADAMARDMTX Summary of Thisfunction goes here%Generate part Hadamard Matrix% M--RowNumber% N--ColumnNumber% Phi--The part Hadamard matrix%%parameter Initialization%because the MATLAB function Hadamard handles only the caseswhereN, n/ A,%or n/ -  isA power of2l_t= max (m,n);%maybe l_t does not meet requirement of function Hadamard l_t1= ( A-MoD (l_t, A)) +l_t; L_t2= ( --MoD (l_t, -)) +l_t; L_t3=2^ceil (log2 (l_t)); L= min ([l_t1,l_t2,l_t3]);Get the minimum L%%Generate part Hadamard Matrix Phi= []; phi_t=Hadamard (L); RowIndex=randperm (L); Phi_t_r= phi_t (RowIndex (1: M),:); Colindex=randperm (L); Phi= Phi_t_r (:, Colindex (1: N)); End

4. Partial Fourier measurement matrix

function [Phi] =partfouriermtx (m,n)%PARTFOURIERMTX Summary of Thisfunction goes here%Generate part Fourier Matrix% M--RowNumber% N--ColumnNumber% Phi--The part Fourier matrix%%Generate part Fourier Matrix phi_t= FFT (eye (N,n))/sqrt (N);Fourier Matrix RowIndex=randperm (N); Phi= phi_t (RowIndex (1: M),:);Select M rows randomly%Normalization forII =1: N Phi (:, II)= Phi (:, II)/Norm (Phi (:, ii)); EndEnd

5. Sparse Random Measurement matrix

function [Phi] =sparserandommtx (m,n,d)%SPARSERANDOMMTX Summary of Thisfunction goes here%Generate sparserandom Matrix% M--RowNumber% N--ColumnNumber% d--the number of'1' inchEvery column,d<M% Phi--The sparserandom matrix%%Generate sparserandom Matrix Phi=zeros (m,n);  forII =1: N colidx=randperm (M); Phi (Colidx (1:D), ii) =1; EndEnd

6. Gnas measurement matrix and cyclic measurement matrix

function [Phi] =toeplitzmtx (m,n)%TOEPLITZMTX Summary of Thisfunction goes here%Generate Toeplitz Matrix% M--RowNumber% N--ColumnNumber% Phi--The Toeplitz matrix%%Generate a random vector%     %(1) Gauss% u = RANDN (1,2*n-1); %(2) Bernoulli u= Randi ([0,1],1,2*n-1); U (U==0) = -1;%%Generate Toeplitz Matrix phi_t= Toeplitz (U (n:end), FLIPLR (U (1: N))); Phi= phi_t (1: M,:); end

function [Phi] =circulantmtx (m,n)%CIRCULANTMTX Summary of Thisfunction goes here%Generate circulant Matrix% M--RowNumber% N--ColumnNumber% Phi--The circulant matrix%%Generate a random vector%     %(1) Gauss% u = RANDN (1, N); %(2) Bernoulli u= Randi ([0,1],1, N); U (U==0) = -1;%%Generate circulant Matrix phi_t= Toeplitz (Circshift (u,[1,1]), FLIPLR (U (1: N))); Phi= phi_t (1: M,:); end

Reference Source: http://blog.csdn.net/jbb0523/article/details/44700735

A brief talk on compression perception (vii): MATLAB implementation of common measurement matrices