下面以文献【吴赟.压缩感知测量矩阵的研究[D]. 西安电子科技大学硕士学位论文，2012】为依据，给出文献中2.2节内容所述的六种测量矩阵MATLAB实现代码，仅为一种参考实现方式，还未验证其正确性。

        以下代码生成的高斯矩阵方差为1，若为改为1/M，只须将除以根号M即可。

function [ Phi ] = GaussMtx( M,N )
%GaussMtx Summary of this function goes here
%   Generate Bernoulli matrix 
%   M -- RowNumber
%   N -- ColumnNumber
%   Phi -- The Gauss matrix

%% Generate Gauss matrix   
    Phi = randn(M,N);
    %Phi = Phi/sqrt(M);
end

        以下代码是按式(2-8)生成的伯努利矩阵，若要按式(2-9)生成则需使用后半部分注释掉的代码即可。注意代码中用到了MATLAB自带的randi函数，若你的MATLAB版本较低，可能要用randint函数代替，后面若用到此函数则一样要注意这一点。

function [ Phi ] = BernoulliMtx( M,N )
%BernoulliMtx Summary of this function 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=0.5
    Phi = randi([0,1],M,N);%If your MATLAB version is too 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);%If your MATLAB version is too 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

        由于MATLAB自带的函数hadamard参数有限制，所以程序中首先计算满足要求的参数L，需要注意的是，hadamard参数并不像文献中所述仅为2的整数次幂，而是12的整数倍或20的整数倍或2的整数次幂，详情在MATLAB查看hadamard的help文件。

function [ Phi ] = PartHadamardMtx( M,N )
%PartHadamardMtx Summary of this function 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 cases where n, n/12,
%or n/20 is a power of 2
    L_t = max(M,N);%Maybe L_t does not meet requirement of function hadamard
    L_t1 = (12 - mod(L_t,12)) + L_t;
    L_t2 = (20 - mod(L_t,20)) + 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

        以下代码生成的是部分傅里叶矩阵，这里要提的一点是，有关“归一化”的概念在网上说法不一，一种说法是向量除以向量各项之和，另一种说法是向量除以向量的2范数（各项平方之和再开方），这里采用后者。

function [ Phi ] = PartFourierMtx( M,N )
%PartFourierMtx Summary of this function 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
    for ii = 1:N
        Phi(:,ii) = Phi(:,ii)/norm(Phi(:,ii));
    end
end

function [ Phi ] = SparseRandomMtx( M,N,d )
%SparseRandomMtx Summary of this function goes here
%   Generate SparseRandom matrix 
%   M -- RowNumber
%   N -- ColumnNumber
%   d -- The number of '1' in every column,d<M 
%   Phi -- The SparseRandom matrix

%% Generate SparseRandom matrix   
    Phi = zeros(M,N);
    for ii = 1:N
        ColIdx = randperm(M);
        Phi(ColIdx(1:d),ii) = 1;
    end
end

        这里先给出托普利兹矩阵，文中说经过M次循环，这里直接利用MATLAB自带函数生成一个托普利兹方阵再取前M行。

function [ Phi ] = ToeplitzMtx( M,N )
%ToeplitzMtx Summary of this function 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

        下面是循环矩阵，仍然利用MATLAB自带函数生成。

function [ Phi ] = CirculantMtx( M,N )
%CirculantMtx Summary of this function 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

        以上都是采用MATLAB自带的toeplitz函数，这需要首先生成一个随机向量，而托普利兹矩阵和循环矩阵的区别也就在于这个随机向量的结构不同，注意代码中有关toeplitz函数的两个输入参数好好体会即可。