浅谈压缩感知（七）：常见测量矩阵的MATLAB实现

1、随机高斯测量矩阵

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

2、随机贝努力测量矩阵

function [ Phi ] = BernoulliMtx( M,N )

%BernoulliMtx Summary of this function goes here

%   Generate Bernoulli matrix

%   M -- RowNumber

%   N -- ColumnNumber

%   Phi -- The Bernoulli matrix

%% ()Generate Bernoulli matrix(The first kind)

% --P=0.5   ---P=0.5

    Phi = randi([,],M,N);%If your MATLAB version is too low,please use randint instead

    Phi(Phi==) = -;

    %Phi = Phi/sqrt(M);

% %% ()Generate Bernoulli matrix(The second kind)

% % --P=/   ---P=/  --/

%     Phi = randi([-,],M,N);%If your MATLAB version is too low,please use randint instead

%     Phi(Phi==) = ;%P=/

%     Phi(Phi==) = ;%P=/

%     Phi(Phi==) = ;%P=/

%     %Phi = Phi*sqrt(/M);

end

3、部分哈达玛测量矩阵

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/,

%or n/ is a power of

    L_t = max(M,N);%Maybe L_t does not meet requirement of function hadamard

    L_t1 = ( - mod(L_t,)) + L_t;

    L_t2 = ( - mod(L_t,)) + L_t;

    L_t3 = ^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(:M),:);

    ColIndex = randperm(L);

    Phi = Phi_t_r(:,ColIndex(:N));

end

4、部分傅里叶测量矩阵

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(:M),:);%Select M rows randomly

    %normalization

    for ii = :N

        Phi(:,ii) = Phi(:,ii)/norm(Phi(:,ii));

    end

end

5、稀疏随机测量矩阵

function [ Phi ] = SparseRandomMtx( M,N,d )

%SparseRandomMtx Summary of this function goes here

%   Generate SparseRandom matrix

%   M -- RowNumber

%   N -- ColumnNumber

%   d -- The number of '' in every column,d<M

%   Phi -- The SparseRandom matrix

%% Generate SparseRandom matrix

    Phi = zeros(M,N);

    for ii = :N

        ColIdx = randperm(M);

        Phi(ColIdx(:d),ii) = ;

    end

end

6、托普利兹测量矩阵与循环测量矩阵

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

%     %()Gauss

%     u = randn(,*N-);

    %()Bernoulli

    u = randi([,],,*N-);

    u(u==) = -;

%% Generate Toeplitz matrix

    Phi_t = toeplitz(u(N:end),fliplr(u(:N)));

    Phi = Phi_t(:M,:);

end

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

%     %()Gauss

%     u = randn(,N);

    %()Bernoulli

    u = randi([,],,N);

    u(u==) = -;

%% Generate Circulant matrix

    Phi_t = toeplitz(circshift(u,[,]),fliplr(u(:N)));

    Phi = Phi_t(:M,:);

end

参考来源：http://blog.csdn.net/jbb0523/article/details/44700735