# 浅谈压缩感知（十八）：常见测量矩阵及其实现

1. 随机高斯矩阵

MATLAB实现：

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. 随机伯努利矩阵

MATLAB实现：

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(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(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. 部分哈达玛矩阵

MATLAB实现：

function [ Phi ] = PartHadamardMtx( M,N )
%PartHadamardMtx Summary of this function goes here
%   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
Phi = [];
RowIndex = randperm(L);
Phi_t_r = Phi_t(RowIndex(1:M),:);
ColIndex = randperm(L);
Phi = Phi_t_r(:,ColIndex(1:N));
end
4. 部分傅里叶矩阵

MATLAB实现：

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
5. 稀疏随机矩阵

MATLAB实现：

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
6. 托普利兹矩阵和循环矩阵

MATLAB实现：

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
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

posted @ 2015-12-31 15:41  AndyJee  阅读(6859)  评论(1编辑  收藏  举报