压缩感知中常用的待还原信号种类

function x = SparseVector(n, k, ensemble, perm)
% SparseVector: Generates a sparse vector with a specified distribution.
%
% Usage:
% x = SparseVector(n, k, ensemble, perm)
% Inputs:
% n vector length
% k number of nonzero entries
% ensemble string containing name of coefficient distribution
% ‘Uniform‘, ‘Gaussian‘, ‘Signs‘, ‘Power‘. 
% Default is ‘Uniform‘.
% perm If =1, the nonzero indices are randomly selected. 
% Otherwise, the nonzero entries are in indices 1..k (default).
% Outputs:
% x Sparse n vector.
% Description:
% This function creates a vector of length n with k nonzero entries, 
% distributed according to the specified input ensemble. 
% The following distributions are supported:
%
% ‘Uniform‘ - Entries are distributed uniformly on the unit interval. 
%
% ‘Gaussian‘ - Entries are distributed N(0,1).
%
% ‘Signs‘ - Entries are distributed Bernoulli over the set {-1,1}, 
% with equal probabilities. 
%
% ‘Power‘ - Entries follow the power law 1/j, j = 1..k
%
% See Also
% MatrixEnsemble

if nargin < 4,
    perm = 0;
end
if nargin < 3,
    ensemble = ‘Uniform‘;
end

switch upper(ensemble)
    case ‘UNIFORM‘
        x = [rand(k,1); zeros(n-k,1)];
        
    case ‘SIGNS‘
        x = sign(rand(k,1) - 0.5);
        zz = find(x == 0);
        Phi(zz) = ones(size(zz));
        x = [x; zeros(n-k,1)];
        
    case ‘GAUSSIAN‘
        x = [randn(k,1); zeros(n-k,1)];

    case ‘POWER‘
        %这里被我修改了，之前是x = [1./[1:k]; zeros(n-k,1)];
        %程序是有问题的，需要转置
        x = [(1./[1:k])‘; zeros(n-k,1)];
end 

if perm
    p = randperm(n);
    x = x(p);
end
    
%
% Copyright (c) 2006. David Donoho
% 

%
% Part of SparseLab Version:100
% Created Tuesday March 28, 2006
% This is Copyrighted Material
% For Copying permissions see COPYING.m
% Comments? e-mail sparselab@stanford.edu
%