MATLAB基于压缩传感理论的单像素照相机图像复原算法

非常经典的由RICE UNIVERSITY开发的压缩传感理论单像素照相机的图像复原算法。压缩传感理论已经是现在数字信号处理的热点问题，而其运用的算法主要基于随机过程理论，很有研究型。这里的算法是个例程。

% l1dantzig_example.m
%
% Test out l1dantzig code （l1 minimization with bounded residual correlation）.
%
% Written by: Justin Romberg Caltech
% Email: jrom@acm.caltech.edu
% Created: October 2005
%

% put optimization code in path if not already there
path（path ‘./Optimization‘）;

% signal length
N = 512;
% number of spikes to put down
T = 20;
% number of observations to make
K = 120;

% random +/- 1 signal
x = zeros（N1）;
q = randperm（N）;
x（q（1:T）） = sign（randn（T1））;

% measurement matrix
disp（‘Creating measurment matrix...‘）;
A = randn（KN）;
A = orth（A‘）‘;
disp（‘Done.‘）;
	
% noisy observations
sigma = 0.005;
e = sigma*randn（K1）;
y = A*x + e;

% initial guess = min energy
x0 = A‘*y;


% Dantzig selection
epsilon = 3e-3;
tic
xp = l1dantzig_pd（x0 A [] y epsilon 5e-2）;
toc

% large scale
%Afun = @（z） A*z;
%Atfun = @（z） A‘*z;
%tic
%xp = l1dantzig_pd（x0 Afun Atfun y epsilon 5e-2 50 1e-8 500）;
%toc

 属性            大小     日期    时间   名称
----------- ---------  ---------- -----  ----

     文件      65728  2005-11-04 09:42  l1magic\Data\boats.mat

     文件      65728  2005-11-04 07:49  l1magic\Data\camera.mat

     文件        543  2005-11-21 14:44  l1magic\Data\RandomStates.mat

     目录          0  2009-12-10 00:37  l1magic\Data

     文件        928  2005-11-02 05:28  l1magic\l1dantzig_example.m

     文件        640  2005-11-16 14:48  l1magic\l1decode_example.m

     文件        969  2006-04-21 05:33  l1magic\l1eq_example.m

     文件     283716  2007-04-06 02:35  l1magic\l1magic_notes.pdf

     文件       1107  2005-11-04 05:11  l1magic\l1qc_example.m

     文件        718  2005-11-04 09:42  l1magic\Measurements\At_f.m

     文件        613  2005-11-10 02:01  l1magic\Measurements\At_fhp.m

     文件        659  2005-11-04 09:42  l1magic\Measurements\A_f.m

     文件        576  2005-11-10 02:01  l1magic\Measurements\A_fhp.m

     文件        832  2005-11-10 02:01  l1magic\Measurements\LineMask.m

     目录          0  2009-12-10 00:37  l1magic\Measurements

     文件         82  2007-04-06 01:29  l1magic\Optimization\._l1eq_pd.m

     文件         82  2007-04-06 01:30  l1magic\Optimization\._l1qc_logbarrier.m

     文件         82  2007-04-06 01:31  l1magic\Optimization\._tveq_logbarrier.m

     文件       1691  2006-05-27 03:14  l1magic\Optimization\cgsolve.m

     文件       6017  2006-04-21 05:33  l1magic\Optimization\l1dantzig_pd.m

     文件       4844  2006-02-23 02:30  l1magic\Optimization\l1decode_pd.m

     文件       5370  2009-11-07 21:56  l1magic\Optimization\l1eq_pd.m

     文件       2763  2007-04-06 01:30  l1magic\Optimization\l1qc_logbarrier.m

     文件       4179  2005-11-04 05:11  l1magic\Optimization\l1qc_newton.m

     文件       2915  2005-11-22 07:31  l1magic\Optimization\tvdantzig_logbarrier.m

     文件       5985  2006-02-23 02:30  l1magic\Optimization\tvdantzig_newton.m

     文件       2729  2007-04-06 01:31  l1magic\Optimization\tveq_logbarrier.m

     文件       5214  2005-11-08 01:23  l1magic\Optimization\tveq_newton.m

     文件       2880  2006-04-21 05:33  l1magic\Optimization\tvqc_logbarrier.m

     文件       5563  2006-04-21 05:33  l1magic\Optimization\tvqc_newton.m

............此处省略11个文件信息