ADMM 交替方向乘子法_matlab源码.zip

% ADMM_lin_inv : A MATLAB Toolbox for solving linear inverse problems % in Hilbert spaces directly. % ------------------------------------------------------------------------- % 1. Introduction % Thank you for downloading the ADMM_lin_inv! % In this package the ADMM is used to solve linear inverse problem % Ax = b^{\delta} direcly with a prior information that x is sparse % undertransformation W. With the stop condition (2.34) in the % paper the ADMM is a iterative regularization method. And the % included M files are used to reproduce the figures in the paper. % ------------------------------------------------------------------------- % 2. Installation and Setup % Add the folder ADMM_lin_inv to your MATLAB path % ------------------------------------------------------------------------- % ------------------------------------------------------------------------- % 3. License % % See License.txt for the license of this program % % 4. Usage % By assume that Wx is sparse and the observation is exact, % one may using the minimizer of % min_{x} f(Wx) s.t. Ax = b with f(t) = \|t\|_1 + nu/2 \|t\|^2_2 % to appoximate the underlying solution. By introducing Wx = y % and using the algmented Lagragian % L_{rho1,rho2}(x,y;lambda,mu) = % \|y\|_1 + nu/2 \|y\|^2 % + rho1/2 \|Ax -b\|^2 + <Ax -b,lambda> % + rho1/2 \|Wx -y\|^2 + <Wx -y,mu> % one may consider solving % Min_{x,y} Max_{lambda,mu}L_{rho1,rho2}(x,y;lambda,mu) % with the alternating direction technique. % When the data contained noise, we proposed stop condition (2.34) % to stop the ADMM. See the M files for detail. % ------------------------------------------------------------------------- % 5. Contact and Citation % % We hope that ADMM_lin_inv is useful for your application. If you have % any bug reports or comments, please feel free to email Yuling Jiao or % Weijei Wang at % yulingjiaomath@whu.edu.cn % wjwang.math@whu.edu.cn % And if you feel it useful please cite: % Yuling Jiao, Qinian Jian, Xiliang Lu and Weijei Wang. ALTERNATING % DIRECTION METHOD OF MULTIPLIERS FOR LINEAR INVERSE % PROBLEMS. % % Enjoy! % -------------------------------------------------------------------------