prox_tv_mex : compute prox of TV operator xstar = prox_tv_mex(y,lambda,...) Solves xstar= min 0.5||y-x||_2 + lambda ||x||_TV The problem is solved thanks to the forward-backward method described in: Multiplicative Noise Removal Using L1 Fidelity on Frame Coefficients, Durand S., Fadili J. and Nikolova M. arXiv:0812.1697v1 Inputs : y - input image lambda - regularization parameter Optional parameters (must be passed in 'name',value pairs) beta (0.249) - parameter for forward-backward splitting algorithm min_rel_obj (0.001) - algorithm will terminate if minimum relative objective is below this value it_max (500) - maximum # of iterations it_min (1) - minimum # of iterations verbose (0) - whether to print output at each iteration Outputs: xstar - returned solution Routine is implemented as mex file This file is part of BPDQ Toolbox (Basis Pursuit DeQuantizer) Copyright (C) 2009, the BPDQ Team (see the file AUTHORS distributed with this library) (See the notice at the end of the file.)
0001 % prox_tv_mex : compute prox of TV operator 0002 % 0003 % xstar = prox_tv_mex(y,lambda,...) 0004 % 0005 % Solves xstar= min 0.5||y-x||_2 + lambda ||x||_TV 0006 % 0007 % The problem is solved thanks to the forward-backward method described 0008 % in: 0009 % Multiplicative Noise Removal Using L1 Fidelity on Frame Coefficients, 0010 % Durand S., Fadili J. and Nikolova M. 0011 % arXiv:0812.1697v1 0012 % 0013 % Inputs : 0014 % y - input image 0015 % lambda - regularization parameter 0016 % 0017 % Optional parameters (must be passed in 'name',value pairs) 0018 % beta (0.249) - parameter for forward-backward splitting algorithm 0019 % min_rel_obj (0.001) - 0020 % algorithm will terminate if minimum relative objective is below this value 0021 % it_max (500) - maximum # of iterations 0022 % it_min (1) - minimum # of iterations 0023 % verbose (0) - whether to print output at each iteration 0024 % 0025 % Outputs: 0026 % xstar - returned solution 0027 % 0028 % Routine is implemented as mex file 0029 % 0030 % This file is part of BPDQ Toolbox (Basis Pursuit DeQuantizer) 0031 % Copyright (C) 2009, the BPDQ Team (see the file AUTHORS distributed with 0032 % this library) (See the notice at the end of the file.) 0033 0034 % The BPDQ Toolbox is free software: you can redistribute it and/or modify 0035 % it under the terms of the GNU General Public License as published by 0036 % the Free Software Foundation, either version 3 of the License, or 0037 % (at your option) any later version. 0038 % 0039 % The BPDQ Toolbox is distributed in the hope that it will be useful, 0040 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0041 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0042 % GNU General Public License for more details. 0043 % 0044 % You should have received a copy of the GNU General Public License 0045 % along with The BPDQ Toolbox. If not, see <http://www.gnu.org/licenses/>.