bpdq_2d_tv : Implementation of BPDQ-TV for 2d reconstruction [xstar,D] = bpdq_2d_tv(yq,A,At,dim,epsilon,p,varargin) Implements reconstruction from quantized Fourier measurements xstar = argmin_x ||x||_TV s.t. ||yq-A*x||_p <= epsilon Inputs: yq - quantized measurements A - function handle implementing sensing matrix At - function handle implementing transpose of sensing matrix dim - 2d dimensions of image 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 % bpdq_2d_tv : Implementation of BPDQ-TV for 2d reconstruction 0002 % 0003 % [xstar,D] = bpdq_2d_tv(yq,A,At,dim,epsilon,p,varargin) 0004 % 0005 % Implements reconstruction from quantized Fourier measurements 0006 % 0007 % xstar = argmin_x ||x||_TV s.t. ||yq-A*x||_p <= epsilon 0008 % 0009 % Inputs: 0010 % yq - quantized measurements 0011 % A - function handle implementing sensing matrix 0012 % At - function handle implementing transpose of sensing matrix 0013 % dim - 2d dimensions of image 0014 % 0015 % This file is part of BPDQ Toolbox (Basis Pursuit DeQuantizer) 0016 % Copyright (C) 2009, the BPDQ Team (see the file AUTHORS distributed with 0017 % this library) (See the notice at the end of the file.) 0018 0019 function [xstar,D] = bpdq_2d_tv(yq,A,At,dim,epsilon,p,varargin) 0020 control_params={'dr_verbosity',0,... 0021 'dr_maxiter',50,... 0022 'dr_gamma',.1,... 0023 'dr_lambda',1}; 0024 argselectAssign(control_params); 0025 argselectCheck(control_params,varargin); 0026 argselectAssign(varargin); 0027 0028 % unpack complex vector into vector of reals 0029 c2r = @(x) [real(x(:));imag(x(:))]; 0030 r2c = @(x) x(1:end/2)+sqrt(-1)*x(end/2+1:end); 0031 0032 % Assuming A*A' = nu * I ; compute nu 0033 x=rand(size(yq)); 0034 nu=(At(x))'*At(x)/(x'*x); 0035 0036 % define prox operators 0037 % f1 is modified lpball. As A is tight frame, fca type iteration 0038 % is not needed, can use direct formula to get prox(f(A(x)) 0039 prox_lp =@(x) r2c(bpdq_proj_lpball_mex( c2r(x),c2r(yq),epsilon,p)); 0040 proxf1 =@(x,tgamma) x+ (1/nu)*At( prox_lp(A(x)) - A(x)); 0041 0042 % f2 is TV norm. Note : the need to reshape back to 2-d array to compute 0043 % prox of TV norm is why dim must given 0044 tvprox_opts={'min_rel_obj',5e-4,'it_max',500,'verbose',0}; 0045 tv_prox=@(x,tgamma)vec(bpdq_prox_tv_mex(real(reshape(x,dim)),tgamma,... 0046 tvprox_opts{:})); 0047 proxf2=tv_prox; 0048 0049 % init point 0050 % x0=real( vec( samp_t(yq))/prod(dim) ); 0051 x0=At(yq)/prod(dim); 0052 [xstar,dr_relerr_save]=bpdq_d_r_iter(proxf1,proxf2,dr_gamma,dr_lambda,x0,... 0053 'dr_verbosity',dr_verbosity,... 0054 'dr_maxiter',dr_maxiter); 0055 D.dr_relerr_save=dr_relerr_save; 0056 0057 % The BPDQ Toolbox is free software: you can redistribute it and/or modify 0058 % it under the terms of the GNU General Public License as published by 0059 % the Free Software Foundation, either version 3 of the License, or 0060 % (at your option) any later version. 0061 % 0062 % The BPDQ Toolbox is distributed in the hope that it will be useful, 0063 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0064 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0065 % GNU General Public License for more details. 0066 % 0067 % You should have received a copy of the GNU General Public License 0068 % along with The BPDQ Toolbox. If not, see <http://www.gnu.org/licenses/>.