bpdq_fft_subsample : Linear operation of Fourier transform and subsampling r=bpdq_fft_subsample(x,ind,dim) Implements the linear operation corresponding to subsampling 2d Fourier transform at locations specified by ind. Output is vectorized, as complex values Inputs: x - input signal (in spatial domain) ind - indices of desired Fourier coefficients (with FT shifted by fftshift so that DC coefficient is in center of image) dim - image size Outputs: r - returned sampled Fourier values, returned as complex vector the same size as input ind 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_fft_subsample : Linear operation of Fourier transform and subsampling 0002 % 0003 % r=bpdq_fft_subsample(x,ind,dim) 0004 % 0005 % Implements the linear operation corresponding to subsampling 2d Fourier 0006 % transform at locations specified by ind. 0007 % 0008 % Output is vectorized, as complex values 0009 % 0010 % Inputs: 0011 % x - input signal (in spatial domain) 0012 % ind - indices of desired Fourier coefficients (with FT shifted by fftshift 0013 % so that DC coefficient is in center of image) 0014 % dim - image size 0015 % 0016 % Outputs: 0017 % r - returned sampled Fourier values, returned as complex vector 0018 % the same size as input ind 0019 % 0020 % This file is part of BPDQ Toolbox (Basis Pursuit DeQuantizer) 0021 % Copyright (C) 2009, the BPDQ Team (see the file AUTHORS distributed with 0022 % this library) (See the notice at the end of the file.) 0023 0024 function r=bpdq_fft_subsample(x,ind,dim) 0025 xdft=fftshift(fft2(reshape(x,dim))); 0026 r=xdft(ind); 0027 0028 0029 % The BPDQ Toolbox is free software: you can redistribute it and/or modify 0030 % it under the terms of the GNU General Public License as published by 0031 % the Free Software Foundation, either version 3 of the License, or 0032 % (at your option) any later version. 0033 % 0034 % The BPDQ Toolbox is distributed in the hope that it will be useful, 0035 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0036 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0037 % GNU General Public License for more details. 0038 % 0039 % You should have received a copy of the GNU General Public License 0040 % along with The BPDQ Toolbox. If not, see <http://www.gnu.org/licenses/>.