bpdq_err_p : Compute appropriate epsilon for BPDQ program epsilon=bpdq_err_p(p,alpha,M) ref : Jacques et al 2009, section III-C Inputs: p - BPDQ moment alpha - quantization bin width M - # of measurements Outputs: epsilon - epsilon large enough so that original signal is feasible solution of BPDQ fidelity constraint, with high probability 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_err_p : Compute appropriate epsilon for BPDQ program 0002 % 0003 % epsilon=bpdq_err_p(p,alpha,M) 0004 % 0005 % ref : Jacques et al 2009, section III-C 0006 % 0007 % Inputs: 0008 % p - BPDQ moment 0009 % alpha - quantization bin width 0010 % M - # of measurements 0011 % 0012 % Outputs: 0013 % epsilon - epsilon large enough so that original signal is feasible 0014 % solution of BPDQ fidelity constraint, with high probability 0015 % 0016 % This file is part of BPDQ Toolbox (Basis Pursuit DeQuantizer) 0017 % Copyright (C) 2009, the BPDQ Team (see the file AUTHORS distributed with 0018 % this library) (See the notice at the end of the file.) 0019 0020 function epsilon=bpdq_err_p(p,alpha,M) 0021 kappa=2; 0022 epsilon = (alpha/2)*(M/(p+1))^(1/p)*(1+kappa*(p+1)/M^(1/2))^(1/p); 0023 0024 % The BPDQ Toolbox is free software: you can redistribute it and/or modify 0025 % it under the terms of the GNU General Public License as published by 0026 % the Free Software Foundation, either version 3 of the License, or 0027 % (at your option) any later version. 0028 % 0029 % The BPDQ Toolbox is distributed in the hope that it will be useful, 0030 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0031 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0032 % GNU General Public License for more details. 0033 % 0034 % You should have received a copy of the GNU General Public License 0035 % along with The BPDQ Toolbox. If not, see <http://www.gnu.org/licenses/>.