bit of documentation

functions/phaseRetrieval/holographic/private/fADMM.m

-%=====================================================================
-% An accelerated version of the ADMM-algorithm that solves a
-% minimization problem of the form
+function [result, stats] = fADMM(proxH, proxG, v_hat_start, settings)
+% Implements the accelerated variant of the Alternating-Direction Method of Multipliers (ADMM)
+% proposed in the article
 % 
-%       result = argmin_x H(x) + G(x)
-%
-% where H and G are convex functionals for which
-% implementations of the proximal operators
-%
-%     proxH(y_0,sigma) = argmin_y H(y) + 1/(2*sigma) ||y-y_0||_2^2
-%     proxG(x_0,sigma) = argmin_x G(x) + 1/(2*sigma) ||x-x_0||_2^2
-%
-% are available. (||x||_2 denotes the 2-norm of x)
-%
-% The algorithm is described (in a more general form than implemented
-% here) in the article:
-%
 % Goldstein, T., O'Donoghue, B., Setzer, S., & Baraniuk, R. (2014). 
 % Fast alternating direction optimization methods. 
 % SIAM Journal on Imaging Sciences, 7(3), 1588-1623.
 %
-% 
-% Last modified on April 24 2019 by Simon Maretzke
-%=====================================================================
+% The algorithm iteratively solves an optimization problem of the form x_res = argmin_x H(x) + G(x)
+% with convex functionals H and G, given implementations of the corresponding proximal operators
+% proxH(x_0) = argmin_x H(x) + ||x-x_0||_2^2 and proxG(x_0) = argmin_x G(x) + ||x-x_0||_2^2, where
+% ||y||_2 denotes the Euclidean 2-norm.
 
+% HoloTomoToolbox
+% Copyright (C) 2019  Institut fuer Roentgenphysik, Universitaet Goettingen
+%
+% This program is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+%
+% This program is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this program.  If not, see <http://www.gnu.org/licenses/>.
 
-function [result, stats] = fADMM(proxH, proxG, v_hat_start, settings)
 
 % Complete settings with default parameters
 defaults.maxIt = 1e2;

functions/phaseRetrieval/holographic/private/projectedGradientDescent.m

 function [result, stats] = projectedGradientDescent(F, initialGuess, settings)
+% Computes a (local) minimum of a functional F by projected/proximal gradient-descent 
+% iterations. The implementation uses of Barzilai-Borwein stepsizes, non-monotone linesearch
+% and a stopping rule based on the relative residual, as proposed in the article:
+% 
+% Goldstein, T., Studer, C., & Baraniuk, R. (2014). A field guide to forward-backward 
+% splitting with a FASTA implementation. arXiv preprint arXiv:1411.3406.
+
+% HoloTomoToolbox
+% Copyright (C) 2019  Institut fuer Roentgenphysik, Universitaet Goettingen
+%
+% This program is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+%
+% This program is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
 
 % Default parameters
 defaults.initialStepsize = 1;
@@ -134,18 +157,6 @@ end
 
 function [stepsize, cache] = bbStepsize(F, x, y, s, cache)
 
-% Input arguments:
-%
-%            F: Objective functional
-%            x: Evaluation point of the gradient descent step
-%            y: Value of the functional at x, y = F(x)
-%            s: Computed gradient descent direction s = grad(F)(x).
-%        cache: Cache-structure, that stores the required information on the preceding iterate
-%
-% Output arguments:
-%
-%    stepsize: The computed stepsize
-
     if ~isfield(cache, 'bb_last_step')
         cache.bb_last_step = 0;
         stepsize = cache.stepsize;
@@ -172,25 +183,12 @@ function [stepsize, cache] = bbStepsize(F, x, y, s, cache)
     cache.s = s;
     cache.stepsize = stepsize;
 
-
 end
 
 
 
 function [stepsize, cache] = constantStepsize(F, x, y, s, cache)
 
-% Input arguments:
-%
-%            F: Objective functional
-%            x: Evaluation point of the gradient descent step
-%            y: Value of the functional at x, y = F(x)
-%            s: Computed gradient descent direction s = grad(F)(x).
-%        cache: Cache-structure, that stores the required information on the preceding iterate
-%
-% Output arguments:
-%
-%    stepsize: The computed stepsize
-
     stepsize = cache.stepsize;
     cache.x = x;
     cache.s = s;