基于压缩感知的SAR成像仿真程序.rar_ISAR_onsl0_压缩感知_压缩感知SAR_压缩感知SL0

function [x,x_debias,objective,times,debias_start,mses,taus]= ... GPSR_BB(y,A,tau,varargin) % % GPSR_BB version 5.0, December 4, 2007 % % This function solves the convex problem % arg min_x = 0.5*|| y - A x ||_2^2 + tau || x ||_1 % using the algorithm GPSR-BB, described in the following paper % % "Gradient Projection for Sparse Reconstruction: Application % to Compressed Sensing and Other Inverse Problems" % by Mario A. T. Figueiredo, Robert D. Nowak, Stephen J. Wright, % Journal of Selected Topics on Signal Processing, December 2007 % (to appear). % % % ----------------------------------------------------------------------- % Copyright (2007): Mario Figueiredo, Robert Nowak, Stephen Wright % % GPSR is distributed under the terms % of the GNU General Public License 2.0. % % Permission to use, copy, modify, and distribute this software for % any purpose without fee is hereby granted, provided that this entire % notice is included in all copies of any software which is or includes % a copy or modification of this software and in all copies of the % supporting documentation for such software. % This software is being provided "as is", without any express or % implied warranty. In particular, the authors do not make any % representation or warranty of any kind concerning the merchantability % of this software or its fitness for any particular purpose." % ---------------------------------------------------------------------- % % % Please check for the latest version of the code and paper at % www.lx.it.pt/~mtf/GPSR % % ===== Required inputs ============= % % y: 1D vector or 2D array (image) of observations % % A: if y and x are both 1D vectors, A can be a % k*n (where k is the size of y and n the size of x) % matrix or a handle to a function that computes % products of the form A*v, for some vector v. % In any other case (if y and/or x are 2D arrays), % A has to be passed as a handle to a function which computes % products of the form A*x; another handle to a function % AT which computes products of the form A'*x is also required % in this case. The size of x is determined as the size % of the result of applying AT. % % tau: usually, a non-negative real parameter of the objective % function (see above). It can also be an array, the same % size as x, with non-negative entries; in this case, % the objective function weights differently each element % of x, that is, it becomes % 0.5*|| y - A x ||_2^2 + tau^T * abs(x) % % ===== Optional inputs ============= % % % 'AT' = function handle for the function that implements % the multiplication by the conjugate of A, when A % is a function handle. If A is an array, AT is ignored. % % 'StopCriterion' = type of stopping criterion to use % 0 = algorithm stops when the relative % change in the number of non-zero % components of the estimate falls % below 'ToleranceA' % 1 = stop when the relative % change in the objective function % falls below 'ToleranceA' % 2 = stop when the norm of the difference between % two consecutive estimates, divided by the norm % of one of them falls below toleranceA % 3 = stop when LCP estimate of relative % distance to solution % falls below 'ToleranceA' % 4 = stop when the objective function % becomes equal or less than toleranceA. % 5 = stop when the norm of the difference between % two consecutive estimates, divided by the norm % of one of them falls below toleranceA % Default = 3. % % 'ToleranceA' = stopping threshold; Default = 0.01 % % 'Debias' = debiasing option: 1 = yes, 0 = no. % Default = 0. % % 'ToleranceD' = stopping threshold for the debiasing phase: % Default = 0.0001. % If no debiasing takes place, this parameter, % if present, is ignored. % % 'MaxiterA' = maximum number of iterations allowed in the % main phase of the algorithm. % Default = 10000 % % 'MiniterA' = minimum number of iterations performed in the % main phase of the algorithm. % Default = 5 % % 'MaxiterD' = maximum number of iterations allowed in the % debising phase of the algorithm. % Default = 200 % % 'MiniterD' = minimum number of iterations to perform in the % debiasing phase of the algorithm. % Default = 5 % % 'Initialization' must be one of {0,1,2,array} % 0 -> Initialization at zero. % 1 -> Random initialization. % 2 -> initialization with A'*y. % array -> initialization provided by the user. % Default = 0; % % 'Monotone' = enforce monotonic decrease in f, or not? % any nonzero -> enforce monotonicity % 0 -> don't enforce monotonicity. % Default = 1; % % 'Continuation' = Continuation or not (1 or 0) % Specifies the choice for a continuation scheme, % in which we start with a large value of tau, and % then decrease tau until the desired value is % reached. At each value, the solution obtained % with the previous values is used as initialization. % Default = 0 % % 'ContinuationSteps' = Number of steps in the continuation procedure; % ignored if 'Continuation' equals zero. % If -1, an adaptive continuation procedure is used. % Default = -1. % % 'FirstTauFactor' = Initial tau value, if using continuation, is % obtained by multiplying the given tau by % this factor. This parameter is ignored if % 'Continuation' equals zero. % Default = such that the first tau is equal to % 0.5*max(abs(AT(y))). % % 'True_x' = if the true underlying x is passed in % this argument, MSE evolution is computed % % 'AlphaMin' = the alphamin parameter of the BB method. % (See the paper for details) % Default = 1e-30; % % 'AlphaMax' = the alphamax parameter of the BB method. % (See the paper for details) % Default = 1e30; % % 'Verbose' = work silently (0) or verbosely (1) % % =================================================== % ============ Outputs ============================== % x = solution of the main algorithm % % x_debias = solution after the debiasing phase; % if no debiasing phase took place, this % variable is empty, x_debias = []. % % objective = sequence of values of the objective function % % times = CPU time after each iteration % % debias_start = iteration number at which the debiasing % phase started. If no debiasing took place, % this variable is returned as zero. % % mses = sequence of MSE values, with respect to True_x, % if it was given; if it was not given, mses is empty, % mses = []. % ======================================================== % test for number of required parametres if (nargin-length(varargin)) ~= 3 error('Wrong number of required parameters'); end % flag for initial x (can take any values except 0,1,2) Initial_X_supplied = 3333; % Set the defaults for the optional parameters stopCriterion = 3; tolA = 0.01; tolD = 0.0001; debias = 0; maxiter = 10000; maxiter_debias = 500; miniter = 5; miniter_debias = 5;