bestrpbasis.m

beamlet变化的工具箱

%  BestRPBasis -- Best Ridgelet Packet Basis Algorithm
%   Usage
%     [btree,vtree] = BestRPBasis(RPtree,D,options,optionParam)
%   Inputs
%     RPtree    stat-RPtree (e.g output of CalcRPStatTree) real values.
%     D           a 2-vector defining maximum depth of splitting (in coordinate1
%                  direction and in coordinate2 direction)  D = [D1,D2]
%     options  Describes the constraints set on the BestBasis Algorithm. The initialization
% 	     of the control tree is dependant on these options.
%                   The values set in the control tree determine the flow of the bestbasis algorithm.
%                   i.e. determine the direction of splits allowed at each tree node.
%                   options may take the value:
%                      'NoConstraint' - any split direction allowed.
% 		optionParam = []
% 	        'GivenCoor1' - The splits in coor1 directions is defined by a 1D ctrlTree
% 		given in optionParam. The splits in coor2 direction can only FOLLOW 
% 		the splits in coor1 direction. The 1D ctrlTree must have same length as
% 		ctrltree (i.e. 2^(D1+1)-1     )
% 		optionParam = [OneDtree]
% 	        'GivenCoor2' - The splits in coor2 directions is defined by a 1D ctrlTree
% 		given in optionParam. The splits in coor1 direction can only FOLLOW 
% 		the splits in coor2 direction. The 1D ctrlTree must have same length as
% 		ctrltree (i.e. 2^(D2+1)-1     )
% 		optionParam = [OneDtree]
% 
%     optionParam    Parameters associated with the options.
% 
%   Outputs
%     btree    basis-RPtree of best basis
%     vtree    value of components of best basis
%                 vtree(1) holds value of best basis
% 
%   Description
% 
%     This routine provides an implementation of the best-ortho-basis
%     algorithm for the setting of dyadic recursive rectangular partitions
%     of the image domain.
%    
%     The algorithm is equally applicable to finding best anisotropic
%     Haar or Alpert bases and to finding best anisotropic cosine
%     packet bases subordinate to the rectangular
%     partitions.
% 
%     The approach differs from the approach in Packets/2-D because
%     the spatial partitioning is allowed to be anisotropic.  In the recursive
%     splitting, the choice at every stage is between vertical and horizontal
%     splitting of a given block. Denoted coordinate1 and coordinate2.
%     The approach is different than the approach in Anisotropic Packets/2-D
%     in that the Packets are calculated on the Pseudo Polar Fourier image.
%     Additionally in the current approach, inputs need not be rectangular, i.e.
%     tree and packets are rectangular based and maximum depth is defined 
%     seperately for coordinate1 and coordinate2.
% 
%     The best-basis algorithm is used to pick out the ``best'' 
%     basis from all the possible bases in the packet table.
%     Here ``best'' means minimizing an additive measure of
%     information, called entropy by Coifman and Wickerhauser.
% 
%     Once the RP-recttree of entropy values is created, BestRPBasis
%     selects the best basis.  The approach is to apply the pruning algorithm 
%     described for example in Wickerhauser's book.
% 
%     Theoretical literature employing the present algorithm and data structures 
%     includes the thesis of Bennett and the article of Donoho.
% 
%   Examples
%      get best basis for ``image''
%     RPtree = CalcRPStatTree(image,D1,D2,'Sine','Entropy');
%     [btree,vtree] = BestRPBasis(RPtree,D1,D2);
% 
%   See Also
%     Structure definitiosn for RPtree
% 
%   References
%     Wickerhauser, M.V.  _Adapted_Wavelet_Analysis_.  AK Peters (1994)
% 	 Bennett, N. Thesis, Yale University, 1997
% 	 Donoho, D. CART and Best Ortho Basis: A Connection. Ann. Stat. 1997
% 
%
%
% Part of BeamLab Version:200
% Built:Friday,23-Aug-2002 00:00:00
% This is Copyrighted Material
% For Copying permissions see COPYING.m
% Comments? e-mail [e-mail]
%
%
% Part of BeamLab Version:200
% Built:Saturday,14-Sep-2002 00:00:00
% This is Copyrighted Material
% For Copying permissions see COPYING.m
% Comments? e-mail [e-mail]
%