www.pudn.com > nsct_toolbox.rar > nsdfbrec.m, change:2005-01-20,size:4931b


function y = nsdfbrec( x, dfilter ) 
% NSDFBREC   Nonsubsampled directional filter bank reconstruct. 
%   NSDFBREC reconstructs the image Y by a nonsubsampled directional filter bank 
%   with a binary-tree structure. The input has totally 2^clevels branches. 
%   There is no subsampling and hence the operation is shift-invariant. 
%   
%       nsdfbrec( x, dfilter ) 
% 
% INPUT: 
%   x: 
%       a cell vector of matrices, directional subbands.  
%	dfilter:	 
%		a string, directional filter name. 
%       a cell of matrices, including two directional filters and eight 
%       parallelogram filters. 
% 
% OUTPUT: 
%	y: 
%       a matrix, reconstructed image. 
% 
% See also:     DFILTERS, PARAFILTERS, NSSFBREC. 
 
% 
% History:  
%   08/07/2004  Created by Jianping Zhou. 
 
% Input check 
clevels = log2( length(x) ) ;     
if clevels ~= round(clevels) 
    error('Number of decomposition levels must be a non-negative integer'); 
end 
if clevels == 0 
    % No reconstruction, simply copy input to output 
    y = x{1};     
    return; 
end 
if ~ischar( dfilter ) 
    if iscell( dfilter ) 
        if length( dfilter ) ~= 4 
            error('You shall provide a cell of two 2D directional filters and two groups of 2D parallelogram filters!'); 
        end 
    else 
        error('You shall provide the name of directional filter or all filters!'); 
    end 
end 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
% Get fan filters, parallelogram filters, and basic sampling matrices 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
% Get the diamond filters, if necessary 
if ischar( dfilter ) 
     
    % Get the directional filters for the critically sampled DFB. 
    [h1, h2] = dfilters(dfilter, 'r'); 
    % A scale is required for the nonsubsampled case. 
    h1 = h1./sqrt(2) ; 
    h2 = h2./sqrt(2) ; 
     
    % Generate the first-level fan filters by modulations. 
    k1 = modulate2(h1, 'c'); 
    k2 = modulate2(h2, 'c');  
     
    % Obtain the parallelogram filters from the diamond filters 
    [f1, f2] = parafilters( h1, h2 ) ; 
 
else 
    % Copy the fan filters directly. 
    k1 = dfilter{1} ; 
    k2 = dfilter{2} ; 
     
    % Copy the parallelogram filters directly. 
    f1 = dfilter{3} ; 
    f2 = dfilter{4} ;     
end 
 
 
% Quincunx sampling matrices 
q1 = [1, -1; 1, 1]; 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
% First-level reconstruction 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
if clevels == 1  
    % No upsampling for filters at the first-level. 
    y = nssfbrec( x{1}, x{2}, k1, k2 ) ;         
     
else %Others 
    
     
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
% Third and higher levels reconstructions 
% To save the memory, we use the input cell vector to store 
% middle outputs. 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
             
    % Third and higher levels reconstructions, if necessary. 
    for l = clevels:-1:3 
        	 
        % The first half channels: 
        for k = 1:2^(l-2) 
             
            % Compute the upsampling matrix by the formula (3.18) of Minh N. Do's  
            % thesis. The upsampling matrix for the channel k in a l-levels DFB is 
            % M_k^{(l-1)} (refer to (3.18), pp. 53, Minh N. Do's thesis) 
             
            % Compute s_{(l-1)}(k): 
            slk = 2*floor( (k-1)/2 ) - 2^(l-3) + 1 ; 
            % Compute the sampling matrix: 
            mkl = 2*[ 2^(l-3), 0; 0, 1 ]*[1, 0; -slk, 1];  
            i = mod(k-1, 2) + 1; 
            % Reconstruct the two-channel filter bank: 
            x{k} = nssfbrec( x{2*k-1}, x{2*k}, f1{i}, f2{i}, mkl ); 
        end	 
	 
        % The second half channels: 
        for k = 2^(l-2)+1 : 2^(l-1) 
             
            % Compute the upsampling matrix by the extension of the formula (3.18)  
            % of Minh N. Do's thesis to the second half channels. 
            % thesis. The upsampling matrix for the channel k in a l-levels DFB is 
            % M_k^{(l-1)} (refer to notes by Jianping Zhou) 
         
            % Compute s_{(l-1)}(k): 
            slk = 2 * floor( (k-2^(l-2)-1) / 2 ) - 2^(l-3) + 1 ; 
            % Compute the sampling matrix: 
            mkl = 2*[ 1, 0; 0, 2^(l-3) ]*[1, -slk; 0, 1];  
            i = mod(k-1, 2) + 3; 
            % Reconstruct the two-channel filter bank: 
            x{k} = nssfbrec( x{2*k-1}, x{2*k}, f1{i}, f2{i}, mkl ); 
        end 
    end 
     
     
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
    % Second-level Decompositions 
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
    % Convolution with upsampled filters for the second-level 
    x{1} = nssfbrec( x{1}, x{2}, k1, k2, q1 ) ; 
    x{2} = nssfbrec( x{3}, x{4}, k1, k2, q1 ) ; 
     
    % No upsampling for filters at the first-level. 
    y = nssfbrec( x{1}, x{2}, k1, k2 ) ; 
     
end