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