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opWavelet2.m
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classdef opWavelet2 < opSpot
%OPWAVELET Wavelet operator.
%
% opWavelet(P,Q,FAMILY) creates a Wavelet operator of given FAMILY for
% signals of size P-by-1. The wavelet transformation is computed using
% the Rice Wavelet Toolbox. The values supported for FAMILY are
% 'Daubechies' and 'Haar'.
%
% opWavelet(P,Q,FAMILY,FILTER,LEVELS,REDUNDANT,TYPE) allows for four
% additional parameters: FILTER (default 8) specifies the filter length,
% which must be even. LEVELS (default 5) gives the number of levels in
% the transformation. P and Q do not need to be divisible by 2^LEVELS.
% However, if LEVELS is bigger than LOG2(MIN(P,Q)), then LEVELS is
% adjusted to be equal to FLOOR(LOG2(MIN(P,Q))).
% The Boolean field REDUNDANT (default false) indicates whether the wavelet
% is redundant. TYPE (default 'min') indictates what type of solution is
% desired; 'min' for minimum phase, 'max' for maximum phase, and 'mid'
% for mid-phase solutions.
%
% The opWavelet operator is linear but not orthogonal. Therefore, the
% transpose of the operator is not the inverse operator. However, the
% inverse of the operator can be obtained through a left-inverse
% operation. For example:
% W = opWavelet(...)
% y = W*x
% if z = W'*y, then z ~= x
% but, u = W\y, then u = x
% Copyright 2007-2009, Rayan Saab, Ewout van den Berg and Michael P. Friedlander
%
% June 6, 2012: Added mirror symmetric extension of signals that are not
% integer multiples of 2^levels.
% Hassan Mansour (hassanm@cs.ubc.ca)
% June 25, 2012: Overloaded mldivide function to compute the inverse of
% the operator.
% Hassan Mansour (hassanm@cs.ubc.ca)
%
% See the file COPYING.txt for full copyright information.
% Use the command 'spot.gpl' to locate this file.
% http://www.cs.ubc.ca/labs/scl/spot
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Properties
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
properties( SetAccess = private, GetAccess = public )
family = 'Daubechies'; % Wavelet family
lenFilter = 8; % Filter length
filter % Filter computed by daubcqf
levels = 5; % Number of levels
typeFilter = 'min'
redundant = false; % Redundant flag
nseg
signal_dims % Dimensions of the signal domain
coeff_dims % Dimensions of extended coefficients
funHandle % Multiplication function
funHandle2 % Divide function
end % Properties
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Methods - public
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
methods
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% opWavelet. Constructor.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function op = opWavelet2(p,q,family,lenFilter,levels,redundant,typeFilter)
if nargin <= 2 || isempty(family)
family = 'Daubechies';
end
if nargin < 5 || isempty(levels)
levels = 5;
end
if nargin >= 6 && redundant
if p == 1 || q == 1
nseg = levels + 1;
else
nseg = 3*levels + 1;
end
n = p*q;
% find coefficient dimensions
[pext, qext, levels] = CoeffDims(p, q, levels);
m = pext*qext*nseg;
redundant = true;
else
nseg = [];
n = p*q;
% find coefficient dimensions
[pext, qext, levels] = CoeffDims(p, q, levels);
m = pext*qext;
redundant = false;
end
op = op@opSpot('Wavelet2', m, n);
op.signal_dims = [p, q];
op.coeff_dims = [pext, qext];
op.levels = levels;
op.redundant = redundant;
op.nseg = nseg;
if nargin >= 4 && ~isempty(lenFilter)
op.lenFilter = lenFilter;
end
if nargin >= 7 && ischar(typeFilter)
op.typeFilter = typeFilter;
end
switch lower(family)
case {'daubechies'}
op.family = 'Daubechies';
op.filter = spot.rwt.daubcqf(op.lenFilter,op.typeFilter);
case {'haar'}
op.family = 'Haar';
op.filter = spot.rwt.daubcqf(0);
otherwise
error('Wavelet family %s is unknown.', family);
end
% Initialize function handle
if redundant
op.funHandle = @multiply_redundant_intrnl;
op.funHandle2 = @divide_redundant_intrnl;
else
op.funHandle = @multiply_intrnl;
op.funHandle2 = @divide_intrnl;
end
end % function opWavelet
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Divide
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function y = mldivide(op,x)
y = op.funHandle2(op,x);
end % function multiply
end % methods - public
methods( Access = private )
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% matvec. Application of Wavlet operator.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function y = multiply_intrnl(op,x,mode)
p = op.signal_dims(1);
q = op.signal_dims(2);
pext = op.coeff_dims(1);
qext = op.coeff_dims(2);
levels = op.levels; filter = op.filter;
if issparse(x), x = full(x); end
% apply matvec operation
R = opExtend(p,q,pext,qext);
if mode == 1
% extend the signal
xext = R*x;
% reshape the extended signal
Xmat = reshape(xext,pext,qext);
if isreal(x)
y = spot.rwt.mdwt(Xmat, filter, levels);
else
y1 = spot.rwt.mdwt(real(Xmat), filter, levels);
y2 = spot.rwt.mdwt(imag(Xmat), filter, levels);
y = y1 + sqrt(-1) * y2;
end
y = y(:);
else % mode == 2
Xmat = reshape(x,pext,qext);
if isreal(x)
y = spot.rwt.midwt(Xmat, filter, levels);
else
y1 = spot.rwt.midwt(real(Xmat), filter, levels);
y2 = spot.rwt.midwt(imag(Xmat), filter, levels);
y = y1 + sqrt(-1) * y2;
end
% apply adjoint of extension operator
y = R'*y(:);
end
end % function matvec
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% matvec_redundant. Application of redundant Wavlet operator.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function y = multiply_redundant_intrnl(op,x,mode)
p = op.signal_dims(1);
q = op.signal_dims(2);
pext = op.coeff_dims(1);
qext = op.coeff_dims(2);
nseg = op.nseg;
levels = op.levels; filter = op.filter;
if issparse(x), x = full(x); end
R = opExtend(p,q,pext,qext);
if mode == 1
% extend the signal
xext = R*x;
% reshape the extended signal
Xmat = reshape(xext,pext,qext);
if isreal(x)
[yl,yh] = spot.rwt.mrdwt(Xmat, filter, levels);
y = [yl,yh];
else
[yl1,yh1] = spot.rwt.mrdwt(real(Xmat), filter, levels);
[yl2,yh2] = spot.rwt.mrdwt(imag(Xmat), filter, levels);
y = [yl1,yh1] + sqrt(-1) * [yl2,yh2];
end
y = y(:);
else % mode == 2
xl = reshape(x(1:pext*qext),pext,qext);
xh = reshape(x(pext*qext+1:end),pext,(nseg-1)*qext);
if isreal(x)
y = spot.rwt.mirdwt(xl, xh, filter, levels);
else
y1 = spot.rwt.mirdwt(real(xl), real(xh), filter, levels);
y2 = spot.rwt.mirdwt(imag(xl), imag(xh), filter, levels);
y = y1 + sqrt(-1) * y2;
end
% apply adjoint of extension operator
y = R'*y(:);
end
end % function matvec_redundant
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% divide_intrnl. Application of redundant Wavlet operator.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function y = divide_intrnl(op,x)
p = op.signal_dims(1);
q = op.signal_dims(2);
pext = op.coeff_dims(1);
qext = op.coeff_dims(2);
levels = op.levels; filter = op.filter;
if issparse(x), x = full(x); end
Xmat = reshape(x,pext,qext);
if isreal(x)
y = spot.rwt.midwt(Xmat, filter, levels);
else
y1 = spot.rwt.midwt(real(Xmat), filter, levels);
y2 = spot.rwt.midwt(imag(Xmat), filter, levels);
y = y1 + sqrt(-1) * y2;
end
% clip signal back to original dimensions
y = y(1:p, 1:q);
y = y(:);
end % function divide
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% divide_intrnl. Application of redundant Wavlet operator.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function y = divide_redundant_intrnl(op,x)
p = op.signal_dims(1);
q = op.signal_dims(2);
pext = op.coeff_dims(1);
qext = op.coeff_dims(2);
nseg = op.nseg;
levels = op.levels; filter = op.filter;
if issparse(x), x = full(x); end
xl = reshape(x(1:pext*qext),pext,qext);
xh = reshape(x(pext*qext+1:end),pext,(nseg-1)*qext);
if isreal(x)
y = spot.rwt.mirdwt(xl, xh, filter, levels);
else
y1 = spot.rwt.mirdwt(real(xl), real(xh), filter, levels);
y2 = spot.rwt.mirdwt(imag(xl), imag(xh), filter, levels);
y = y1 + sqrt(-1) * y2;
end
% clip signal back to original dimensions
y = y(1:p, 1:q);
y = y(:);
end % function divide
end % methods - private
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Methods - protected
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
methods( Access = protected )
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Multiply
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function y = multiply(op,x,mode)
y = op.funHandle(op,x,mode);
end % function multiply
end % methods - protected
end % classdef
function [pext, qext, levels] = CoeffDims(p, q, levels)
if p >= 2^levels
plevels = levels;
if q >= 2^levels
qext = ceil(q/(2^levels))*2^levels;
elseif q > 1
qlevels = floor(log2(q));
levels = min(plevels,qlevels);
qext = ceil(q/(2^levels))*2^levels;
else
qext = q;
end
pext = ceil(p/(2^levels))*2^levels;
elseif p > 1
plevels = floor(log2(p));
if q >= 2^levels
levels = min(levels,plevels);
qext = ceil(q/(2^levels))*2^levels;
elseif q > 1
qlevels = floor(log2(q));
levels = min(plevels,qlevels);
qext = ceil(q/(2^levels))*2^levels;
else
levels = min(levels,plevels);
qext = q;
end
pext = ceil(p/(2^levels))*2^levels;
else
pext = p;
if q >= 2^levels
qext = ceil(q/(2^levels))*2^levels;
elseif q > 1
levels = floor(log2(q));
qext = ceil(q/(2^levels))*2^levels;
else
qext = q;
end
end
end