thfig31.m

％ Atomizer Main Directory, Version .802 里面信号含有分解去噪合成过程的代码 ％---------------------------------------

% thfig31: BP Thesis Figure 3.1 -- Analyzing Carbon
%
%	(1) BOB cannot separate nonorthogonal atoms
%	(2) MP has difficulty in separate similar (close, overlapping) atoms
%	(3) BasisPursuit could handle both nonorthogonal and similar atoms
%
% Signal: Carbon
% Signal Length: 512
% Dictionary: Wavelet Packets with D = log2(n) and qmf = (Symmlet, 8)
% Observation:
%	(a) The signal: Carbon, which is made up of 4 close atoms from WP
%	(b) MOF phase plane is smeared out and very weak.
%	(c) BOB fails to pick up the dirac and two other atoms.
%	    Instead, it is using orthogonal atoms to represent the 
%	    nonorthogonal structure.
%	(d) MP picks up the dirac and the sinusoid, but it fails to 
%	    separate the four close WP atoms. MP initially selects 
%	    neither one of the 4 true atoms. Instead, it selects
%	    the atom at the center of the 4 true atoms, the atom which
%	    has a bigger cosine product with the signal than any of
%	    the 4 true atoms. Because of this mistake, MP is forced to
%	    make a series of alternating corrections, which suggests
%	    a rather complicated structure.
%	(e) BP does a perfect job.
%

help thfig31

n = 512; D = log2(n);
qmf = MakeONFilter('Symmlet', 8);
x = InputSignal('Carbon', n);

time = cputime;
cMOF = MOF(x, 'WP', D, qmf, 0);
cputime1 = cputime - time;
time = cputime;
cBOB = BOB(x, 'WP', D, qmf, 0);
cputime2 = cputime - time;
time = cputime;
cMP = MP(x, 'WP', D, qmf, 0);
cputime3 = cputime - time;
time = cputime;
cBP = BP_Interior(x, 'WP', D, qmf, 0);
cputime4 = cputime - time;

fprintf('\n')
fprintf('CPU Running Time of MOF = %8.4e\n', cputime1);
fprintf('CPU Running Time of BOB = %8.4e\n', cputime2);
fprintf('CPU Running Time of  MP = %8.4e\n', cputime3);
fprintf('CPU Running Time of  BP = %8.4e\n', cputime4);


%%%Figures
figure(1);clf
subplot(3,2,1);
t = (1:n)' / n;
plot(t, x);title('(a) Signal: Carbon');
NameOfDict = 'WP'; par2 = qmf; TFScale = 1;
subplot(3,2,3);PhasePlane(cMOF, NameOfDict, n, par2, 256, TFScale);
subplot(3,2,4);PhasePlane(cBOB, NameOfDict, n, par2, 256, TFScale);
subplot(3,2,5);PhasePlane(cMP, NameOfDict, n, par2, 256, TFScale);
subplot(3,2,6);PhasePlane(cBP, NameOfDict, n, par2, 256, TFScale);
subplot(3,2,3); title('(b) Phase Plane: MOF')
subplot(3,2,4); title('(c) Phase Plane: BOB')
subplot(3,2,5); title('(d) Phase Plane: MP')
subplot(3,2,6); title('(e) Phase Plane: BP')