FRANAITER Iterative analysis
Usage: c=franaiter(F,f);
[c,relres,iter]=franaiter(F,f,...);
Input parameters:
F : Frame.
f : Signal.
Ls : Length of signal.
Output parameters:
c : Array of coefficients.
relres : Vector of residuals.
iter : Number of iterations done.
c=FRANAITER(F,f) computes the frame coefficients c of the signal f*
using an iterative method such that perfect reconstruction can be
obtained using FRSYN. FRANAITER always works, even when FRANA
cannot generate perfect reconstruction coefficients.
[c,relres,iter]=FRANAITER(...) additionally returns the relative
residuals in a vector relres and the number of iteration steps iter.
*Note:* If it is possible to explicitly calculate the canonical dual
frame then this is usually a much faster method than invoking
FRANAITER.
FRANAITER takes the following parameters at the end of the line of
input arguments:
'tol',t Stop if relative residual error is less than the
specified tolerance. Default is 1e-9 (1e-5 for single precision)
'maxit',n Do at most n iterations.
'pg' Solve the problem using the Conjugate Gradient
algorithm. This is the default.
'pcg' Solve the problem using the Preconditioned Conjugate Gradient
algorithm.
'print' Display the progress.
'quiet' Don't print anything, this is the default.
Examples
--------
The following example shows how to rectruct a signal without ever
using the dual frame:
f=greasy;
F=frame('dgtreal','gauss',40,60);
[c,relres,iter]=franaiter(F,f,'tol',1e-14);
r=frsyn(F,c);
norm(f-r)/norm(f)
semilogy(relres);
title('Conversion rate of the CG algorithm');
xlabel('No. of iterations');
ylabel('Relative residual');
Url: http://ltfat.github.io/doc/frames/franaiter.html
See also: frame, frana, frsyn, frsyniter.
Package: ltfat