GABELITISTLASSO Elitist LASSO regression in Gabor domain
Usage: [tc,xrec] = gabelitistlasso(x,g,a,M,lambda,C,tol,maxit)
Input parameters:
x : Input signal
g : Synthesis window function
a : Length of time shift
M : Number of channels
lambda : Regularization parameter, controls sparsity of the
solution
Output parameters:
tc : Thresholded coefficients
relres : Vector of residuals.
iter : Number of iterations done.
xrec : Reconstructed signal
GABELITISTLASSO(x,g,a,M,lambda) solves the elitist LASSO regression
problem in the Gabor domain: minimize a functional of the synthesis
coefficients defined as the sum of half the l^2 norm of the
approximation error and the mixed l^2 / l^1 norm of the coefficient
sequence, with a penalization coefficient lambda.
The matrix of Gabor coefficients is labelled in terms of groups and
members. The obtained expansion is sparse in terms of groups, no
sparsity being imposed to the members of a given group. This is achieved
by a regularization term composed of l^2 norm within a group, and l^1 norm
with respect to groups.
[tc,relres,iter] = GABELITISTLASSO(...) returns the residuals relres*
in a vector and the number of iteration steps done, maxit.
[tc,relres,iter,xrec] = GABELITISTLASSO(...) returns the reconstructed
signal from the coefficients, xrec. Note that this requires additional
computations.
The function takes the following optional parameters at the end of
the line of input arguments:
'freq' Group in frequency (search for tonal components). This is the
default.
'time' Group in time (search for transient components).
'C',cval Landweber iteration parameter: must be larger than
square of upper frame bound. Default value is the upper
frame bound.
'tol',tol Stopping criterion: minimum relative difference between
norms in two consecutive iterations. Default value is
1e-2.
'maxit',maxit
Stopping criterion: maximal number of iterations to do. Default value is 100.
'print' Display the progress.
'quiet' Don't print anything, this is the default.
'printstep',p
If 'print' is specified, then print every p'th
iteration. Default value is 10;
The parameters C, itermax and tol may also be specified on the
command line in that order: gabgrouplasso(x,g,a,M,lambda,C,tol,maxit).
The solution is obtained via an iterative procedure, called Landweber
iteration, involving iterative group thresholdings.
The relationship between the output coefficients is given by :
xrec = idgt(tc,g,a);
Url: http://ltfat.github.io/doc/deprecated/gabelitistlasso.html
See also: gablasso, gabframebounds.
Package: ltfat