Function: gabelitistlasso
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