GABCONVEXOPT Compute a window using convex optimization
Usage: gout=gabconvexopt(g,a,M);
gout=gabconvexopt(g,a,M, varagin);
Input parameters:
g : Window function /initial point (tight case)
a : Time shift
M : Number of Channels
Output parameters:
gout : Output window
iter : Number of iterations
relres : Reconstruction error
GABCONVEXOPT(g,a,M) computes a window gout which is the optimal
solution of the convex optimization problem below
gd = argmin_x ||alpha x||_1 + ||beta Fx||_1
+ ||omega (x -g_l) ||_2^2 + delta ||x ||_S0
+ gamma ||nabla F x ||_2^2 + mu ||nabla x ||_2^2
such that x satifies the constraints
Three constraints are possible:
x is dual with respect of g
x is tight
x is compactly supported on Ldual
*Note**: This function require the unlocbox. You can download it at
http://unlocbox.sourceforge.net
The function uses an iterative algorithm to compute the approximate.
The algorithm can be controlled by the following flags:
'alpha',alpha Weight in time. If it is a scalar, it represent the
weights of the entire L1 function in time. If it is a
vector, it is the associated weight assotiated to each
component of the L1 norm (length: Ldual).
Default value is alpha=0.
*Warning**: this value should not be too big in order to
avoid the the L1 norm proximal operator kill the signal.
No L1-time constraint: alpha=0
'beta',beta Weight in frequency. If it is a scalar, it represent the
weights of the entire L1 function in frequency. If it is a
vector, it is the associated weight assotiated to each
component of the L1 norm in frequency. (length: Ldual).
Default value is beta=0.
*Warning**: this value should not be too big in order to
avoid the the L1 norm proximal operator kill the signal.
No L1-frequency constraint: beta=0
'omega',omega Weight in time of the L2-norm. If it is a scalar, it represent the
weights of the entire L2 function in time. If it is a
vector, it is the associated weight assotiated to each
component of the L2 norm (length: Ldual).
Default value is omega=0.
No L2-time constraint: omega=0
'glike',g_l g_l is a windows in time. The algorithm try to shape
the dual window like g_l. Normalization of g_l is done
automatically. To use option omega should be different
from 0. By default g_d=0.
'mu', mu Weight of the smooth constraint Default value is 1.
No smooth constraint: mu=0
'gamma', gamma Weight of the smooth constraint in frequency. Default value is 1.
No smooth constraint: gamma=0
'delta', delta Weight of the S0-norm. Default value is 0.
No S0-norm: delta=0
'support' Ldual Add a constraint on the support. The windows should
be compactly supported on Ldual.
'tight' Look for a tight windows
'dual' Look for a dual windows (default)
'painless' Construct a starting guess using a painless-case
approximation. This is the default
'zero' Choose a starting guess of zero.
'rand' Choose a random starting phase.
'tol',t Stop if relative residual error is less than the
specified tolerance.
'maxit',n Do at most n iterations. default 200
'print' Display the progress.
'debug' Display all the progresses.
'quiet' Don't print anything, this is the default.
'fast' Fast algorithm, this is the default.
'slow' Safer algorithm, you can try this if the fast algorithm
is not working. Before using this, try to iterate more.
'printstep',p If 'print' is specified, then print every p'th
iteration. Default value is p=10;
'hardconstraint' Force the projection at the end (default)
'softconstaint' Do not force the projection at the end
Url: http://ltfat.github.io/doc/gabor/gabconvexopt.html
See also: gaboptdual, gabdual, gabtight, gabfirtight, gabopttight.
Package: ltfat