RANDSC Generate compressible signals from a specified distribution
% RANDSC Generate compressible signals from a specified distribution.
%---
% USAGE x = randcs(N, q, lambda, dist)
%
% N : signal length
% q : compressibility of the signal
%
% [Magnitudes of the generated signal coefficients, when sorted
% in decreasing order, has an expected power-law decay rate of
% 1/q. When q is in (0 1], the signal is considered compressible.
% Negative q input uses the default value:
%
% (default) q=1 ]
%
% lambda : positive scaling parameter
%
% (default) lambda=1
%
% dist : signal distribution
%
% [Options
% (default) 't' Student's t
% 'gpd' generalized Pareto
% 'logn' log-normal
% 'ev' extreme value (Frechet)
% 'logl' log-logistic
% -distributions with forced compressibility-
% 'ggd' generalized Gaussian
% 'wbl' Weibull
% 'gam' gamma ]
%
% Output vector x is a (1 x N)-dimensional compressible signal
% realization from the specified distribution.
%
% When q and lambda are (M x 1) vectors, x is an (M x N) matrix whose
% i-th row corresponds to the compressible signal realization from
% (q(i),lambda(i))-pair. When one of q and lambda is a scalar, it is
% replicated M times.
%
% -see
%
% @inproceedings{cevherNIPS09,
% author = "Cevher, V.",
% title = "Learning with compressible priors",
% booktitle = "NIPS",
% address= "Vancouver, B.C., Canada",
% year = "7--9 December 2009",}
%
%--------------------------------------------------------------------
% 9/20/2009, by Volkan Cevher. volkan@rice.edu. ver.1.0. For FUN. -RiceU.
%--------------------------------------------------------------------
% NOTES:
% 1. Distribution definitions can be found in cite{cevherNIPS09}.
% 2. Negative input values forces default parameters.
% 3. The distributions 'ggd', 'wbl', and 'gam' lose their
% compressibility as the dimensions grow. RANDCS automatically
% adjusts the distribution paramters to provide the desired decay for
% the specified dimension; see \cite{cevherNIPS09}.
%
%--------------------------------------------------------------------
Author: Volkan Cevher