wICA(data,varargin)

%--------------- function [wIC,A,W] = wICA(data,varargin) -----------------
%
% Performs ICA on data matrix (row vector) and subsequent wavelet
% thresholding to remove low-amplitude activity from the computed ICs.
% This is useful for extracting artifact-only ICs in EEG (for example), and
% then subtracting the artifact-reconstruction from the original data.
%
% Code is interpretation/implementation of:
% Castellanos & Makarov, J. Neurosci. Method. 2006
%
% >>> INPUTS >>>
% Required:
% data = data matrix in row format
% Optional:
% type = "fastica" or "radical"...two different ICA algorithms based on
% entropy. "fastica" (default) is parametric, "radical" is nonparametric.
% mult = threshold multiplier...multiplies the computed threshold from
% "ddencmp" by this number. Higher thresh multipliers = less
% "background" (or low amp. signal) is kept in the wICs.
% plotting = 1 or 0. If 1, plots wIC vs. non-wavelet thresholded ICs
% Fs = sampling rate, (for plotting...default = 1);
% L = level set for stationary wavelet transform. Higher levels give
% better frequency resolution, but less temporal resolution.
% Default = 5
% wavename = wavelet family to use. type "wavenames" to see a list of
% possible wavelets. (default = "coif5");
%
% <<< OUTPUTS <<<
% wIC = wavelet-thresholded ICs
% A = mixing matrix (inv(W)) (optional)
% W = demixing matrix (inv(A)) (optional)
% IC = non-wavelet ICs (optional)
%
% * you can reconstruct the artifact-only signals as:
% artifacts = A*wIC;
% - upon reconstruction, you can then subtract the artifacts from your
% original data set to remove artifacts, for instance.
%
% Example:
% n = rand(10,1000);
% a = [zeros(1,400),[.5,.8,1,2,2.4,2.5,3.5,5,6.3,6,4,3.2,3,1.7,1,-.6,-2.2,-4,-3.6,-3,-1,0],zeros(1,578)];
% data = n + linspace(0,2,10)'*a;
% [wIC,A] = wICA(data,[],5,1);
% ahat = A*wIC;
% nhat = data-ahat;
% err = sum(sqrt((nhat-n).^2));
%
% By JMS, 11/10/2015
%---------------------------------------------------------------------------------------