% mexSphericalPolarFourierImaging: estimate continuous DWI signal and EAP represented by coefficients of given basis.
%
% Usage:
% [signal] = mexSphericalPolarFourierImaging(dwi4DNoramlized, grad, bVec, params)
%
% Inputs:
% dwi4DNoramlized: 4D DWI data, normalized by b0 image;
% grad : orientation matrix where each row is an orientation (x,y,z), caresian format
% bVector: b values in a vector, each row is a b value
%
% params.MD0 : Typical mean diffusivity (MD) value. The default value is 0.7e-3.
% params.tau : Tau value. The default is calculated based on 4*pi*pi*tau=1.
% param.scale : Scale value for the SPF basis in radial part, the default value is set by tau and MD0 and tau
% params.sh: SH order
% params.ra: order in radial part
% params.lambdaSH : lambda in spherical part
% params.lambdaRA : lambda in radial part
% params.lambdaL1 : lambda for L1 solver
% params.odfOrder : odf order
% params.radius : Radius for EAP profile.
% params.mdImage : Mean diffusivity Image for adaptive scale.
% params.estimation : (LS, L1_2, L1_DL) LS: least square.
% L1_2 means Laplace-Beltrami weight (two regularization parameters lambdaSH and lambdaRA);
% L1_DL only use lambdaL1, because the learned dictionary corresponses the regularization matrix.
% params.solver : (FISTA_LS, SPAMS)
% FISTA_LS: FISTA using least square initialization.
% SPAMS (default): use spams' weighted lasso solver.
% params.maxIter : Maximal number of iteration in L1 FISTA.
% params.minChange : Minimal change percentage of the cost function and variable for l1 oprimization.
% params.mask : Mask file. 2D or 3D matrix.
%
% params.thread : Number of thread. Default is -1, which means it is automatically determined.
% params.verbose : Verbose level. 0: no output log. 1: normal log. 2: large log for debug.
%
% Outputs:
% signal: coefficient under a given basis, 4D image
%
%
% Reference:
% 1. "Model-Free, Regularized, Fast, and Robust Analytical Orientation Distribution Function Estimation",
% Jian Cheng, Aurobrata Ghosh, Rachid Deriche, Tianzi Jiang, Medical Image Computing and Computer-Assisted Intervention (MICCAI'10), vol. 6361, pp. 648–656, sep, 2010.
% 2. "Model-free and Analytical EAP Reconstruction via Spherical Polar Fourier Diffusion MRI",
% Jian Cheng, Aurobrata Ghosh, Tianzi Jiang, Rachid Deriche, Medical Image Computing and Computer-Assisted Intervention (MICCAI'10), vol. 6361, pp. 590–597, sep, 2010.
%
% Copyright (c) 2013, Jian Cheng <jian.cheng.1983@gmail.com>
%
