Error function to optimize Berg parameters for multilayer sphere model
INPUTS:
berg : Berg parameters (2*NJ-1) x 1
R : Sphere Radii from innermost to outermost NL x 1
f : Legendre Expansion Weights to fit Berg Parameters ( Nmax x 1 )
NL = # of sphere layers;
Nmax = # of Legendre Expansion
NJ = # of Berg Dipoles
OUTPUTS:
delta: Error function value to be minimized
Z. Zhang, Phys. Med. Biol., vol.40, pp. 335-349, 1995.
Copyright (C) 2011, ATR All Rights Reserved.
License : New BSD License(see VBMEG_LICENSE.txt)0001 function delta = vb_berg_error(berg, R, f) 0002 % Error function to optimize Berg parameters for multilayer sphere model 0003 % 0004 % INPUTS: 0005 % berg : Berg parameters (2*NJ-1) x 1 0006 % R : Sphere Radii from innermost to outermost NL x 1 0007 % f : Legendre Expansion Weights to fit Berg Parameters ( Nmax x 1 ) 0008 % 0009 % NL = # of sphere layers; 0010 % Nmax = # of Legendre Expansion 0011 % NJ = # of Berg Dipoles 0012 % 0013 % OUTPUTS: 0014 % delta: Error function value to be minimized 0015 % 0016 % Z. Zhang, Phys. Med. Biol., vol.40, pp. 335-349, 1995. 0017 % 0018 % 0019 % Copyright (C) 2011, ATR All Rights Reserved. 0020 % License : New BSD License(see VBMEG_LICENSE.txt) 0021 0022 NL = length(R); % Number of Sphere Layers 0023 Nmax = length(f); % Number of Legendre Series Terms 0024 NJ = (length(berg)+1)/2; % Number of Berg Dipoles 0025 mu = berg(1:NJ); % Berg Eccentricity Factors 0026 lam = [0.0 berg(NJ+1:2*NJ-1)]; % Berg Magnitude Factors 0027 0028 % Error function defined by Zhang Eq. (5i") 0029 delta = 0.0; 0030 r = R(1)/R(NL); 0031 0032 for n = 2:Nmax 0033 err0 = 0; 0034 for j=2:NJ 0035 err0 = err0 + lam(j)*( mu(j)^(n-1) - mu(1)^(n-1) ); 0036 end 0037 0038 err = ( r^(n-1) )*( f(n) - f(1)*mu(1)^(n-1) - err0 ); 0039 delta = delta + err*err; 0040 end 0041