s2let_spin_curvelet_tiling - Tile scaling functions and curvelets in harmonic space.
Default usage :
[cur_lm scal_l] = s2let_spin_curvelet_tiling(B, L, J_min, <options>)
cur_lm is an array containing the unrotated curvelets spherical harmonic coefficients.
scal_l is an array containing the scaling function spherical harmonic coefficients (l only).
B is the wavelet parameter,
L is the harmonic band-limit;
J_min the first wavelet to be used.
% Valid options include:
'Spin' = { Spin; (default=0) }
'SpinLowered' = { true [Apply normalisation factors for spin-lowered
wavelets and scaling function.],
false [Apply the usual normalisation factors such
that the wavelets fulfil the admissibility
condition (default)]}
'SpinLoweredFrom' = [integer; if the SpinLowered option is used, this
option indicates which spin number the wavelets
should be lowered from (default = 0)]
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S2LET package to perform wavelets transform on the Sphere.
Copyright (C) 2012-2016 Boris Leistedt, Jennifer Chan & Jason McEwen
See LICENSE.txt for license details
-----------------------------------------------------------0001 function [cur_lm scal_l] = s2let_spin_curvelet_tiling(B, L, J_min, varargin) 0002 % s2let_spin_curvelet_tiling - Tile scaling functions and curvelets in harmonic space. 0003 % 0004 % Default usage : 0005 % 0006 % [cur_lm scal_l] = s2let_spin_curvelet_tiling(B, L, J_min, <options>) 0007 % 0008 % cur_lm is an array containing the unrotated curvelets spherical harmonic coefficients. 0009 % scal_l is an array containing the scaling function spherical harmonic coefficients (l only). 0010 % B is the wavelet parameter, 0011 % L is the harmonic band-limit; 0012 % J_min the first wavelet to be used. 0013 % 0014 % % Valid options include: 0015 % 0016 % 'Spin' = { Spin; (default=0) } 0017 % 'SpinLowered' = { true [Apply normalisation factors for spin-lowered 0018 % wavelets and scaling function.], 0019 % false [Apply the usual normalisation factors such 0020 % that the wavelets fulfil the admissibility 0021 % condition (default)]} 0022 % 'SpinLoweredFrom' = [integer; if the SpinLowered option is used, this 0023 % option indicates which spin number the wavelets 0024 % should be lowered from (default = 0)] 0025 % 0026 % ----------------------------------------------------------- 0027 % S2LET package to perform wavelets transform on the Sphere. 0028 % Copyright (C) 2012-2016 Boris Leistedt, Jennifer Chan & Jason McEwen 0029 % See LICENSE.txt for license details 0030 % ----------------------------------------------------------- 0031 0032 p = inputParser; 0033 p.addRequired('B', @isnumeric); 0034 p.addRequired('L', @isnumeric); 0035 p.addRequired('J_min', @isnumeric); 0036 p.addParamValue('Spin', 0, @isnumeric); 0037 p.addParamValue('SpinLowered', false, @islogical); 0038 p.addParamValue('SpinLoweredFrom', 0, @isnumeric); 0039 p.parse(B, L, J_min, varargin{:}); 0040 args = p.Results; 0041 0042 J = s2let_jmax(L, B); 0043 Spin = args.Spin; 0044 if (args.SpinLowered ~= 0) 0045 original_spin= args.SpinLoweredFrom; % For spin-lowered curvelet: (i.e. use scalar curvelets for the transform : spin =0, SpinLoweredFrom = e.g. 2) 0046 else 0047 original_spin = 0 ; % (default - not to use spin-lowered wavelets). 0048 end 0049 0050 % ---------- 0051 % Curvelet directional component s_lm 0052 % ---------- 0053 signs = zeros(L,1); 0054 s_lm = zeros(L^2,1); 0055 % Perform precomputation. 0056 for (m=1:2:L-1) 0057 signs(m) = -1.0; 0058 signs(m+1) = 1.0; 0059 end 0060 % Skip the s_00 component as it is zero 0061 for el = 1:L-1 0062 % N.B. for curvelets, m = el; 0063 % N.B. the condition : m < L is satisfied; 0064 m = el; 0065 % for positive m 0066 ind_pm = ssht_elm2ind(el, m); 0067 s_lm(ind_pm)= sqrt(1./2.); 0068 % for negative m 0069 ind_nm = ssht_elm2ind(el, -m); 0070 s_lm(ind_nm)= signs(m)*conj(s_lm(ind_pm)); 0071 end 0072 0073 0074 % ---------- 0075 % Curvelet angular components: 0076 % ---------- 0077 [kappa kappa0] = s2let_transform_axisym_tiling(B, L, J_min); 0078 el_min = max(abs(Spin), abs(original_spin)); 0079 for j = J_min:J 0080 for el = el_min:L-1 0081 m = el; 0082 % positive m 0083 ind_pm = ssht_elm2ind(el, m); 0084 cur_lm{j-J_min+1}(ind_pm) = s_lm(ind_pm) * sqrt((2*el+1)/(8.0*pi*pi))* kappa(j+1,el+1) ; 0085 % negative m 0086 ind_nm = ssht_elm2ind(el, -m); 0087 cur_lm{j-J_min+1}(ind_nm) =((-1)^m)* conj(cur_lm{j-J_min+1}(ind_pm)) ; 0088 % if SpinLowered == true 0089 if (args.SpinLowered ~= 0) 0090 s2let_spin_lowered_norm_factor = s2let_spin_lowered_normalization(el, 'original_spin',original_spin); 0091 cur_lm{j-J_min+1}(ind_pm) = cur_lm{j-J_min+1}(ind_pm)*s2let_spin_lowered_norm_factor ; 0092 cur_lm{j-J_min+1}(ind_nm) = cur_lm{j-J_min+1}(ind_nm)*s2let_spin_lowered_norm_factor ; 0093 end 0094 end 0095 end 0096 0097 % ---------- 0098 % Scaling Function 0099 % ---------- 0100 scal_l = zeros(L^2,1); 0101 for el = el_min:L-1 0102 scal_l(el^2+el+1,1) = sqrt((2*el+1)/(4.0*pi)) *kappa0(el+1); 0103 % if SpinLowered == true 0104 if (args.SpinLowered ~= 0) 0105 s2let_spin_lowered_norm_factor = s2let_spin_lowered_normalization(el, 'original_spin',original_spin); 0106 scal_l(el^2+el+1,1) = scal_l(el^2+el+1,1) *s2let_spin_lowered_norm_factor ; 0107 end 0108 end 0109 0110 0111 end