s2let_transform_synthesis_lm2wav
Compute spin directional wavelet transform, input harmonic space output
in pixel space.
Default usage :
flm = s2let_transform_synthesis_lm2wav(f_wav, f_scal, <options>)
f_wav contains the input wavelet contributions -- MW sampling,
f_scal contains the input scaling contributions -- MW sampling,
flm is the output field -- harmonic space,
Option :
'Reality' = { false [do not assume corresponding signal f real (default)],
true [assume f real (improves performance)] }
'B' = { Dilation factor; B > 1 (default=2) }
'L' = { Harmonic band-limit; L > 1 (default=guessed from input) }
'N' = { Azimuthal/directional band-limit; N > 1 (default=L) }
'Spin' = { Spin; (default=0) }
'Upsample' = { false [multiresolution algorithm (default)],
true [full resolution wavelets] }
'Sampling' = { 'MW' [McEwen & Wiaux sampling (default)],
'MWSS' [McEwen & Wiaux symmetric sampling] }
'J_min' = { Minimum wavelet scale to consider;
0 <= J_min < log_B(L) (default=0) }
'OriginalSpin' = [integer; if the SpinLowered option is used, this
option indicates which spin number the wavelets
should be lowered from (default = 0)]
S2LET package to perform Wavelets transform on the Sphere.
Copyright (C) 2012-2015 Boris Leistedt & Jason McEwen
See LICENSE.txt for license details0001 function flm = s2let_transform_synthesis_lm2wav(f_wav, f_scal, varargin) 0002 0003 % s2let_transform_synthesis_lm2wav 0004 % Compute spin directional wavelet transform, input harmonic space output 0005 % in pixel space. 0006 % 0007 % Default usage : 0008 % 0009 % flm = s2let_transform_synthesis_lm2wav(f_wav, f_scal, <options>) 0010 % 0011 % f_wav contains the input wavelet contributions -- MW sampling, 0012 % f_scal contains the input scaling contributions -- MW sampling, 0013 % flm is the output field -- harmonic space, 0014 % 0015 % Option : 0016 % 'Reality' = { false [do not assume corresponding signal f real (default)], 0017 % true [assume f real (improves performance)] } 0018 % 'B' = { Dilation factor; B > 1 (default=2) } 0019 % 'L' = { Harmonic band-limit; L > 1 (default=guessed from input) } 0020 % 'N' = { Azimuthal/directional band-limit; N > 1 (default=L) } 0021 % 'Spin' = { Spin; (default=0) } 0022 % 'Upsample' = { false [multiresolution algorithm (default)], 0023 % true [full resolution wavelets] } 0024 % 'Sampling' = { 'MW' [McEwen & Wiaux sampling (default)], 0025 % 'MWSS' [McEwen & Wiaux symmetric sampling] } 0026 % 'J_min' = { Minimum wavelet scale to consider; 0027 % 0 <= J_min < log_B(L) (default=0) } 0028 % 'OriginalSpin' = [integer; if the SpinLowered option is used, this 0029 % option indicates which spin number the wavelets 0030 % should be lowered from (default = 0)] 0031 % 0032 % S2LET package to perform Wavelets transform on the Sphere. 0033 % Copyright (C) 2012-2015 Boris Leistedt & Jason McEwen 0034 % See LICENSE.txt for license details 0035 0036 len = size(f_wav); 0037 temp = f_wav{len}; 0038 sz = size(temp); 0039 if sz(1) == 2*sz(2)-1 || sz(2) == 2*sz(1)-1 0040 Lguessed = min([sz(1) sz(2)]); 0041 else 0042 Lguessed = min([sz(1) sz(2)])-1; 0043 end 0044 0045 p = inputParser; 0046 p.addRequired('f_wav'); 0047 p.addRequired('f_scal', @isnumeric); 0048 p.addParamValue('B', 2, @isnumeric); 0049 p.addParamValue('L', Lguessed, @isnumeric); 0050 p.addParamValue('J_min', 0, @isnumeric); 0051 p.addParamValue('N', Lguessed, @isnumeric); 0052 p.addParamValue('Spin', 0, @isnumeric); 0053 p.addParamValue('Upsample', false, @islogical); 0054 p.addParamValue('Sampling', 'MW', @ischar); 0055 p.addParamValue('Reality', false, @islogical); 0056 p.addParamValue('OriginalSpin', 0, @isnumeric); 0057 p.parse(f_wav, f_scal, varargin{:}); 0058 args = p.Results; 0059 0060 if strcmp(args.Sampling, 'MWSS') 0061 f_scal_vec = s2let_mwss_arr2vec(f_scal); 0062 else 0063 f_scal_vec = s2let_mw_arr2vec(f_scal); 0064 end 0065 if(all(isreal(f_scal_vec))) 0066 f_scal_vec = complex(f_scal_vec,0); 0067 end 0068 J = s2let_jmax(args.L, args.B); 0069 0070 f_wav_vec = []; 0071 0072 offset = 0; 0073 if strcmp(args.Sampling, 'MWSS') 0074 for j = args.J_min:J 0075 for en = 1:args.N 0076 if args.Upsample 0077 band_limit = args.L; 0078 else 0079 band_limit = min([ s2let_bandlimit(j,args.J_min,args.B,args.L) args.L ]); 0080 end 0081 temp = f_wav{j+1-args.J_min, en}; 0082 for t = 1:band_limit+1 0083 for p = 1:2*band_limit 0084 ind = offset + (t-1) * 2 * band_limit + p; 0085 f_wav_vec = [f_wav_vec temp(t,p)]; 0086 end 0087 end 0088 offset = offset + (band_limit+1) * 2 * band_limit; 0089 end 0090 end 0091 else 0092 for j = args.J_min:J 0093 for en = 1:args.N 0094 if args.Upsample 0095 band_limit = args.L; 0096 else 0097 band_limit = min([ s2let_bandlimit(j,args.J_min,args.B,args.L) args.L ]); 0098 end 0099 temp = f_wav{j+1-args.J_min, en}; 0100 for t = 1:band_limit 0101 for p = 1:2*band_limit-1 0102 ind = offset + (t-1) * ( 2 * band_limit - 1) + p; 0103 f_wav_vec = [f_wav_vec temp(t,p)]; 0104 end 0105 end 0106 offset = offset + band_limit * (2 * band_limit - 1); 0107 end 0108 end 0109 end 0110 0111 0112 if(all(isreal(f_wav_vec))) 0113 f_wav_vec = complex(f_wav_vec,0); 0114 end 0115 0116 flm = s2let_transform_synthesis_lm2wav_mex(f_wav_vec, f_scal_vec, args.B, args.L, args.J_min, ... 0117 args.N, args.Spin, args.Reality, args.Upsample, ... 0118 args.OriginalSpin, ... 0119 args.Sampling); 0120 0121 end