-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy pathDictionary_gen_and_Fig4.m
334 lines (288 loc) · 16.3 KB
/
Dictionary_gen_and_Fig4.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
%% MTF dictionary generation script. Daniel West 2020.
close all; clear all; clc;
%% Generate different parameter combinations.
% Specify ranges for tissue parameters.
T1f = 0.2:0.5:4; T1s = 0.1:0.2:1; T1d = 2e-3:4e-3:25e-3;
T2f = 50e-3:70e-3:500e-3; T2s = 5e-6:3e-6:20e-6;
M0s = 0:0.05:0.25; delta = 0:0.2:1; k = 40:20:100;
B0_var = -pi:pi/3:pi;
T12x_cv = combvec(T1f,T1s,T1d,T2f,T2s).'; T12x_initial_size = size(T12x_cv,1);
% Remove entries where T2a >= T1a (as per Hilbert et al.)
for ii = 1:T12x_initial_size
if T12x_cv(ii,4) >= T12x_cv(ii,1)
T12x_cv(ii,:) = NaN;
end
end
T12x_cv(any(isnan(T12x_cv),2),:) = []; T12x = unique(T12x_cv,'rows'); % Remove repeated rows (if any).
M0_cv = combvec(M0s,delta,k).'; M0_initial_size = size(M0_cv,1);
% If M0b = 0, set f and K to 0.
for ii = 1:M0_initial_size
if M0_cv(ii,1) == 0
M0_cv(ii,2:3) = 0;
end
end
M0f = 1-M0_cv(:,1); M0_comp = unique([M0f, M0_cv],'rows'); % M0f is first dim, M0s is second and delta is third.
noMT_idx = find(M0_comp(:,2) == 0); M0_noMT = M0_comp(noMT_idx,:);
MT_idx = find(M0_comp(:,3) == 0 & M0_comp(:,2) ~= 0); M0_MT = M0_comp(MT_idx,:);
ihMT_idx = find(M0_comp(:,3) ~= 0); M0_ihMT = M0_comp(ihMT_idx,:);
% Form M0 matrix and remove repeated rows (if any).
M0_noMT = unique([M0_noMT(:,1) , M0_noMT(:,2).*(1-M0_noMT(:,3)) , M0_noMT(:,2).*M0_noMT(:,3)],'rows');
M0_MT = unique([M0_MT(:,1) , M0_MT(:,2).*(1-M0_MT(:,3)) , M0_MT(:,2).*M0_MT(:,3)],'rows');
M0_ihMT = unique([M0_ihMT(:,1) , M0_ihMT(:,2).*(1-M0_ihMT(:,3)) , M0_ihMT(:,2).*M0_ihMT(:,3)],'rows');
% Combine all input parameters into a single matrix.
Var_Params_noMT = unique(combvec(M0_noMT.',T12x.',0,B0_var).','rows');
Var_Params_MT = unique(combvec(M0_MT.',T12x.',k,B0_var).','rows');
Var_Params_ihMT = unique(combvec(M0_ihMT.',T12x.',k,B0_var).','rows');
% Remove infeasible elements for each tissue.
for ii = 1:size(Var_Params_noMT,1)
if Var_Params_noMT(ii,4) < 2.5 || Var_Params_noMT(ii,7) < 300e-3
Var_Params_noMT(ii,:) = NaN;
end
end
Var_Params_noMT(any(isnan(Var_Params_noMT),2),:) = [];
for ii = 1:size(Var_Params_MT,1)
if Var_Params_MT(ii,4) > 2.5 || Var_Params_MT(ii,7) > 300e-3
Var_Params_MT(ii,:) = NaN;
end
end
Var_Params_MT(any(isnan(Var_Params_MT),2),:) = [];
for ii = 1:size(Var_Params_ihMT,1)
if Var_Params_ihMT(ii,4) > 1.5 || Var_Params_ihMT(ii,7) > 150e-3
Var_Params_ihMT(ii,:) = NaN;
end
end
Var_Params_ihMT(any(isnan(Var_Params_ihMT),2),:) = [];
%% Specify sequence details.
flips = d2r(29.51); TR = 5.33e-3; Dur = 2.51e-3; Delta = 8058.48; n1B = 300; nMB = 300;
TBW = 2; B1rms = 4;
% Generate pulses.
pulses = {};
[pulses{1,1},~,~,~,~] = gen_CSMT_pulse_Diffnp(flips,Dur,TR,B1rms,Delta,2,nMB,n1B,'sigma',2);
[pulses{1,2},~,~,~,~] = gen_CSMT_pulse_Diffnp(flips,Dur,TR,B1rms,Delta,3,nMB,n1B,'sigma',2);
dt = 6.4e-6;
ff = linspace(-20e3,20e3,1000)';
df = ff(2)-ff(1);
nt = length(pulses{1});
tt = dt*(1:nt);
F = exp(-1i*2*pi*ff*tt)*(dt*1e3)/sqrt(numel(ff));
b1sqrd_tau = {}; b1sqrd = {};
band_ix = {};
bw = 2e3;
band_ix{1} = find((ff>-(Delta+bw/2))&(ff<-(Delta-bw/2)));
band_ix{2} = find((ff>-bw/2)&(ff<bw/2));
band_ix{3} = find((ff>(Delta-bw/2))&(ff<(Delta+bw/2)));
for jj = 1:2
pwr_spec = abs(F*pulses{1,jj}).^2;
b1sqrd_tau{1,jj} = zeros([1 3]);
for kk=1:3
b1sqrd_tau{1,jj}(kk) = sum(pwr_spec(band_ix{kk}))*df;
end
tau = 1e3*dt*nt;
b1sqrd{1,jj} = b1sqrd_tau{1,jj}/tau;
end
np_Total = (2*nMB)+(2*n1B); % Total number of pulses.
% Pre-compute lineshape for different T2b - removed loop because T2b fixed.
df_1B = [0 0 0]; df_2B = [0 0 Delta]; df_3B = [-Delta 0 Delta];
for ii = 1:length(T2s)
[G_3B(ii,:),wloc_3B(ii)] = SuperLorentzian_LSint(T2s(ii),df_3B);
[G_2B(ii,:),wloc_2B(ii)] = SuperLorentzian_LSint(T2s(ii),df_2B);
[G_1B(ii,:),wloc_1B(ii)] = SuperLorentzian_LSint(T2s(ii),df_1B);
end
% Calculates signals for one sequence "period".
Mss_Total_noMT = zeros(size(Var_Params_noMT,1),np_Total); whos Mss_Total_noMT;
Mss_Total_MT = zeros(size(Var_Params_MT,1),np_Total); whos Mss_Total_MT;
Mss_Total_ihMT = zeros(size(Var_Params_ihMT,1),np_Total); whos Mss_Total_ihMT;
%% Simulate signals for different cparameter combinations.
delete(gcp('nocreate')); c = parcluster('local'); c.NumWorkers = 16; parpool(c, c.NumWorkers);
% No MT dictionary creation.
tic
parfor mm = 1:size(Var_Params_noMT,1)
if Var_Params_noMT(mm,8) == T2s(1)
Mss_Total_noMT(mm,:) = Dictionary_function_CSS(flips,TR,Dur,Var_Params_noMT(mm,10),Var_Params_noMT(mm,4:6),Var_Params_noMT(mm,7:8),Var_Params_noMT(mm,1:3),Var_Params_noMT(mm,9),Delta,TBW,nMB,n1B,b1sqrd,G_1B(1,:),G_2B(1,:),G_3B(1,:),wloc_1B(1),wloc_2B(1),wloc_3B(1));
end
if Var_Params_noMT(mm,8) == T2s(2)
Mss_Total_noMT(mm,:) = Dictionary_function_CSS(flips,TR,Dur,Var_Params_noMT(mm,10),Var_Params_noMT(mm,4:6),Var_Params_noMT(mm,7:8),Var_Params_noMT(mm,1:3),Var_Params_noMT(mm,9),Delta,TBW,nMB,n1B,b1sqrd,G_1B(2,:),G_2B(2,:),G_3B(2,:),wloc_1B(2),wloc_2B(2),wloc_3B(2));
end
if Var_Params_noMT(mm,8) == T2s(3)
Mss_Total_noMT(mm,:) = Dictionary_function_CSS(flips,TR,Dur,Var_Params_noMT(mm,10),Var_Params_noMT(mm,4:6),Var_Params_noMT(mm,7:8),Var_Params_noMT(mm,1:3),Var_Params_noMT(mm,9),Delta,TBW,nMB,n1B,b1sqrd,G_1B(3,:),G_2B(3,:),G_3B(3,:),wloc_1B(3),wloc_2B(3),wloc_3B(3));
end
if Var_Params_noMT(mm,8) == T2s(4)
Mss_Total_noMT(mm,:) = Dictionary_function_CSS(flips,TR,Dur,Var_Params_noMT(mm,10),Var_Params_noMT(mm,4:6),Var_Params_noMT(mm,7:8),Var_Params_noMT(mm,1:3),Var_Params_noMT(mm,9),Delta,TBW,nMB,n1B,b1sqrd,G_1B(4,:),G_2B(4,:),G_3B(4,:),wloc_1B(4),wloc_2B(4),wloc_3B(4));
end
if Var_Params_noMT(mm,8) == T2s(5)
Mss_Total_noMT(mm,:) = Dictionary_function_CSS(flips,TR,Dur,Var_Params_noMT(mm,10),Var_Params_noMT(mm,4:6),Var_Params_noMT(mm,7:8),Var_Params_noMT(mm,1:3),Var_Params_noMT(mm,9),Delta,TBW,nMB,n1B,b1sqrd,G_1B(5,:),G_2B(5,:),G_3B(5,:),wloc_1B(5),wloc_2B(5),wloc_3B(5));
end
if Var_Params_noMT(mm,8) == T2s(6)
Mss_Total_noMT(mm,:) = Dictionary_function_CSS(flips,TR,Dur,Var_Params_noMT(mm,10),Var_Params_noMT(mm,4:6),Var_Params_noMT(mm,7:8),Var_Params_noMT(mm,1:3),Var_Params_noMT(mm,9),Delta,TBW,nMB,n1B,b1sqrd,G_1B(6,:),G_2B(6,:),G_3B(6,:),wloc_1B(6),wloc_2B(6),wloc_3B(6));
end
end
toc
% MT dictionary creation.
tic
parfor mm = 1:size(Var_Params_MT,1)
if Var_Params_MT(mm,8) == T2s(1)
Mss_Total_MT(mm,:) = Dictionary_function_CSS(flips,TR,Dur,Var_Params_MT(mm,10),Var_Params_MT(mm,4:6),Var_Params_MT(mm,7:8),Var_Params_MT(mm,1:3),Var_Params_MT(mm,9),Delta,TBW,nMB,n1B,b1sqrd,G_1B(1,:),G_2B(1,:),G_3B(1,:),wloc_1B(1),wloc_2B(1),wloc_3B(1));
end
if Var_Params_MT(mm,8) == T2s(2)
Mss_Total_MT(mm,:) = Dictionary_function_CSS(flips,TR,Dur,Var_Params_MT(mm,10),Var_Params_MT(mm,4:6),Var_Params_MT(mm,7:8),Var_Params_MT(mm,1:3),Var_Params_MT(mm,9),Delta,TBW,nMB,n1B,b1sqrd,G_1B(2,:),G_2B(2,:),G_3B(2,:),wloc_1B(2),wloc_2B(2),wloc_3B(2));
end
if Var_Params_MT(mm,8) == T2s(3)
Mss_Total_MT(mm,:) = Dictionary_function_CSS(flips,TR,Dur,Var_Params_MT(mm,10),Var_Params_MT(mm,4:6),Var_Params_MT(mm,7:8),Var_Params_MT(mm,1:3),Var_Params_MT(mm,9),Delta,TBW,nMB,n1B,b1sqrd,G_1B(3,:),G_2B(3,:),G_3B(3,:),wloc_1B(3),wloc_2B(3),wloc_3B(3));
end
if Var_Params_MT(mm,8) == T2s(4)
Mss_Total_MT(mm,:) = Dictionary_function_CSS(flips,TR,Dur,Var_Params_MT(mm,10),Var_Params_MT(mm,4:6),Var_Params_MT(mm,7:8),Var_Params_MT(mm,1:3),Var_Params_MT(mm,9),Delta,TBW,nMB,n1B,b1sqrd,G_1B(4,:),G_2B(4,:),G_3B(4,:),wloc_1B(4),wloc_2B(4),wloc_3B(4));
end
if Var_Params_MT(mm,8) == T2s(5)
Mss_Total_MT(mm,:) = Dictionary_function_CSS(flips,TR,Dur,Var_Params_MT(mm,10),Var_Params_MT(mm,4:6),Var_Params_MT(mm,7:8),Var_Params_MT(mm,1:3),Var_Params_MT(mm,9),Delta,TBW,nMB,n1B,b1sqrd,G_1B(5,:),G_2B(5,:),G_3B(5,:),wloc_1B(5),wloc_2B(5),wloc_3B(5));
end
if Var_Params_MT(mm,8) == T2s(6)
Mss_Total_MT(mm,:) = Dictionary_function_CSS(flips,TR,Dur,Var_Params_MT(mm,10),Var_Params_MT(mm,4:6),Var_Params_MT(mm,7:8),Var_Params_MT(mm,1:3),Var_Params_MT(mm,9),Delta,TBW,nMB,n1B,b1sqrd,G_1B(6,:),G_2B(6,:),G_3B(6,:),wloc_1B(6),wloc_2B(6),wloc_3B(6));
end
end
toc
% ihMT dictionary creation.
tic
parfor mm = 1:size(Var_Params_ihMT,1)
if Var_Params_ihMT(mm,8) == T2s(1)
Mss_Total_ihMT(mm,:) = Dictionary_function_CSS(flips,TR,Dur,Var_Params_ihMT(mm,10),Var_Params_ihMT(mm,4:6),Var_Params_ihMT(mm,7:8),Var_Params_ihMT(mm,1:3),Var_Params_ihMT(mm,9),Delta,TBW,nMB,n1B,b1sqrd,G_1B(1,:),G_2B(1,:),G_3B(1,:),wloc_1B(1),wloc_2B(1),wloc_3B(1));
end
if Var_Params_ihMT(mm,8) == T2s(2)
Mss_Total_ihMT(mm,:) = Dictionary_function_CSS(flips,TR,Dur,Var_Params_ihMT(mm,10),Var_Params_ihMT(mm,4:6),Var_Params_ihMT(mm,7:8),Var_Params_ihMT(mm,1:3),Var_Params_ihMT(mm,9),Delta,TBW,nMB,n1B,b1sqrd,G_1B(2,:),G_2B(2,:),G_3B(2,:),wloc_1B(2),wloc_2B(2),wloc_3B(2));
end
if Var_Params_ihMT(mm,8) == T2s(3)
Mss_Total_ihMT(mm,:) = Dictionary_function_CSS(flips,TR,Dur,Var_Params_ihMT(mm,10),Var_Params_ihMT(mm,4:6),Var_Params_ihMT(mm,7:8),Var_Params_ihMT(mm,1:3),Var_Params_ihMT(mm,9),Delta,TBW,nMB,n1B,b1sqrd,G_1B(3,:),G_2B(3,:),G_3B(3,:),wloc_1B(3),wloc_2B(3),wloc_3B(3));
end
if Var_Params_ihMT(mm,8) == T2s(4)
Mss_Total_ihMT(mm,:) = Dictionary_function_CSS(flips,TR,Dur,Var_Params_ihMT(mm,10),Var_Params_ihMT(mm,4:6),Var_Params_ihMT(mm,7:8),Var_Params_ihMT(mm,1:3),Var_Params_ihMT(mm,9),Delta,TBW,nMB,n1B,b1sqrd,G_1B(4,:),G_2B(4,:),G_3B(4,:),wloc_1B(4),wloc_2B(4),wloc_3B(4));
end
if Var_Params_ihMT(mm,8) == T2s(5)
Mss_Total_ihMT(mm,:) = Dictionary_function_CSS(flips,TR,Dur,Var_Params_ihMT(mm,10),Var_Params_ihMT(mm,4:6),Var_Params_ihMT(mm,7:8),Var_Params_ihMT(mm,1:3),Var_Params_ihMT(mm,9),Delta,TBW,nMB,n1B,b1sqrd,G_1B(5,:),G_2B(5,:),G_3B(5,:),wloc_1B(5),wloc_2B(5),wloc_3B(5));
end
if Var_Params_ihMT(mm,8) == T2s(6)
Mss_Total_ihMT(mm,:) = Dictionary_function_CSS(flips,TR,Dur,Var_Params_ihMT(mm,10),Var_Params_ihMT(mm,4:6),Var_Params_ihMT(mm,7:8),Var_Params_ihMT(mm,1:3),Var_Params_ihMT(mm,9),Delta,TBW,nMB,n1B,b1sqrd,G_1B(6,:),G_2B(6,:),G_3B(6,:),wloc_1B(6),wloc_2B(6),wloc_3B(6));
end
end
toc
%% Select representative samples from dictionary.
rng('default');
% Truncate dictionary by a certain factor/make dictionary representative.
k_noMT = randperm(size(Var_Params_noMT,1),10000).';
k_MT = randperm(size(Var_Params_MT,1),200000).';
k_ihMT = randperm(size(Var_Params_ihMT,1),200000).';
Tr_Mss_Total_noMT = Mss_Total_noMT(k_noMT,:);
Tr_Mss_Total_MT = Mss_Total_MT(k_MT,:);
Tr_Mss_Total_ihMT = Mss_Total_ihMT(k_ihMT,:);
Tr_Var_Params_noMT = Var_Params_noMT(k_noMT,:);
Tr_Var_Params_MT = Var_Params_MT(k_MT,:);
Tr_Var_Params_ihMT = Var_Params_ihMT(k_ihMT,:);
clear Mss_Total_noMT Mss_Total_MT Mss_Total_ihMT % Saves memory.
% Create truncated dictionary.
Tr_Mss_AllSigs = [repmat(Tr_Mss_Total_noMT,20,1) ; Tr_Mss_Total_MT ; Tr_Mss_Total_ihMT];
Tr_VP_AllSigs = [repmat(Tr_Var_Params_noMT,20,1) ; Tr_Var_Params_MT ; Tr_Var_Params_ihMT];
%% Take SVD of dictionary.
[U,S,V] = svd(Tr_Mss_AllSigs,'econ');
disp(['5 largest singular values: ', num2str(S(1,1)), ', ', num2str(S(2,2)), ', ', num2str(S(3,3)), ', ', num2str(S(4,4)), ', ', num2str(S(5,5)), '.'])
%% Dictionary analysis for different simulated tissues.
% WM parameters.
T1x_WM = [1090 1000 6.2]*1e-3;
T2x_WM = [69e-3, 9e-6];
f_WM = 1;
K_WM = 59.6;
M0b_WM = 0.101;
M0f_WM = 1-M0b_WM;
M0_WM = [M0f_WM M0b_WM*(1-f_WM) M0b_WM*f_WM];
VP_WM = [M0_WM, T1x_WM, T2x_WM, K_WM];
[GWM_3B,wlocWM_3B] = SuperLorentzian_LSint(T2x_WM(2),df_3B);
[GWM_2B,wlocWM_2B] = SuperLorentzian_LSint(T2x_WM(2),df_2B);
[GWM_1B,wlocWM_1B] = SuperLorentzian_LSint(T2x_WM(2),df_1B);
% GM parameters.
T1x_GM = [1820 1000 5.9]*1e-3;
T2x_GM = [99e-3, 7.58e-6];
f_GM = 1;
K_GM = 50.8;
M0b_Varma_GM = (7.3*(1/T1x_GM(1)))/K_GM;
M0b_GM = 0.0348;
M0f_GM = 1-M0b_GM;
M0_GM = [M0f_GM M0b_GM*(1-f_GM) M0b_GM*f_GM];
VP_GM = [M0_GM, T1x_GM, T2x_GM, K_GM];
[GGM_3B,wlocGM_3B] = SuperLorentzian_LSint(T2x_GM(2),df_3B);
[GGM_2B,wlocGM_2B] = SuperLorentzian_LSint(T2x_GM(2),df_2B);
[GGM_1B,wlocGM_1B] = SuperLorentzian_LSint(T2x_GM(2),df_1B);
% CSF parmeters.
T1x_CSF = [3000 1000 1000]*1e-3;
T2x_CSF = [2, 1];
f_CSF = 0;
K_CSF = 0;
M0b_Varma_CSF = 0;
M0b_CSF = M0b_Varma_CSF/(1 + M0b_Varma_CSF);
M0f_CSF = 1-M0b_CSF;
M0_CSF = [M0f_CSF M0b_CSF*(1-f_CSF) M0b_CSF*f_CSF];
VP_CSF = [M0_CSF, T1x_CSF, T2x_CSF, K_CSF];
[GCSF_3B,wlocCSF_3B] = SuperLorentzian_LSint(T2x_CSF(2),df_3B);
[GCSF_2B,wlocCSF_2B] = SuperLorentzian_LSint(T2x_CSF(2),df_2B);
[GCSF_1B,wlocCSF_1B] = SuperLorentzian_LSint(T2x_CSF(2),df_1B);
Rank_no = 1:20;
dphi = 0;
x_WM = zeros(length(Rank_no),1200);xprime_WM = zeros(length(Rank_no),1200);
x_GM = zeros(length(Rank_no),1200);xprime_GM = zeros(length(Rank_no),1200);
x_CSF = zeros(length(Rank_no),1200);xprime_CSF = zeros(length(Rank_no),1200);
for ii = 1:length(Rank_no)
% Generate signals.
x_WM(ii,:) = (Dictionary_function_CSS(flips,TR,Dur,dphi,VP_WM(4:6),VP_WM(7:8),VP_WM(1:3),VP_WM(9),Delta,TBW,nMB,n1B,b1sqrd,GWM_1B,GWM_2B,GWM_3B,wlocWM_1B,wlocWM_2B,wlocWM_3B));
w_WM = pinv(V(:,1:Rank_no(ii)))*x_WM(ii,:).';
xprime_WM(ii,:) = V(:,1:Rank_no(ii))*w_WM;
x_GM(ii,:) = (Dictionary_function_CSS(flips,TR,Dur,dphi,VP_GM(4:6),VP_GM(7:8),VP_GM(1:3),VP_GM(9),Delta,TBW,nMB,n1B,b1sqrd,GGM_1B,GGM_2B,GGM_3B,wlocGM_1B,wlocGM_2B,wlocGM_3B));
w_GM = pinv(V(:,1:Rank_no(ii)))*x_GM(ii,:).';
xprime_GM(ii,:) = V(:,1:Rank_no(ii))*w_GM;
x_CSF(ii,:) = (Dictionary_function_CSS(flips,TR,Dur,dphi,VP_CSF(4:6),VP_CSF(7:8),VP_CSF(1:3),VP_CSF(9),Delta,TBW,nMB,n1B,b1sqrd,GCSF_1B,GCSF_2B,GCSF_3B,wlocCSF_1B,wlocCSF_2B,wlocCSF_3B));
w_CSF = pinv(V(:,1:Rank_no(ii)))*x_CSF(ii,:).';
xprime_CSF(ii,:) = V(:,1:Rank_no(ii))*w_CSF;
end
% Plot results of analysis for Figure 4.
cm = lines(10);
figure(1);
labels = {'R = 1','R = 2','R = 3','R = 4','R = 5','R = 6','R = 7','R = 8','R = 9','R = 10'};
a_plot(:,2) = V(:,1); a_plot(:,1) = zeros(1200,1);
b_plot(:,2) = V(:,2); b_plot(:,1) = zeros(1200,1);
c_plot(:,2) = V(:,3); c_plot(:,1) = zeros(1200,1);
d_plot(:,2) = V(:,4); d_plot(:,1) = zeros(1200,1);
e_plot(:,2) = V(:,5); e_plot(:,1) = zeros(1200,1);
f_plot(:,2) = V(:,6); f_plot(:,1) = zeros(1200,1);
g_plot(:,2) = V(:,7); g_plot(:,1) = zeros(1200,1);
h_plot(:,2) = V(:,8); h_plot(:,1) = zeros(1200,1);
i_plot(:,2) = V(:,9); i_plot(:,1) = zeros(1200,1);
j_plot(:,2) = V(:,10); j_plot(:,1) = zeros(1200,1);
t = table(a_plot,b_plot,c_plot,d_plot,e_plot,f_plot,g_plot,h_plot,i_plot,j_plot);
subplot(10,2,1:2:19)
s = stackedplot(t); set(gca,'FontSize',18); s.GridVisible = 'on'; s.XLabel = {'Pulse No.'};
for ii = 1:10
s.AxesProperties(ii).YLimits = [-0.2 0.2];
s.AxesProperties(ii).LegendVisible = 'off';
s.DisplayLabels(ii) = labels(ii);
s.LineProperties(ii).Color = [[0.6 0.6 0.6];cm(ii,:)];
s.LineProperties(ii).LineStyle = {'--','-'};
s.LineProperties(ii).LineWidth = 3;
end
annotation('textbox','String','(a)','FontSize',24,'LineStyle','none','Position',[0.0644,0.905,0.05,0.07])
subplot(10,2,2:2:10)
plot((diag(S)/S(1,1)),'-o','LineWidth',3,'MarkerSize',10,'Color','k'); xlim([1 10])
set(gca,'FontSize',16); grid on; grid minor; xlabel('R','FontSize',20); ylabel('Norm. Singular Values');
annotation('textbox','String','(b)','FontSize',24,'LineStyle','none','Position',[0.5221875,0.905,0.05,0.069999999999999])
% Compute mean and max residuals.
Maxres_WM = max(((abs(x_WM(5,:)-xprime_WM(5,:)))./abs(x_WM(5,:)))*100);
Maxres_GM = max(((abs(x_GM(5,:)-xprime_GM(5,:)))./abs(x_GM(5,:)))*100);
Maxres_CSF = max(((abs(x_CSF(5,:)-xprime_CSF(5,:)))./abs(x_CSF(5,:)))*100);
Meanres_WM = zeros(1,10); Meanres_GM = zeros(1,10); Meanres_CSF = zeros(1,10);
for ii = 1:10
Meanres_WM(ii) = mean(((abs(x_WM(ii,:)-xprime_WM(ii,:)))./abs(x_WM(ii,:)))*100);
Meanres_GM(ii) = mean(((abs(x_GM(ii,:)-xprime_GM(ii,:)))./abs(x_GM(ii,:)))*100);
Meanres_CSF(ii) = mean(((abs(x_CSF(ii,:)-xprime_CSF(ii,:)))./abs(x_CSF(ii,:)))*100);
end
cm2 = gray(20);
subplot(10,2,14:2:20)
plot(Meanres_WM,'-o','LineWidth',3,'MarkerSize',10,'Color',cm2(1,:)); hold on
plot(Meanres_GM,'-o','LineWidth',3,'MarkerSize',10,'Color',cm2(8,:));
plot(Meanres_CSF,'-o','LineWidth',3,'MarkerSize',10,'Color',cm2(15,:));
set(gca,'FontSize',16); xlabel('R','FontSize',20); ylabel('Mean Residuals (%)');
grid on; grid minor; ll = legend('WM','GM','CSF'); ll.FontSize = 20; ll.Orientation = 'horizontal'; legend boxoff; xlim([1 10])
annotation('textbox','String','(c)','FontSize',24,'LineStyle','none','Position',[0.5221875,0.418,0.05,0.07]); ylim([0 15])