-
Notifications
You must be signed in to change notification settings - Fork 9
/
LRPR_prac_mc.m
171 lines (152 loc) · 6.87 KB
/
LRPR_prac_mc.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
function [B_hat, Uo, Xhat3, Uo_track, err_iter] = ...
LRPR_prac_mc(Params, Paramsrwf, Y, Afull, Afull_t, Afull_tk, Masks2, X)
Ysqrt = sqrt(Y);
err_iter = zeros(Params.tnew+1, 1);
%%contains some changes to consider the CDP setting. Check if it can be
%%made general to be able to handle simulated data too
%X_hat = zeros(100);
for o = 1 :Params.tnew % Main loop
fprintf('outer loop iteration %d\n', o)
%%%%%%%
% Initialization
%%%%%%%
if o == 1
fprintf('initialization\n');
%Den_X = norm(X,'fro');
%truncating the measurements
Ytrk = zeros(Params.n_1,Params.n_2,Params.L,Params.q);
for ni = 1 : Params.q
Yk = reshape( Y(:,:,:,ni) , Params.n_1*Params.n_2*Params.L, 1);
normest = sum(Yk(:))/Params.m;
Eyk = ( Yk <= Params.alpha_y^2 *normest);
Ytrk(:,:,:,ni) = reshape(Eyk.*Yk,Params.n_1,Params.n_2,Params.L);
end
%initializing U
U_tmp1 = randn(Params.n_1*Params.n_2,Params.r);
[U_upd_vec, ~, ~] = qr(U_tmp1, 0);
Uupdt = reshape(U_upd_vec, Params.n_1, Params.n_2, Params.r);
U_tmp = zeros(Params.n_1,Params.n_2,Params.r);
for t = 1 : Params.itr_num_pow_mth
fprintf('power method iteration %d\n', t);
for nr = 1 : Params.r
U_tmp(:,:,nr) = Afull_t( Ytrk.* Afull(repmat(Uupdt(:,:,nr), [1,1,Params.q])));
end
[Uupdt3, ~, ~] = qr(reshape(U_tmp, Params.n_1*Params.n_2, Params.r), 0);
Uupdt = reshape(Uupdt3, Params.n_1, Params.n_2, Params.r);
end
Uhat_vec = reshape(Uupdt, Params.n_1*Params.n_2, Params.r);
Uhat = Uhat_vec;
%[Qu, ~] = BlockIter(Uhat, 100, Params.r);
[Qu, ~] = qr(Uhat, 0);
Uo = Qu(:, 1 : Params.r);
Uo_track{o} = Uo;
end
% AUnew = zeros(Params.n_1*Params.n_2*Params.L,Params.q,Params.r);
% Ybk = zeros(Params.n_1,Params.n_2,Params.r,Params.q);
%
% for nr = 1 : Params.r
% AUnew(:,:,nr) = reshape(Afull(repmat(Uupdt(:,:,nr),[1,1,Params.q])), Params.n_1*Params.n_2*Params.L,Params.q);
% Ybk(:,:,nr,:) = Afull_tk(Y.* Afull(repmat(Uupdt(:,:,nr), [1,1,Params.q])));
% end
B_hat = zeros(Params.r, Params.q);
%Chat = zeros(Params.n_1 * Params.n_2, Params.q);
%Xhat3 = zeros(Params.n_1 * Params.n_2, Params.q);
Chat = zeros(size(Y));
for ni = 1 : Params.q
%fprintf('RWF for %d\n', ni);
Masks = Masks2(:,:,:,ni);
A_pr = @(I) reshape(fft2( Masks .* ...
reshape(repmat(Uo, Params.L, 1) * I, Params.n_1, Params.n_2, Params.L)), [],1);
At_pr = @(W) Params.n_1 * Params.n_2 * Uo' * reshape(sum(conj(Masks) .* ...
ifft2(reshape(W, Params.n_1, Params.n_2, Params.L)), 3), [], 1);
y_tmp = reshape(Y(:, :, :, ni), [], 1);
Paramsrwf.Tb_LRPRnew = Params.Tb_LRPRnew(o);
[bhat] = RWFsimple(sqrt(y_tmp), Paramsrwf, A_pr, At_pr);
B_hat(:, ni) = bhat;
%x_k = Uo * B_hat(:,ni);
Chat3 = exp(1i * angle(A_pr(B_hat(:,ni))));
%Xhat3(:, ni) = x_k;
Chat(:, :, :, ni) = reshape(Chat3, Params.n_1, Params.n_2, Params.L, 1); %reshape(repmat(Chat3, Params.L, 1), Params.n_1, Params.n_2, Params.L, 1);
end
Xhat3 = Uo * B_hat;
Den_X = norm(X,'fro');
Tmp_Err_X2 = zeros(Params.q, 1);
for ct = 1 : Params.q
xa_hat = Xhat3(:,ct);
xa = X(:,ct);
Tmp_Err_X2(ct) = norm(xa - exp(-1i*angle(trace(xa'*xa_hat))) * xa_hat, 'fro');
end
Nom_Err_X_twf = sum(Tmp_Err_X2);
err_iter(o) = Nom_Err_X_twf / Den_X;
% [Qb,~] = BlockIter(B_hat', 100, Params.r);
[Qb,~] = qr(B_hat', 0);% 100, Params.r);
Bo = Qb(:, 1:Params.r)';
if (o==1)
D = Uo*B_hat;
Den_X = norm(X,'fro');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%initialization error
for na = 1 : Params.q
xa_hat = D(:,na);
xa = X(:,na);
% % Tmp_Err_X(na) = min(norm(xa-xa_hat)^2, norm(xa+xa_hat)^2);
Tmp_Err_X1(na) = norm(xa - exp(-1i*angle(trace(xa'*xa_hat))) * xa_hat, 'fro');
end
% Rel_Err(:,t)= Tmp_Err_X;
Err = sum(Tmp_Err_X1);
ERRinit = Err / Den_X;
fprintf('Our initialization Error is:\t%2.2e\n',ERRinit);
end
K1 = Chat .* Ysqrt; %sqrt;
Zvec = reshape(K1,Params.n_1*Params.n_2*Params.L*Params.q,1);
Uvec = cgls_new(@mult_H2, @mult_Ht2 , Zvec, 0,1e-6 ,3);
U_hat = reshape(Uvec, Params.n_1*Params.n_2, Params.r);
%[Qu,~] = BlockIter(U_hat, 100, Params.r);
[Qu,~] = qr(U_hat, 0);
Uo = Qu(:, 1:Params.r);
Uo_track{o} = Uo;
end
%%%model correction step to improve residual error
fprintf('model correction step\n')
Xhat_MC = zeros(Params.n_1 * Params.n_2, Params.q);
for ni = 1 : Params.q
Masks = Masks2(:,:,:,ni);
xk = Xhat3(:, ni);
ytmp = sqrt(reshape(Y(:, :, :, ni), [], 1));
A_pr = @(I) reshape(fft2(Masks .* ...
reshape(repmat(I, Params.L, 1), Params.n_1, Params.n_2, Params.L)), [],1);
At_pr = @(W) Params.n_1 * Params.n_2 * reshape(sum(conj(Masks) .* ...
ifft2(reshape(W, Params.n_1, Params.n_2, Params.L)), 3), [], 1);
Paramsrwf.Tb_LRPRnew = 5;
Paramsrwf.r = Params.n_1 * Params.n_2;
[what_mc] = RWFsimple(sqrt(ytmp) - A_pr(xk), Paramsrwf, A_pr, At_pr);
Xhat_MC(:, ni) = what_mc + xk;
%x_k = Uo * B_hat(:,ni);
%Chat3 = exp(1i * angle(A_pr(Xhat_MC(:,ni))));
%Xhat3(:, ni) = x_k;
%Chat(:, :, :, ni) = reshape(Chat3, Params.n_1, Params.n_2, Params.L, 1);
end
Tmp_Err_X2 = zeros(Params.q, 1);
for ct = 1 : Params.q
xa_hat = Xhat_MC(:,ct);
xa = X(:,ct);
Tmp_Err_X2(ct) = norm(xa - exp(-1i*angle(trace(xa'*xa_hat))) * xa_hat, 'fro');
end
Nom_Err_X_twf = sum(Tmp_Err_X2);
err_iter(Params.tnew+1) = Nom_Err_X_twf / Den_X;
function i_out = mult_H2(i_in)
I_mat = reshape(i_in, Params.n_1*Params.n_2, Params.r);
% i_out = zeros(Params.q*Params.m, 1);
Xmat = I_mat * Bo;
Xmat2 = reshape(Xmat,Params.n_1,Params.n_2,Params.q);
Iout = Afull(Xmat2);
i_out = reshape(Iout,Params.q*Params.m, 1);
end
% Defining mult_Ht
function w_out = mult_Ht2(w_in)
w_out = zeros(Params.n_1*Params.n_2*Params.r, 1);
TmpVec = permute(Afull_tk(reshape(w_in, Params.n_1,Params.n_2,Params.L,Params.q)), [1,2,4,3]);
for nk = 1: Params.q
w_out = w_out + kron(Bo(:,nk), reshape(TmpVec(:,:,nk), Params.n_1*Params.n_2, 1));
end
end
end