homework7.m

%% ----- Homework 7 ----- %%
clc;
clear;
close all;

% Full HOSVD
load('homework7_HOSVD.mat');
[tenS_hat,U_hat] = tensor.HOSVD_full(tenX);
tenX_hat = tensor.n_mod_prod(tenS_hat,U_hat);

% Checking the orthogonality
disp(['Checking the orthogonality propertie between the subtensors'...
    'formed from the core tensor:'])
reshape(tenS_hat(:,:,1),[],1)'*reshape(tenS_hat(:,:,4),[],1)

disp(['Checking the NMSE (dB) between the original tensor X and its'...
    'reconstruction:'])
nmsex = (norm(tensor.unfold(tenX - tenX_hat,1),'fro')^2)...
    /(norm(tensor.unfold(tenX,1),'fro')^2);
nmsex = 20*log10(nmsex)
disp(['Checking the NMSE (dB) between the original core tensor S and its'... 
    'reconstruction:'])
nmses = (norm(tensor.unfold(tenS - tenS_hat,1),'fro')^2)...
    /(norm(tensor.unfold(tenS,1),'fro')^2);
nmses = 20*log10(nmses)

disp(['Checking the NMSE (dB) between the original matrices and its'... 
    'estimations:'])
nmseU1 = (norm(U1 - U_hat{1},'fro')^2)/(norm(U1,'fro')^2)
nmseU2 = (norm(U2 - U_hat{2},'fro')^2)/(norm(U2,'fro')^2)
nmseU3 = (norm(U3 - U_hat{3},'fro')^2)/(norm(U3,'fro')^2)

% Truncated HOSVD and Denoising
X = randn(8,4,10) + 1i*randn(8,4,10);
Y = randn(5,5,5) + 1i*randn(5,5,5);

[S1,U1] = tensor.HOSVD_truncated(X);
multilinear_rank1 = size(S1);
[S2,U2] = tensor.HOSVD_truncated(Y);
multilinear_rank2 = size(S2);

Xhat = tensor.n_mod_prod(S1,U1);
Yhat = tensor.n_mod_prod(S2,U2);

disp(['Checking the NMSE (dB) between the original noisy tensor X and'... 
    'its reconstruction:'])
nmsex = (norm(tensor.unfold(X- Xhat,1),'fro')^2)...
    /(norm(tensor.unfold(X,1),'fro')^2);
nmsex = 20*log10(nmsex)
disp(['Checking the NMSE (dB) between the original noisy tensor Y'...
    'and its reconstruction:'])
nmsey = (norm(tensor.unfold(Y- Yhat,1),'fro')^2)...
    /(norm(tensor.unfold(Y,1),'fro')^2);
nmsey = 20*log10(nmsey)

disp('The multilinear rank for the tensor X is:')
size(S1)
disp('The multilinear rank for the tensor Y is:')
size(S2)