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stubI_souden11.m
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function [Y data] = stubI_souden11(X,fail,fs,inFile,refMic,L_init)
% Perform MVDR beamforming with noise covariance matrix based on [1]. And
% MVDR formula based on[2] (equation 18 with beta = 0)
%
% Y= stubI_souden11(X,fail,fs,inFile,refMic,L_init)
%
% [1]Souden, M., Chen, J., Benesty, J., & Affes, S. (2011).
% An integrated solution for online multichannel noise tracking and reduction.
% IEEE Transactions on Audio, Speech, and Language Processing, 19(7), 2159-2169.
% [2] Souden, M., Benesty, J., & Affes, S. (2010).
% On optimal frequency-domain multichannel linear filtering for noise reduction.
%
% Inputs:
% X:FxTxC tensor of complex input spectrograms for each channel,
% L_Init:Assume the first L_init there is no speech, only noise
% refMic:microphone used as reference for reconstruction
% Outputs:
% Y: FxT matrix of estimated complex spectrum of target
[F T C] = size(X)
if ~exist('refMic', 'var') || isempty(refMic), refMic = 1; end
if ~exist('L_init', 'var') || isempty(L_init), L_init = 6; end
pickMic = zeros(C,1);
pickMic(refMic) = 1 / length(refMic);
X = permute(X,[3,1,2]); % now X is C F T
X = cat(3, zeros(C,F,1), X);
epsilon = 0.01;
alpha_noisy = 0.92; % follow the paper at V.Numerical Examples
alpha_v = 0.92;
alpha_p = 0.6;
K1 = 15;
%syms x;
L = 32;
psi_0 = 18.1;
psi_tilde_0 = 28.85;
% find psi_0 by
% Hotelling_cdf = @(x)(x/L)^C * L * gamma(L)* hypergeom([C,L+1],C+1,(-x/L))/(gamma(C+1)*gamma(L-C+1)) - 0.99;
% z = fzero(Hotelling_cdf,10)
% round up psi_0 to 18.1
% find psi_tilde_0 by
% a = 2 * C * L;
% B= (2*L - 2*C - 1)*(L-1)/((L-2*C-3)*(L-2*C));
% b = 4 + (a+2)/(B-1);
% c = a*(b-2)/(b *(L-2*C-1))
% psi_tilde_0 = c* finv(0.99,a,b) = 28.8427
% round up psi_tilde_0 to 28.85
Mcov = zeros(C,C,F,T+1);
Ncov = zeros(C,C,F,T+1);
Scov = zeros(C,C,F,T+1);
psi = zeros(F,T+1);
psi_tilde = zeros(F,T+1);
psi_global = zeros(F,T+1);
psi_local= zeros(F,T+1);
psi_frame = zeros(T+1);
q_frame = zeros(T+1);
q_global = zeros(F,T+1);
q_local = zeros(F,T+1);
p= zeros(F,T+1);
p1= zeros(F,T+1);
pfinal= zeros(F,T+1);
for k = 1:F
Ncov(:,:,k,1) = 0;
Mcov(:,:,k,1) = 0;
end
%-------------------- Iteration 1 -------------------- %
% equation (3)
for l=2:(L_init + 1)
for k = 1:F
p(k,l) = 0;
Mcov(:,:,k,l) = alpha_noisy * Mcov(:,:,k,l-1) + (1 - alpha_noisy)* X(:,k,l)*X(:,k,l)';
Ncov(:,:,k,l) = Mcov(:,:,k,l); % Assume the first L_init there is no speech, only noise
end
end
for l = (L_init + 2):(T+1)
for k=1:F
Mcov(:,:,k,l) = alpha_noisy * Mcov(:,:,k,l-1) + (1 - alpha_noisy)* X(:,k,l)*X(:,k,l)';
end
end
for l = (L_init + 2):(T+1)
for k=1:F
Scov(:,:,k,l) = Mcov(:,:,k,l) - Ncov(:,:,k,l-1); %2a
psi(k,l) = X(:,k,l)' * inv(Ncov(:,:,k,l-1)) * X(:,k,l); %2b
psi_tilde(k,l) = trace(Ncov(:,:,k,l-1) \ Mcov(:,:,k,l)); %2c
xi(k,l) = psi_tilde(k,l) - C; %2d
beta(k,l) = X(:,k,l)' * inv(Ncov(:,:,k,l-1)) * Scov(:,:,k,l) * inv(Ncov(:,:,k,l-1))* Scov(:,:,k,l) * X(:,k,l);
% Equation(18)
if (psi_tilde(k,l) < C) && (psi(k,l) < psi_0)
q_local(k,l) = 1;
elseif (C <= psi_tilde(k,l)) && (psi_tilde(k,l) < psi_tilde_0) && (psi(k,l) < psi_0)
q_local(k,l) = (psi_tilde_0 - psi_tilde(k,l))/(psi_tilde_0 - C);
else
q_local(k,l) = 0;
end
end
% Equation 20
for i =1:F
psi_frame(l) = psi(i,l) * psi_frame(l);
end
psi_frame(l) = 1/F*psi_frame(l);
if (psi_frame(l) < psi_0)
q_frame(l) = 1;
else
q_frame(l) = 0;
end
% Equation (19)
% split into [1,K1], [(K1+1):(F-K1)] and (F-K1+1):F
for k= 1:K1
psi_global(k,l) = 1;
for i =-K1:0
psi_global(k,l) = psi_global(k,l) * 0.5*(1 - cos(pi*i/K1))* psi(k-i,l);
end
end
for k= (K1+1):(F-K1)
psi_global(k,l) = 1;
for i =(-K1):K1
psi_global(k,l) = psi_global(k,l) * 0.5*(1 - cos(pi*i/K1))* psi(k-i,l);
end
end
for k= (F-K1+1):F
psi_global(k,l) = 1;
for i =0:K1
psi_global(k,l) = psi_global(k,l) * 0.5*(1 - cos(pi*i/K1))* psi(k-i,l);
end
end
for k=1:F
if (psi_global(k,l) < psi_0)
q_global(k,l) = 1;
else
q_global(k,l) = 0;
end
end
for k=1:F
q(k,l) = q_local(k,l) * q_global(k,l) * q_frame(l);
q(k,l) = min(q(k,l), 0.99);
p1(k,l) = 1/(1 + q(k,l)/(1-q(k,l))*(1 + xi(k,l))*exp(-beta(k,l)/(1+xi(k,l))));
p(k,l) = alpha_p * p(k,l-1) + (1-alpha_p)* p1(k,l);
alpha_noise(k,l) = alpha_v + (1- alpha_v) * p(k,l);
Ncov(:,:,k,l) = alpha_noise(k,l) * Ncov(:,:,k,l-1) + (1 - alpha_noise(k,l))*X(:,k,l)*X(:,k,l)';
end
end
%-------------------- Iteration 2 -------------------- %
% Same as Iteration 1 but replace Ncov(:,:,k,l-1) by Ncov(:,:,k,l);
for l=2:(L_init + 1)
for k = 1:F
p(k,l) = 0;
Mcov(:,:,k,l) = alpha_noisy * Mcov(:,:,k,l-1) + (1 - alpha_noisy)* X(:,k,l)*X(:,k,l)';
Ncov(:,:,k,l) = Mcov(:,:,k,l); % Assume the first L_init there is no speech, only noise
end
end
for l = (L_init + 2):(T+1)
for k=1:F
Mcov(:,:,k,l) = alpha_noisy * Mcov(:,:,k,l-1) + (1 - alpha_noisy)* X(:,k,l)*X(:,k,l)';
end
end
for l = (L_init + 2):(T+1)
for k=1:F
Scov(:,:,k,l) = Mcov(:,:,k,l) - Ncov(:,:,k,l); %2a
psi(k,l) = X(:,k,l)' * inv(Ncov(:,:,k,l)) * X(:,k,l); %2b
psi_tilde(k,l) = trace(Ncov(:,:,k,l) \ Mcov(:,:,k,l)); %2c
xi(k,l) = psi_tilde(k,l) - C; %2d
beta(k,l) = X(:,k,l)' * inv(Ncov(:,:,k,l)) * Scov(:,:,k,l) * inv(Ncov(:,:,k,l))* Scov(:,:,k,l) * X(:,k,l);
% Equation(18)
if (psi_tilde(k,l) < C) && (psi(k,l) < psi_0)
q_local(k,l) = 1;
elseif (C <= psi_tilde(k,l)) && (psi_tilde(k,l) < psi_tilde_0) && (psi(k,l) < psi_0)
q_local(k,l) = (psi_tilde_0 - psi_tilde(k,l))/(psi_tilde_0 - C);
else
q_local(k,l) = 0;
end
end
% Equation 20
for i =1:F
psi_frame(l) = psi(i,l) * psi_frame(l);
end
psi_frame(l) = 1/F*psi_frame(l);
if (psi_frame(l) < psi_0)
q_frame(l) = 1;
else
q_frame(l) = 0;
end
% Equation (19)
% split into [1,K1], [(K1+1):(F-K1)] and (F-K1+1):F
for k= 1:K1
psi_global(k,l) = 1;
for i =-K1:0
psi_global(k,l) = psi_global(k,l) * 0.5*(1 - cos(pi*i/K1))* psi(k-i,l);
end
end
for k= (K1+1):(F-K1)
psi_global(k,l) = 1;
for i =(-K1):K1
psi_global(k,l) = psi_global(k,l) * 0.5*(1 - cos(pi*i/K1))* psi(k-i,l);
end
end
for k= (F-K1+1):F
psi_global(k,l) = 1;
for i =0:K1
psi_global(k,l) = psi_global(k,l) * 0.5*(1 - cos(pi*i/K1))* psi(k-i,l);
end
end
for k=1:F
if (psi_global(k,l) < psi_0)
q_global(k,l) = 1;
else
q_global(k,l) = 0;
end
end
for k=1:F
q(k,l) = q_local(k,l) * q_global(k,l) * q_frame(l);
q(k,l) = min(q(k,l), 0.99);
p_final(k,l) = 1/(1 + q(k,l)/(1-q(k,l))*(1 + xi(k,l))*exp(-beta(k,l)/(1+xi(k,l))));
alpha_noise(k,l) = alpha_v + (1- alpha_v) * p(k,l);
Ncov(:,:,k,l) = alpha_noise(k,l) * Ncov(:,:,k,l-1) + (1 - alpha_noise(k,l))*X(:,k,l)*X(:,k,l)';
end
end
Ncov = Ncov(:,:,:,2:end);
Mcov = Mcov(:,:,:,2:end);
for l = 1:T
for k = 1:F
Ncov(:,:,k,l) = 0.5 * ( Ncov(:,:,k,l) + Ncov(:,:,k,l)'); % Ensure Hermitian symmetry
Mcov(:,:,k,l) = 0.5 * ( Mcov(:,:,k,l) + Mcov(:,:,k,l)'); % Ensure Hermitian symmetry
end
end
Y = zeros(F,T);
beta_MVDR = 0;
regulN = 1e-3;
minCor = 1;
eyeCoef = 1;
for t = 1:T
for f = 1:F
RNcov = Ncov(:,:,f,t) + regulN * diag(diag(Ncov(:,:,f,t)));
RMcov = Mcov(:,:,f,t) + regulN * diag(diag(Mcov(:,:,f,t)));
num = (RNcov \ RMcov - eyeCoef*eye(C));
%lambda = real(trace(num));
lambda = max(minCor, real(trace(num)));
den = beta_MVDR + lambda;
h = (num * pickMic) / den;
Y(f,t) = h' * X(:,f,t);
end
end
data =[];
end