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apply_cgmm_beamforming.m
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apply_cgmm_beamforming.m
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function apply_cgmm_beamforming(prefix, output, iters)
% Apply MVDR based on mask estimated by CGMM
if nargin < 1 || nargin > 3
error('format error: apply_cgmm_beamforming(prefix, output, [iters = 20])');
end
if nargin <= 2
iters = 20;
end
if nargin == 1
output = 'CGMM_ENHANCED';
end
assert(ischar(prefix));
assert(ischar(output));
num_channels = 6;
num_iters = iters;
frame_length = 1024;
fft_length = 1024;
frame_shift = 256;
theta = 10^-4;
beta = 10^-6;
% hamming_wnd = hamming(frame_length, 'periodic');
hanning_wnd = hanning(frame_length, 'periodic');
for c = 1: num_channels
samples = audioread([prefix '.CH' int2str(c) '.wav']);
frames = enframe(samples, hanning_wnd, frame_shift);
frames_size = size(frames);
frames_padding = zeros(frames_size(1), fft_length);
frames_padding(:, 1: frame_length) = frames;
% rfft: T x F
spectrums(:, :, c) = rfft(frames_padding, fft_length, 2);
end
specs = permute(spectrums(:, :, [1, 3, 4, 5, 6]), [3, 1, 2]);
[num_channels, num_frames, num_bins] = size(specs);
% CGMM parameters
lambda_noise = zeros(num_frames, num_bins);
lambda_noisy = zeros(num_frames, num_bins);
phi_noise = ones(num_frames, num_bins);
phi_noisy = ones(num_frames, num_bins);
R_noise = zeros(num_channels, num_channels, num_bins);
R_noisy = zeros(num_channels, num_channels, num_bins);
% R_xn = zeros(num_channels, num_channels, num_bins);
yyh = zeros(num_channels, num_channels, num_frames, num_bins);
% init R_noisy R_noise R_xn
for f = 1: num_bins
for t = 1: num_frames
y = specs(:, t, f);
h = y * y';
yyh(:, :, t, f) = h;
R_noisy(:, :, f) = R_noisy(:, :, f) + h;
end
R_noisy(:, :, f) = R_noisy(:, :, f) / num_frames;
R_noise(:, :, f) = eye(num_channels, num_channels);
end
R_xn = R_noisy;
% start CGMM training
p_noise = ones(num_frames, num_bins);
p_noisy = ones(num_frames, num_bins);
d = 1 / sqrt((pi * 2) ^ 5);
for iter = 1: num_iters
for f = 1: num_bins
R_noisy_onbin = R_noisy(:, :, f);
R_noise_onbin = R_noise(:, :, f);
if rcond(R_noisy_onbin) < theta
% R_noisy_onbin = R_noisy_onbin + theta * eye(num_channels) * max(diag(R_noisy_onbin));
R_noisy_onbin = R_noisy_onbin + beta * eye(num_channels);
% fprintf('WARNING: ILL-CONDITION\n');
end
if rcond(R_noise_onbin) < theta
% R_noise_onbin = R_noise_onbin + theta * eye(num_channels) * max(diag(R_noise_onbin));
R_noise_onbin = R_noise_onbin + beta * eye(num_channels);
% fprintf('WARNING: ILL-CONDITION\n');
end
R_noisy_inv = inv(R_noisy_onbin);
R_noise_inv = inv(R_noise_onbin);
R_noisy_accu = zeros(num_channels, num_channels);
R_noise_accu = zeros(num_channels, num_channels);
for t = 1: num_frames
corre = yyh(:, :, t, f);
obs = specs(:, t, f);
% update phi
phi_noise(t, f) = trace(corre * R_noise_inv) / num_channels;
phi_noisy(t, f) = trace(corre * R_noisy_inv) / num_channels;
% update lambda
k_noise = obs' * (R_noise_inv / phi_noise(t, f)) * obs / 2;
det_noise = det(phi_noise(t, f) * R_noise_onbin);
p_noise(t, f) = exp(-k_noise) / sqrt(det_noise);
k_noisy = obs' * (R_noisy_inv / phi_noisy(t, f)) * obs / 2;
det_noisy = det(phi_noisy(t, f) * R_noisy_onbin);
p_noisy(t, f) = exp(-k_noisy) / sqrt(det_noisy);
lambda_noise(t, f) = p_noise(t, f) / (p_noise(t, f) + p_noisy(t, f));
lambda_noisy(t, f) = p_noisy(t, f) / (p_noise(t, f) + p_noisy(t, f));
% accu R
R_noise_accu = R_noise_accu + lambda_noise(t, f) / phi_noise(t, f) * corre;
R_noisy_accu = R_noisy_accu + lambda_noisy(t, f) / phi_noisy(t, f) * corre;
end
% update R
R_noise(:, :, f) = R_noise_accu / sum(lambda_noise(:, f));
R_noisy(:, :, f) = R_noisy_accu / sum(lambda_noisy(:, f));
end
Q = sum(sum(lambda_noise .* log(d * p_noise) + lambda_noisy .* log(d * p_noisy))) / (num_frames * num_bins);
fprintf('iter = %2d, Q = %.4f\n', iter, Q);
end
% bigger entropy assigned to noise part
% seems no use
%{
for f = 1: num_bins
eig_value1 = eig(R_noise(:, :, f));
eig_value2 = eig(R_noisy(:, :, f));
en_noise = -eig_value1' / sum(eig_value1) * log(eig_value1 / sum(eig_value1));
en_noisy = -eig_value2' / sum(eig_value2) * log(eig_value2 / sum(eig_value2));
if en_noise < en_noisy
Rn = R_noise(:, :, f);
R_noise(:, :, f) = R_noisy(:, :, f);
R_noisy(:, :, f) = Rn;
end
end
%}
% get Rn, reference to eq.4
R_n = zeros(num_channels, num_channels, num_bins);
for f = 1: num_bins
for t = 1: num_frames
R_n(:, :, f) = R_n(:, :, f) + lambda_noise(t, f) * yyh(:, :, t, f);
end
R_n(:, :, f) = R_n(:, :, f) / sum(lambda_noise(:, f));
end
R_x = R_xn - R_n;
% apply MVDR beamforming
specs_enhan = zeros(num_frames, num_bins);
for f = 1: num_bins
% using Rx to estimate steer vector
[vector, ~, ~] = svd(R_x(:, :, f));
steer_vector = vector(:, 1);
if rcond(R_n(:, :, f)) < theta
R_n(:, :, f) = R_n(:, :, f) + beta * eye(num_channels);
% fprintf('WARNING: ILL-CONDITION\n');
end
% feed Rn into MVDR
% Rn_inv = inv(R_n(:, :, f));
% w: M x 1
% w = Rn_inv * steer_vector / (steer_vector' * Rn_inv * steer_vector);
numerator = R_n(:, :, f) \ steer_vector;
w = numerator / (steer_vector' * numerator);
% specs M x T x F
specs_enhan(:, f) = w' * specs(:, :, f);
end
% reconstruction
frames_enhan = irfft(specs_enhan, fft_length, 2);
% size(frames_enhan)
signal_enhan = overlapadd(frames_enhan(:, 1: frame_length), hanning_wnd, frame_shift);
audiowrite([output '.wav'], signal_enhan ./ norm(signal_enhan, inf), 16000);
save([output '.mat'], 'lambda_noise');
end