A method for performing audio restauration, wherein missing temporal coefficients of an input audio signal x are recovered and a recovered audio signal is obtained, comprising steps of - initializing a variance tensor V such that it is a low rank tensor that can be composed from component matrices H, Q, W, or initializing said component matrices H, Q, W to obtain the low rank variance tensor V; - iteratively applying the following steps, until convergence of the component matrices H, Q, W: i. computing conditional expectations of source power spectra of the input audio signal, wherein estimated source power spectra P ( f, n, j) are obtained according to P ( f, n, j) = E{| S ( f, n, j)| 2 | x, I s, I L, V}, with I S being time domain information on sources, and I L being time domain information on loss, and S ∈ C F × N × J is an array of Short Time Fourier Transform (STFT) coefficients of the sources, wherein f = 1,..., F is a frequency bin index, n = 1,..., N is a frame index and j = 1,..., J is a source index; ii. re-calculating the component matrices H, Q, W and the variance tensor V using the estimated source power spectra P ( f, n, j) and current values of the component matrices H, Q, W; - upon convergence of the component matrices H, Q, W, computing a resulting variance tensor V', and computing an array of a posterior mean of Short Time Fourier Transform (STFT) samples Ŝ ( f, n, j) of the recovered audio signal as Ŝ ( f, n, j) = E{ S ( f, n, j)| x, I s, I L, V}; and - converting coefficients of the array of the posterior mean of the STFT samples Ŝ ( f, n, j) to the time domain, thereby obtaining coefficients ( s̃ 1, s̃ 2,..., s̃ J) of the recovered audio signal, wherein the time domain information on sources ( I S) comprises at least one of: information about which sources are active or silent for a particular time instant, information about a number of how many components each source is composed in the low rank representation, and specific information on a harmonic structure of the sources, wherein the time domain information on loss ( I L) comprises at least one of: a clipping threshold, a sign of an unknown value in the input audio signal, an upper limit for the signal magnitude, and the quantized value of an unknown signal in the input audio signal, wherein the variance tensor V is computed from matrices H ∈ R + N × K, W ∈ R + F × K, Q ∈ R + J × K of rank K according to V f n j = ∑ k = 1 K H n k W f k Q j k, wherein the component matrices H, Q, W are recalculated according to: Q ′ j k ← Q j k ∑ f, n W f k H n k P f n j V f n j − 2 ∑ f, n W f k H n k V f n j − 1 W ′ f k ← W f k ∑ j, n Q j k H n k P f n j V f n j − 2 ∑ j, n Q j k H n k V f n j − 1 H ′ n k ← H n k ∑ f, j W f k Q j k P f n j V f n j − 2 ∑ f, j W f k Q j k P f n j − 1, wherein Q (j, k), W (f, k), H (n, k) are the current values of the component matrices H, Q, W and Q' ( j,k), W' ( f,k), H' ( n,k) are the recalculated values of the component matrices. - initializing a variance tensor V such that it is a low rank tensor that can be composed from component matrices H, Q, W, or initializing said component matrices H, Q, W to obtain the low rank variance tensor V; - iteratively applying the following steps, until convergence of the component matrices H, Q, W: i. computing conditional expectations of source power spectra of the input audio signal, wherein estimated source power spectra P ( f, n, j) are obtained according to P ( f, n, j) = E{| S ( f, n, j)| 2 | x, I s, I L, V}, with I S being time domain information on sources, and I L being time domain information on loss, and S ∈ C F × N × J is an array of Short Time Fourier Transform (STFT) coefficients of the sources, wherein f = 1,..., F is a frequency bin index, n = 1,..., N is a frame index and j = 1,..., J is a source index; ii. re-calculating the component matrices H, Q, W and the variance tensor V using the estimated source power spectra P ( f, n, j) and current values of the component matrices H, Q, W; i. computing conditional expectations of source power spectra of the input audio signal, wherein estimated source power spectra P ( f, n, j) are obtained according to P ( f, n, j) = E{| S ( f, n, j)| 2 | x, I s, I L, V}, with I S being time domain information on sources, and I L being time domain information on loss, and S ∈ C F × N × J is an array of Short Time Fourier Transform (STFT) coefficients of the sources, wherein f = 1,..., F is a frequency bin index, n = 1,..., N is a frame index and j = 1,..., J is a source index; ii. re-calculating the component matrices H, Q, W and the variance tensor V using the estimated source power spectra P ( f, n, j) and current values of the component matrices H, Q, W; - upon convergence of the component matrices H, Q, W, computing a resulting variance tensor V', and computing an array of a posterior mean of Short Time Fourier Transform (STFT) samples Ŝ ( f, n, j) of the recovered audio signal as Ŝ ( f, n, j) = E{ S ( f, n, j)| x, I s, I L, V}; and - converting coefficients of the array of the posterior mean of the STFT samples Ŝ ( f, n, j) to the time domain, thereby obtaining coefficients ( s̃ 1, s̃ 2,..., s̃ J) of the recovered audio signal,