This project was on solving audio inverse problems where time domain signal is lost or corrupted (ex. audio declipping or declicking). We have proposed a maximum likelihood estimation algorithm that relies on nonnegative tensor factorization (NTF) for probabilistic modeling of the time frequency domain audio samples.
We soon realized that this algorithm can in fact be used for many other problems, such as source separation with audio inpainting, informed source separation (multisource audio compression), compressed sensing based audio recovery, etc.
Our algorithm is capable of audio signal recovery and source separation in various scenarious, some of which has never been solved by any other algorithm before. We have also extended this algorithm for multichannel problems.