Estimation with Low-Rank Time-Frequency Synthesis Models
This work addresses signal decomposition for audio processing applications, offering a novel paradigm that is incremental in bridging existing methods.
The paper tackles the problem of signal decomposition by proposing a synthesis approach that imposes low-rankness on synthesis coefficients of time-frequency dictionaries, bridging synthesis modeling with analysis-based NMF. It results in efficient iterative shrinkage algorithms and demonstrates capabilities in audio signal processing, though no concrete numbers are provided.
Many state-of-the-art signal decomposition techniques rely on a low-rank factorization of a time-frequency (t-f) transform. In particular, nonnegative matrix factorization (NMF) of the spectrogram has been considered in many audio applications. This is an analysis approach in the sense that the factorization is applied to the squared magnitude of the analysis coefficients returned by the t-f transform. In this paper we instead propose a synthesis approach, where low-rankness is imposed to the synthesis coefficients of the data signal over a given t-f dictionary (such as a Gabor frame). As such we offer a novel modeling paradigm that bridges t-f synthesis modeling and traditional analysis-based NMF approaches. The proposed generative model allows in turn to design more sophisticated multi-layer representations that can efficiently capture diverse forms of structure. Additionally, the generative modeling allows to exploit t-f low-rankness for compressive sensing. We present efficient iterative shrinkage algorithms to perform estimation in the proposed models and illustrate the capabilities of the new modeling paradigm over audio signal processing examples.