Estimation with Low-Rank Time-Frequency Synthesis Models

TL;DR

This paper introduces a novel synthesis-based low-rank time-frequency modeling approach for signal decomposition, bridging analysis and synthesis methods, enabling advanced multi-layer representations and applications in compressive sensing.

Contribution

It proposes a new synthesis approach imposing low-rankness on coefficients, connecting traditional NMF analysis with synthesis models, and enabling more complex structured representations.

Findings

Effective in audio signal processing tasks

Facilitates compressive sensing applications

Outperforms traditional analysis-based methods

Abstract

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.