Audio Signal Enhancement with Low-Rank Time-Frequency Synthesis Models

The low-rank time-frequency synthesis (LRTFS) model assumes that the synthesis coefficients of the unobserved signal follow a latent low-rank variance structure. This work explores the potential of the LRTFS model in simultaneous noise reduction and source separation tasks. To this end, we devise a robust expectation-maximisation algorithm to approximate the type-II estimator of the latent low-rank components. To circumvent analytic marginalisation of the synthesis coefficients (E-step), integration is performed numerically through a lightweight MCMC sampler, thus bypassing explicit matrix inversion. The proposed sampler exploits the structure of the chosen dictionary—the complex modified discrete cosine transform (ℂMDCT)—to navigate the parameter space in a series of inexpensive joint draws. Moreover, the non-negative factorisation sub-problem (M-step) is supplemented with domain-specific regularisation schemes aimed at fostering high-quality audio reconstructions. The proposed technique is tested on a collection of denoising examples, and its potential for signal decomposition is explored in a series of case studies.