Bayesian Restoration of Audio Degraded by Low-Frequency Pulses Modeled via Gaussian Process

TL;DR

Controlled experiments indicate that the proposed Bayesian approach, while requiring significantly less user intervention, achieves perceptual results similar to those of previous approaches and performs well when dealing with naturally degraded signals.

Abstract

A common defect found when reproducing old vinyl and gramophone recordings with mechanical devices are the long pulses with significant low-frequency content caused by the interaction of the arm-needle system with deep scratches or even breakages on the media surface. Previous approaches to their suppression on digital counterparts of the recordings depend on a prior estimation of the pulse location, usually performed via heuristic methods. This paper proposes a novel Bayesian approach capable of jointly estimating the pulse location; interpolating the almost annihilated signal underlying the strong discontinuity that initiates the pulse; and also estimating the long pulse tail by a simple Gaussian Process, allowing its suppression from the corrupted signal. The posterior distribution for the model parameters as well for the pulse is explored via Markov-Chain Monte Carlo (MCMC) algorithms. Controlled experiments indicate that the proposed method, while requiring significantly less user intervention, achieves perceptual results similar to those of previous approaches and performs well when dealing with naturally degraded signals.

Figures (7)

• Figure 1: Model for the pulse shape following Equation \ref{['eq:model-parametric-pulse']}.
• Figure 2: Graphical dependence structure in the proposed model. Arrows, solid lines and dotted lines indicate, respectively: direct dependence, display of vector components, and both modeling possibilities for $\bm{\theta}_\mathrm{t}$.
• Figure 3: First 200 iterations of the simulated chain for $n_0$, $M$, and $\sigma_{\mathrm{d}}^2$ in experiment (A) for the Gaussian Process model. The rest of the iterations show similar behavior: $n_0$ and $M$ are constant, and analogous oscillations occur for $\sigma_{\mathrm{d}}^2$.
• Figure 4: Comparison between true and estimated pulses in experiment (A): light continuous and dark dashed lines represent the underlying distorted signal and the superimposed pulse, respectively, in both graphs; in the upper panel, the solid dark continuous line is the pulse estimate by the shape-based algorithm, and the point-dashed line is the pulse generated by the initial values of $\bm{\theta}_{\mathrm{t}}^{\mathrm{s}}$; in the lower panel, the solid dark line is the pulse estimated by the Gaussian Process algorithm.
• Figure 5: Function $\Delta \mu$ -- output of the initialization procedure (with associated threshold) for the "jazz" signal in experiment (B).