A Bayesian Approach to Imputation of Missing Data Values in Audio Time Series

• Activity Number: 130
• Type: Topic Contributed
• Date/Time: Monday, August 8, 2005 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Patrick J. Wolfe*+
• Companies: Harvard University
• Keywords: Monte Carlo Methods ; Time-Frequency Analysis ; Regression ; Missing Data

Abstract

Audio time series such as digital speech and music recordings may suffer from degradations that result in missing data values, such as in the case of a damaged vinyl disc in need of restoration or as a result of packet loss in voice-over-IP transmission. As shown in previous work, the structures of such series lend themselves to natural prior specifications in terms of time-frequency behavior via a decomposition according to the principles of Gabor analysis over finite cyclic groups. Here, such a method is applied to address the inherently ill-posed problem of interpolating over repeated short gaps in audio signals. Bayesian models for time-frequency coefficients are postulated based on the idea of a Gabor regression, in which a signal is represented as a superposition of translated, modulated versions of a window function exhibiting good time-frequency concentration. Prior structures suitable for typical audio time series are used in conjunction with stochastic computation via Markov chain Monte Carlo methods to impute missing data values; qualities of the resultant reconstructions are shown to be in keeping with those of the time series under consideration.