Bayesian methods for deconvolution of sparse processes

Abstract

In this work, various Bayesian methods for deconvolution and blind deconvolu- tion of sparse processes are studied. By using the prior assumption of sparsity, decon- volution and blind deconvolution operations are mapped to inference and parameter estimation methods in a Bayesian framework. For blind deconvolution of sparse processes, inverse-gamma model is proposed as a relaxation of the well known Bernoulli-Gaussian model. Methods based on expectation- maximization algorithm are investigated for both models, and several statistical infer- ence and parameter estimation techniques are presented for expectation and maximiza- tion steps. The improvement in the performance is demonstrated by experiments on simulated data. Receiver function analysis, a research topic in seismology, is studied as a real life application. Bayesian deconvolution is proposed as an alternative method to iterative deconvolution for estimating receiver functions. The superiority of Bayesian deconvo- lution is demonstrated both by experiments on both simulated and real data. Also, in this way, the assumption of sparsity for receiver functions is validated by the obtained results. Finally, a preliminary theoretical solution to a challenging problem of blind es- timation of receiver function analysis is developed. The performances of proposed methods for the solution are tested on simulated data.