Bayesian Deconvolution of Sparse Processes: In this work, various Bayesian methods for deconvolution and blind deconvolution of sparse processes are studied. For blind deconvolution of sparse processes, the inverse-gamma model is proposed as a relaxation of the well known Bernoulli-Gaussian model. Methods based on the expectation-maximization algorithm are investigated for both models, and several statistical inference and parameter estimation techniques are presented for expectation and maximization steps. The improvement in 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 deconvolution is demonstrated by experiments on both simulated and real data. Finally, a preliminary theoretical solution to a challenging problem of blind estimation of receiver function analysis is developed. The performances of proposed methods for the solution are tested on simulated data.