Defocus deconvolution signal restoration based on Bayesian inference

In this study, we propose a Bayesian inference-based model and numerical algorithm to restore signals degraded by defocus convolution and white noise. To address uncertainties in estimating convolution kernel parameter, we introduce a model discrepancy term, whose statistical properties are characterized by a Gaussian distribution. Exploiting the Bayesian framework, the posterior distribution is partitioned into multiple sub-problems. Specifically, the degraded signal, model discrepancy, and convolution kernel parameter are iteratively updated using the primal-dual hybrid gradient (PDHG) method, Gaussian conjugate priors, and the random-walk Metropolis algorithm, respectively. This approach not only achieves effective signal restoration but also quantifies uncertainties in kernel parameter estimation, thereby mitigating error propagation. Numerical experiments demonstrate that the proposed method can simultaneously achieve accurate kernel parameter estimation and high-quality signal restoration.