Robust Markov Random Field outlier detection and removal in subsampled images

Certain imaging technologies, such as fibred optical microscopy, operate with irregularly-spaced sparse sub-samples from their field of view. In this work, we address the problem of data restoration for applications where the observed irregularly distributed samples are corrupted by additive observation noise and sparse outliers (such as broken and damaged fibre cores). This problem is formulated as joint outlier detection and de-noising of irregularly sampled data and is addressed within a classical Bayesian framework. A Markov Random Field is considered to capture the intrinsic spatial correlation of the underlying intensity field and binary labels are used to locate the spatial position of the outliers. A Markov Chain Monte Carlo method is then used to perform Bayesian inference using the posterior distribution associated with the resulting Bayesian model. Simulations conducted on simulated data show the potential benefits of the proposed method in terms of data restoration and outlier identification.