A von Mises-Fisher prior to Remove Scale Ambiguity in Blind Deconvolution

We propose a von Mises-Fisher prior to remove scale ambiguity arising in blind deconvolution (BD). Indeed, traditional Bayesian BD methods rely on Gaussian priors that address only partially this ambiguity. We first derive the posteriors in closed-form to underline the benefit of a von Mises-Fisher prior compared with a conventional Gaussian prior. We also showcase its applicability within an augmented Gibbs sampler that includes a state-of-the-art re-scaling step. However, state-space exploration issues may still occur owing to the multimodal nature of the posteriors. These preliminary results encourage the design of BD-specific sphere-constrained sampling techniques.