Bridging data-driven priors via the score function for posterior sampling -- Comparative review and experimental study
For practitioners of Bayesian inverse problems, this provides a versatile framework to incorporate diverse priors, though the contribution is incremental as it primarily reviews and integrates existing methods.
This paper unifies several data-driven priors for Bayesian inverse problems through their score functions and integrates them into a sampling algorithm, demonstrating efficiency in image inpainting and super-resolution tasks with real geological images.
This paper reviews how a diverse set of popular data-driven priors commonly used in Bayesian inverse problems can be unified through their respective score functions. By framing these priors under this common perspective, we show that they can benefit from their straightfoward and effective integration into a recently proposed sampling algorithm. The applicability of this common framework is illustrated by considering several data-driven priors, namely regularization-by-denoising, normalizing flow-based priors, score-based generative models, and convex-ridge regularizers. For these four particular priors, the performance of the method is evaluated when conducting image inpainting and single image super-resolution. These results, as well as those obtained when restoring real images acquired in a geological context, demonstrate the efficiency of the method. This unified framework proves versatile enough to handle any posterior distribution defined by a broad class of score function-based priors, beyond the specific cases considered in this paper.