A Probabilistic Model for Image Processing with Positivity Constraint and Spectral Density Control

This paper introduces a novel probabilistic model for images that addresses the challenge of simultaneously (1) maintaining pixel value positivity, (2) controlling the Power Spectral Density, and (3) ensuring an explicit partition function. This work serves as a preliminary step toward a fully self-supervised image deconvolution technique with these properties. The approach leverages a white positive field and introduces correlation through a filtering preserving the positivity. An example featuring an auto-regressive filter and a truncated normal distribution is developed. To facilitate parameter estimation and model manipulation, the probability density function of the resulting field is derived in the Fourier domain. A detailed analysis of the positivity constraint is also provided based on this example. Additionally, a Random Walk Metropolis sampler is proposed, with two complete parameter estimation examples: one using synthetic image data and the other based on real-world image data.