A Single-Parameter Factor-Graph Image Prior

TL;DR

This work introduces a single-parameter, train-free image prior based on normal-with unknown parameters (NUP) priors formulated as a factor-graph, enabling automatic local adaptation of piecewise-smooth image structure. By coupling row and column state-space models and employing iterative reweighted least squares with conjugate-gradient steps and Gaussian message passing, the method infers locally varying scales $R_n$ and a global data-fit parameter $oldsymbol{ au_Z^2}$. The framework yields competitive denoising results and supports flexible tasks such as contrast enhancement and inpainting, with an augmented variant recovering texture details. Overall, the approach demonstrates a principled, model-based alternative to data-hungry deep nets that scales to diverse image-processing tasks with a single interpretable parameter.

Abstract

We propose a novel piecewise smooth image model with piecewise constant local parameters that are automatically adapted to each image. Technically, the model is formulated in terms of factor graphs with NUP (normal with unknown parameters) priors, and the pertinent computations amount to iterations of conjugate-gradient steps and Gaussian message passing. The proposed model and algorithms are demonstrated with applications to denoising and contrast enhancement.

Figures (74)

• Figure 1: Factor graph of the basic model, focussing on pixel $n$ of some row with noisy observation $\breve Y_n = \breve y_n$. The small gray numbers (e.g., ${\footnotesize\color{gray} 1(3)}$) indicate the dimension of the corresponding variables for gray scale and color. The dashed box uses the trick from loeliger2023nup to reduce the MAP estimation of the slope noise scale factors $R_n$ to Gaussian message passing.
• Figure 2: Factor graph of the augmentation of Section \ref{['sec:Phase2']}, focussing on a single pixel with noisy observation $\breve Y_n = \breve y_n$. (The variables $R_n$ and $S_n$ are unrelated to the variables with these names in Fig. \ref{['fig:BasicModel']}.)
• Figure 3: Example of denoising and comparison with two prior-art methods (BM3D dabov2006imagedabov2007image and ZS-N2N mansour2023zero). The image is #5 in McMaster18 zhang2011color. The (actual) added Gaussian noise level is $\sigma = 20/255$, the assumed parameter $\sigma_Z$ is $1/21$. Bold and underline indicate the best and second best scores, respectively. The proposed method produces arguably fewer artifacts.
• Figure 6: Visual comparison of image Hill in dabov2006image for Gaussian noise level $\sigma = 10/255$. The quantitative PSNR/LPIPS results are given below the image. Bold indicates the best results.
• Figure 8: Visual comparison of image #1 in McMaster18 zhang2011color for Gaussian noise level $\sigma = 10/255$ and Poissonian noise with peak intensity 100. Bold and underline indicate the best and second best results, respectively.