Bayesian inference on multiscale models for poisson intensity estimation: applications to photon-limited image...

Area of Science:

• Statistical Modeling
• Image Processing
• Photon-Limited Imaging

Background:

• Poisson processes are fundamental in modeling count data, particularly in photon-limited imaging where noise is significant.
• Existing multiscale models for Poisson processes often struggle with accurately representing image edge structures and inter-scale dependencies.

Purpose of the Study:

• To introduce an improved statistical model for analyzing Poisson processes, specifically enhancing the analysis of photon-limited images.
• To develop a robust method for estimating rate-ratio density parameters directly from noisy Poisson data.
• To explore novel image representations for better edge modeling and improved performance in low-light imaging.

Main Methods:

• A multiscale representation of the Poisson process using mixtures of conjugate parametric distributions for rate ratios.
• A regularized expectation-maximization (EM) algorithm for maximum-likelihood estimation of parameters from observed Poisson data.
• Extension to a multiscale hidden Markov tree model (HMT) to capture inter-scale dependencies near image edges.
• Investigation of a 2-D recursive quad-tree image representation and a novel Poisson-Haar decomposition.

Main Results:

• The proposed regularized EM algorithm provides robust parameter estimation for rate-ratio densities.
• The HMT extension effectively models inter-scale dependencies, crucial for image edge analysis.
• The Poisson-Haar decomposition demonstrates superior modeling of image edge structures compared to conventional methods.
• Experimental results show significant performance improvements on both simulated and real photon-limited images.

Conclusions:

• The developed statistical model and associated algorithms offer a significant advancement in analyzing Poisson processes for photon-limited imaging.
• The novel Poisson-Haar decomposition and quad-tree representation provide enhanced capabilities for modeling image edges and reducing noise.
• The proposed techniques are effective in improving image quality and analysis under low-light conditions.