Image Denoising with Probabilistic Models

This project implements and compares different probabilistic approaches for image denoising, developed as part of ISYE 6416 - Computational Statistics.

Overview

The repository contains implementations of:

• EPLL (Expected Patch Log Likelihood): Uses Gaussian Mixture Models (GMM) to learn patch priors
• MRF (Markov Random Fields): Implements both Gibbs and Metropolis-Hastings-based denoising approaches

You can read the full report here

Project Structure

.
├── data/
│   ├── Set12/          # Training and test images
│   └── BSDS300/        # Additional test dataset
├── model/
│   ├── EPLL/
│   │   ├── exploration.ipynb
│   │   └── learned_priors/
│   └── MRF/
│       └── MRF.ipynb
├── Report/             # Project Report
└── README.md

Methods Implemented

EPLL (Expected Patch Log Likelihood)

• Patch-based prior learning using GMM
• Half-Quadratic Splitting (HQS) optimization
• Auto-differentiation based optimization
• Supports multiple patch sizes and stride configurations

MRF (Markov Random Fields)

• Iterative Conditional Modes (ICM)
• MCMC with Metropolis-Hastings sampling
• Energy-based formulation with smoothness and fidelity terms

Usage

See individual notebooks in model/EPLL/ and model/MRF/ for detailed implementations and examples.