[Paper Review] Markov Random Field Model-Based Salt and Pepper Noise Removal

Ahmadreza Baghaie|arXiv (Cornell University)|Sep 20, 2016

Image and Signal Denoising Methods44 references3 citations

TL;DR

This paper proposes a Markov Random Field (MRF) model with graph cuts using α-expansion moves for salt and pepper noise removal, formulating the problem as image inpainting with smoothness priors. The method achieves superior peak signal-to-noise ratio (PSNR) and faster computational time compared to belief propagation, tree-reweighted message passing, and iterated conditional modes, demonstrating its effectiveness for fixed-value impulse noise reduction in images with up to 90% corruption.

ABSTRACT

Problem of impulse noise reduction is a very well studied problem in image processing community and many different approaches have been proposed to tackle this problem. In the current work, the problem of fixed value impulse noise (salt and pepper) removal from images is investigated by use of a Markov Random Field (MRF) models with smoothness priors. After the formulation of the problem as an inpainting problem, graph cuts with $α$-expansion moves are considered for minimization of the energy functional. As for comparisons, several other minimization techniques that are widely used for MRF models' optimization are considered and the results are compared using Peak-Signal-to-Noise-Ratio (PSNR) and Structural Similarity Index (SSIM) as metrics. The investigations show the superiority of graph cuts with $α$-expansion moves over the other techniques both in terms of PSNR and also computational times.

Motivation & Objective

• To address the long-standing problem of fixed-value impulse noise (salt and pepper) in digital images using probabilistic graphical models.
• To explore the application of Markov Random Fields (MRFs) with smoothness priors for image inpainting in the context of noise removal.
• To evaluate and compare multiple energy minimization techniques for MRF-based noise reduction, focusing on performance and efficiency.
• To demonstrate the feasibility of extending the proposed framework to single-image super-resolution by treating up-sampling as a structured inpainting problem.

Proposed method

• The method begins with min/max detection to identify corrupted pixels, generating a binary mask indicating noisy locations.
• The noise removal problem is formulated as an image inpainting task using a Markov Random Field (MRF) model with smoothness priors.
• An energy functional is defined, combining data fidelity (based on the mask) and smoothness terms to encourage spatial consistency in reconstructed regions.
• Graph cuts with α-expansion moves are employed to minimize the energy functional, leveraging efficient optimization via expansion moves.
• The approach uses a first-order 4-connected neighborhood system to define local smoothness constraints in the MRF model.
• Performance is evaluated using PSNR and SSIM on standard test images with noise levels from 10% to 90%.

Experimental results

Research questions

• RQ1 Can Markov Random Field models with smoothness priors effectively restore images corrupted by salt and pepper noise?
• RQ2 How does graph cuts with α-expansion moves compare to other MRF optimization techniques (e.g., belief propagation, TRW-S, ICM) in terms of PSNR and computational time for noise removal?
• RQ3 Does the proposed MRF-based inpainting framework generalize to other image restoration tasks, such as single-image super-resolution?
• RQ4 How do different neighborhood systems (e.g., first-order vs. higher-order) affect the quality of reconstructed images?

Key findings

• The proposed method using graph cuts with α-expansion moves achieves the highest PSNR values across all tested noise levels, significantly outperforming belief propagation, tree-reweighted message passing, and iterated conditional modes.
• Despite having higher per-iteration cost, graph cuts with α-expansion converge in fewer iterations, resulting in lower overall computational time compared to other optimization techniques.
• The method maintains high structural similarity (SSIM), with minimal differences across techniques, indicating consistent preservation of image structure.
• The framework is extendable to single-image super-resolution, where it successfully reconstructs high-resolution images from low-resolution inputs with a 2× up-sampling factor.
• The results show that the proposed method achieves PSNR of 28.58 and SSIM of 0.81 on the Peppers image for ×2 super-resolution, outperforming other MRF optimization methods.
• Future improvements may come from using higher-order neighborhood systems to incorporate more contextual information, especially near edges.