Interpretable Deep Image Denoiser by Unrolling Graph Laplacian Regularizer

Abstract

Image denoising is a fundamental problem in image restoration. Researchers have studied the problem for decades and proposed numerous algorithms. In the past ten years, deep learning has produced complex models that deliver high-quality denoised images, but these models require on large numbers of parameters, lack interpretability, and depend heavily on random parameter initialization.

As a result, they frequently converge to poor-performing local minima.

This thesis proposes an image denoising neural net constructed by unrolling an iterative algorithm solving a maximum a posteriori (MAP) optimization problem regularized using a graph Laplacian prior.

To guarantee a minimum level of performance, we initialize the network to a known (pseudo-)linear denoiser, which is mapped to a corresponding graph Laplacian matrix specifying the MAP problem, leveraging a previous linear algebraic theorem.

The performance of the network is further enhanced by learning an appropriate perturbation matrix to augment the graph Laplacian via a lightweight convolutional neural net (CNN).

This design bridges the gap between classical model-based methods with modern deep learning, eliminates the need for random initialization, reduces parameter count, and improves interpretability of the constructed network.

Experiments show that our method demonstrates competitive image quality reconstruction compared to state-of-the-art deep learning models, while offering improved robustness, interpretability, and parameter efficiency.