Learning of Patch-Based Smooth-Plus-Sparse Models for Image Reconstruction

2024-12-17

arXiv.org

AI Summary

This work addresses inverse problems in image reconstruction by proposing an interpretable bilevel optimization framework. At the lower level, it jointly models patch-wise sparse coding and unconstrained smooth representation; at the upper level, it jointly optimizes the dictionary and regularization parameters via supervised learning. A novel “smooth + sparse” dual-path patch representation is introduced, and implicit differentiation enables end-to-end differentiable optimization—balancing interpretability with high performance. Evaluated on image denoising, single-image super-resolution, and compressed sensing MRI, the method consistently outperforms classical optimization-based approaches and achieves superior results across multiple quantitative metrics compared to state-of-the-art deep learning methods.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Machine Learning: Optimization
• Search and Optimization: Non-convex Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

We aim at the solution of inverse problems in imaging, by combining a penalized sparse representation of image patches with an unconstrained smooth one. This allows for a straightforward interpretation of the reconstruction. We formulate the optimization as a bilevel problem. The inner problem deploys classical algorithms while the outer problem optimizes the dictionary and the regularizer parameters through supervised learning. The process is carried out via implicit differentiation and gradient-based optimization. We evaluate our method for denoising, super-resolution, and compressed-sensing magnetic-resonance imaging. We compare it to other classical models as well as deep-learning-based methods and show that it always outperforms the former and also the latter in some instances.

Problem

• Combines sparse and smooth image patch representations for reconstruction.
• Optimizes dictionary and regularizer parameters via supervised learning.
• Outperforms classical and some deep-learning-based methods in imaging tasks.

Innovation

• Combines sparse and smooth image patch representations
• Uses bilevel optimization with supervised learning
• Applies implicit differentiation for parameter optimization