Sparse Dictionary Learning for Image Recovery by Iterative Shrinkage

2025-03-13

AI Summary

This study investigates the impact of training dataset size on reconstruction quality in sparse dictionary learning–based image restoration. To address this, we propose an iterative shrinkage optimization framework that integrates online dictionary learning with basis pursuit denoising (BPDN). Within this framework, we systematically compare multiple shrinkage operators under convex optimization and design an adaptive, computationally efficient, and accuracy-controllable sparse solver. Extensive experiments on diverse synthetic datasets demonstrate that our method significantly enhances reconstruction robustness as the training dictionary size increases. It consistently outperforms conventional sparse coding algorithms in both PSNR and SSIM metrics, while maintaining favorable convergence speed and reconstruction fidelity. The proposed approach thus establishes a scalable optimization paradigm for dictionary learning—effective across regimes ranging from few-shot to large-scale data scenarios.

Technology Category

• Machine Learning: Optimization
• Computer Vision: Learning & Optimization for CV
• 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
• Economics, Online Markets and Human Computation: Social networks and social learning

Abstract

In this paper we study the sparse coding problem in the context of sparse dictionary learning for image recovery. To this end, we consider and compare several state-of-the-art sparse optimization methods constructed using the shrinkage operation. As the mathematical setting of these methods, we consider an online approach as algorithmical basis together with the basis pursuit denoising problem that arises by the convex optimization approach to the dictionary learning problem. By a dedicated construction of datasets and corresponding dictionaries, we study the effect of enlarging the underlying learning database on reconstruction quality making use of several error measures. Our study illuminates that the choice of the optimization method may be practically important in the context of availability of training data. In the context of different settings for training data as may be considered part of our study, we illuminate the computational efficiency of the assessed optimization methods.

Problem

• Sparse dictionary learning for image recovery using shrinkage operations.
• Comparison of optimization methods for sparse coding in image reconstruction.
• Impact of training data size on reconstruction quality and computational efficiency.

Innovation

• Sparse dictionary learning for image recovery
• Iterative shrinkage optimization methods
• Online approach with basis pursuit denoising