A Set-Theoretic Study of the Relationships of Image Models and Priors for Restoration Problems
This work addresses a foundational gap in understanding image priors for researchers in computational imaging and inverse problems, though it is incremental in bridging theory and applications.
The paper tackles the unclear relationships among popular image models like sparsity and low-rankness for image restoration, providing a theoretical analysis and experimental validation that shows combining multiple models improves denoising performance, with quantitative demonstrations of complementary properties in deep learning methods.
Image prior modeling is the key issue in image recovery, computational imaging, compresses sensing, and other inverse problems. Recent algorithms combining multiple effective priors such as the sparse or low-rank models, have demonstrated superior performance in various applications. However, the relationships among the popular image models are unclear, and no theory in general is available to demonstrate their connections. In this paper, we present a theoretical analysis on the image models, to bridge the gap between applications and image prior understanding, including sparsity, group-wise sparsity, joint sparsity, and low-rankness, etc. We systematically study how effective each image model is for image restoration. Furthermore, we relate the denoising performance improvement by combining multiple models, to the image model relationships. Extensive experiments are conducted to compare the denoising results which are consistent with our analysis. On top of the model-based methods, we quantitatively demonstrate the image properties that are inexplicitly exploited by deep learning method, of which can further boost the denoising performance by combining with its complementary image models.