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Image prior modeling is the key issue in image recovery, computationalimaging, compresses sensing, and other inverse problems. Recent algorithmscombining multiple effective priors such as the sparse or low-rank models, havedemonstrated superior performance in various applications. However, therelationships among the popular image models are unclear, and no theory ingeneral is available to demonstrate their connections. In this paper, wepresent a theoretical analysis on the image models, to bridge the gap betweenapplications and image prior understanding, including sparsity, group-wisesparsity, joint sparsity, and low-rankness, etc. We systematically study howeffective each image model is for image restoration. Furthermore, we relate thedenoising performance improvement by combining multiple models, to the imagemodel relationships. Extensive experiments are conducted to compare thedenoising results which are consistent with our analysis. On top of themodel-based methods, we quantitatively demonstrate the image properties thatare inexplicitly exploited by deep learning method, of which can further boostthe denoising performance by combining with its complementary image models.

A Set-Theoretic Study of the Relationships of Image Models and Priors for Restoration Problems