  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.
