Journal
IEEE TRANSACTIONS ON IMAGE PROCESSING
Volume 23, Issue 3, Pages 1060-1072Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIP.2014.2299065
Keywords
Analysis operator learning; loss-specific training; bi-level optimization; image restoration; MRFs
Funding
- Austrian Science Fund through the China Scholarship Council Scholarship Program
- START Project BIVISION [Y729]
- Austrian Science Fund (FWF) [Y729] Funding Source: Austrian Science Fund (FWF)
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This paper addresses a new learning algorithm for the recently introduced co-sparse analysis model. First, we give new insights into the co-sparse analysis model by establishing connections to filter-based MRF models, such as the field of experts model of Roth and Black. For training, we introduce a technique called bi-level optimization to learn the analysis operators. Compared with existing analysis operator learning approaches, our training procedure has the advantage that it is unconstrained with respect to the analysis operator. We investigate the effect of different aspects of the co-sparse analysis model and show that the sparsity promoting function (also called penalty function) is the most important factor in the model. In order to demonstrate the effectiveness of our training approach, we apply our trained models to various classical image restoration problems. Numerical experiments show that our trained models clearly outperform existing analysis operator learning approaches and are on par with state-of-the-art image denoising algorithms. Our approach develops a framework that is intuitive to understand and easy to implement.
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