Simultaneous Sparse Dictionary Learning and Pruning
This addresses a crucial efficiency and precision issue in signal processing for imaging applications, though it is an incremental improvement over existing dictionary learning methods.
The paper tackles the problem of arbitrary dictionary size selection in dictionary learning by proposing a novel regularization method (GSCAD) that simultaneously learns a sparse dictionary and selects the appropriate size, achieving state-of-the-art results in image denoising compared to other approaches.
Dictionary learning is a cutting-edge area in imaging processing, that has recently led to state-of-the-art results in many signal processing tasks. The idea is to conduct a linear decomposition of a signal using a few atoms of a learned and usually over-completed dictionary instead of a pre-defined basis. Determining a proper size of the to-be-learned dictionary is crucial for both precision and efficiency of the process, while most of the existing dictionary learning algorithms choose the size quite arbitrarily. In this paper, a novel regularization method called the Grouped Smoothly Clipped Absolute Deviation (GSCAD) is employed for learning the dictionary. The proposed method can simultaneously learn a sparse dictionary and select the appropriate dictionary size. Efficient algorithm is designed based on the alternative direction method of multipliers (ADMM) which decomposes the joint non-convex problem with the non-convex penalty into two convex optimization problems. Several examples are presented for image denoising and the experimental results are compared with other state-of-the-art approaches.