Data-Driven Tight Frame Construction for Impulsive Noise Removal (Journal of Computational Mathematics, 2021)
The method of data-driven tight frame has been shown very useful in image restoration problems. We consider in this paper extending this important technique, by incorporating $L_1$ data fidelity into the original data-driven model, for removing impulsive noise which is a very common and basic type of noise in image data. The model contains three variables and can be solved through an efficient iterative alternating minimization algorithm in patch implementation, where the tight frame is dynamically updated. It constructs a tight frame system from the input corrupted image adaptively, and then removes impulsive noise by the derived system. We also show that the sequence generated by our algorithm converges globally to a stationary point of the optimization model. Numerical experiments and comparisons demonstrate that our approach performs well for various kinds of images. This benefits from its data-driven nature and the learned tight frames from input images capture richer image structures adaptively.
Keywords: Tight frame; Impulsive noise; Sparse approximation; Data-driven; Convergence analysis.