Weighted average denoising with Sparse Orthonormal Transforms

Sparse orthonormal transforms (SOT) has recently been proposed as a data compression method that can achieve sparser representations in transform domain. Given initial conditions, the optimization method utilized to generate the dictionary of SOT also achieves the optimal orthonormal transform for hard thresholding. In the context of translation-invariant denoising, one can use this dictionary to represent the local neighborhood around each pixel and obtain denoised estimates for that neighborhood with hard thresholding. Building upon this approach, here we propose a method to fuse the overlapping denoised estimates via weighted linear averaging to compute final denoised signal.