Wavelets on Intervals for Image Denoising
Quanhan Li, Michelle Michelle, Bin Han, Xiaosheng Zhuang · 2025
The method of obtaining (bi)-orthogonal wavelets on intervals (boundary wavelets) by a direct approach is employed. The tensor product can then be applied for the construction of high-dimensional boundary wavelets. The ℓ1optimization model integrating with such high-dimensional boundary wavelets for regularization was then used for image denoising and can be solved through the ADMM algorithm. Comparisons with the traditional wavelets (without boundary) are done to demonstrate the effectiveness of boundary wavelets and the advantages of the model with ADMM in the presence of large noise levels.