🤖 AI Summary
This study addresses the challenge that existing orthogonal multiwavelets struggle to simultaneously achieve ultra-compact support, symmetry, and high regularity. Building upon the matrix product filter structure of CL multiwavelets and leveraging the fast Bauer matrix spectral factorization method, this work constructs two novel classes of orthogonal multiwavelets. The proposed filters exhibit orthogonality, symmetry or antisymmetry, and ultra-compact support, with one class demonstrating superior coding efficiency and regularity compared to existing designs. Experimental results show that the new multiwavelets significantly outperform classical counterparts—including GHM, SA4, CL, Integer Haar, and Alpert multiwavelets—in image compression and denoising tasks, as measured by SSIM, MS-SSIM, and human visual perception metrics.
📝 Abstract
The paper considers the construction of two new orthogonal multiwavelets with supercompact support by using the Fast Bauer's method for matrix spectral factorization on the matrix product filter of the orthogonal CL multiwavelet filter. The new multiwavelets possess orthogonality, symmetry/antisymmetry, and one of them provides better coding and smoothness than other supercompact multiwavelets.
The performance of the new multiwavelet filters in subband-based edge detection, grayscale and color image compression and 1D and 2D signal denoising is compared with the GHM, SA4, CL, Integer Haar and Alpert multifilters. The comparative analysis shows that new multiwavelets can provides better human visual measures, SSIM and MS-SSIM in image compression and denoising applications.