提出两种新型正交小波滤波器，性能优于现有超紧凑支持小波。
New Orthogonal Multiwavelet Filters Derived by Matrix Spectral Factorization
- 用快速Bauer法对正交CL小波滤波器的矩阵乘积进行谱分解构造新滤波器。
- 在图像压缩与去噪中，峰值信噪比和结构相似性指标均更优。
- 适合需要高保真度的图像处理场景，如医学影像或高清视频压缩。
本文利用快速Bauer法对正交CL小波滤波器的矩阵乘积进行矩阵谱分解，构造出两种新的具有超紧凑支持的正交多小波。这些新小波具备正交性、对称/反对称特性，其中一种在编码效率和光滑性方面优于其他超紧凑多小波。在基于子带的边缘检测、灰度与彩色图像压缩以及一维和二维信号去噪任务中，新小波滤波器与GHM、SA4、CL、整数Haar及Alpert多滤波器进行了对比分析。结果表明，新小波在图像压缩与去噪应用中可提供更优的人眼视觉感知指标、结构相似性（SSIM）和多尺度结构相似性（MS-SSIM）。
原文摘要 · Abstract (English)
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.
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