Numerical design of nonstationary wavelets: Enhanced filter design andapplications in image compression

Document Type : Research Article

Authors

• A. Boussaad
• Y. Fourar
• K. Melkemi

Department of Mathematics, Faculty of Mathematics And Computer Science, University of Batna 2, Algeria.

10.22067/ijnao.2025.91265.1571

Abstract

In this study, we propose a novel method for computing both primal and dual filters for nonstationary biorthogonal wavelets, offering an advanced approach to wavelet filter design. The key challenge in image compres-sion that this study addresses is the inefficiency of conventional station-ary wavelets, which rely on fixed filter banks that do not adapt to local variations in an image. This limitation results in suboptimal compression performance, particularly for images with varying statistical properties and localized features. To address this, we use a nonstationary biorthogonal fil-ter banks, which modify basis functions at different scaling levels, leading to improved frequency resolution, signal representation, and compression efficiency. Our technique employs cardinal Chebyshev B-splines to derive explicit formulas for the primal filters, enabling precise calculation of filter coeffi-cients essential for wavelet transforms. Additionally, we enforce normality and biorthogonality conditions within nonstationary multiresolution anal-ysis to maintain the relationship between primal and dual wavelet filters at each scaling level. This structured approach allows for explicit formulation of the dual filters while ensuring accurate decomposition and reconstruc-tion. Experimental results confirm that the proposed method improves compression efficiency over conventional Daubechies biorthogonal filters, increasing the number of zero coefficients in compressed images. This leads to better visual quality and reduced storage requirements while maintaining computational efficiency. Such improvements are particularly beneficial in applications requiring high-fidelity image reconstruction, such as medical imaging, satellite data processing, and video compression. MATLAB sim-ulations validate the effectiveness of the approach, making it a promising alternative for image processing and data compression applications.

Keywords

• Cardinal Chebyshev B-splines
• Biorthogonality
• Wavelets
• Im-age compression

Main Subjects

• Computational Mathematics

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