| Sumario: | With a wide range of applications in digital image processing, including multimedia editing, medical imaging, and cultural heritage preservation, image restoration is a fundamental task. In this work, we present a hybrid image restoration framework that combines a diffusion model based on the Cahn-Hilliard equation with a single-level wavelet transform to decompose an image into distinct frequency components. To maintain structural continuity, this hybrid method leverages the benefits of wavelets in the frequency domain for texture reconstruction and their propagation capabilities in the spatial domain. To achieve smooth information propagation and maintain edge sharpness, the finite implicit finite difference approach is used to solve the problem numerically. The effect of several types of wavelets was analyzed, including Haar, db1, sym1, bior1.1, db4, sym4, coif3, and others. The results indicate that the performance of wavelets varies depending on the length of the support and the smoothness of the fundamental functions, and provide practical guidance for selecting the most suitable wavelet for image restoration in modern image processing applications.
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