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Mathematical Problems in Engineering
Volume 2013, Article ID 309418, 10 pages
Research Article

HPM-Based Dynamic Wavelet Transform and Its Application in Image Denoising

College of Information and Electrical Engineering, China Agricultural University, Postbox 53, East Campus, 17 Qinghua Donglu Road, Haidian District, Beijing 100083, China

Received 26 April 2013; Revised 10 August 2013; Accepted 25 August 2013

Academic Editor: Claudio R. Fuerte-Esquivel

Copyright © 2013 Shu-Li Mei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Wavelet-based multiscale interpolation operator is often employed to construct the adaptive numerical method for PDEs, in which the computational complexity of the wavelet transform is one of the main factors affecting the algorithm efficiency. As the wavelet transform just acts as the detector of the characteristic points in the interpolation operator, the multiscale wavelet interpolation operator can be viewed as a nonlinear problem. Based on this assumption, we construct an approximate dynamic interpolation operator with the homotopy perturbation method (HPM), which decreases the computational complexity of the wavelet transform appearing in the wavelet interpolation operator from to , where is the amount of the wavelet scales. Then an adaptive algorithm solving the Perona-Malik model on image denoising is constructed with the HPM-based interpolation operator. Last, the quasi-Shannon wavelet is employed to design the experiments on the medical image and some artificial images denoising. The experiment results show that the simplified wavelet interpolation operator based on HPM possesses the adaptability and nonsensitivity to the time step, which is helpful to improve the algorithm efficiency. This illustrates that the HPM-based wavelet interpolation operator is an effective tool to solve the problems in image processing.