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Received: 23 May 2019 Accepted: 20 September 2019 This paper attempts to construct a suitable wavelet for image denoising based on wavelet thresholding algorithm. First, the author discussed how image thresholding is affected by the wavelet orthogonality and bi-orthogonality, the features of vanishing moments and the odd or even symmetry of the decomposition end filter. The discussion shows that the most desirable wavelet for image denoising is the biorthogonal wavelet, in which the decomposition end filter has zero point even symmetry, the low-pass decomposition enjoys a wide support interval, and the high-pass decomposition filter has a short support and attenuates fast. On this basis, three zero point even symmetric biorthogonal wavelets with different vanishing moment features were developed through the parametric construction of fixed-length tightly-supported (FLTS) biorthogonal wavelet, and a self-adaptive hierarchical thresholding algorithm was designed. The simulation results show that the developed wavelets have excellent denoising ability and enhance the images with rich details. Coupled with the self-adaptive hierarchical thresholding algorithm, these wavelets can effectively improve the image quality.

Wavelet-Based Self-adaptive Hierarchical Thresholding Algorithm and Its Application in Image Denoising