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Edge-Preserving Image Denoising Based on Orthogonal Wavelet Transform and Level Sets

Junmei Zhong 1 and Huifang Sun 2
1. Inspur USA Inc, Suite 150 2010 156th AVE NE, Bellevue, WA, USA 98052
2. Mitsubishi Electric Research Laboratories, 201 Broadway, Cambridge, MA 02139

Abstract—The level set approach has the potential to accomplish simultaneous noise reduction and edge preservation when it is used for image denoising. However, this kind of techniques is not very efficient for denoising very noisy images for their non-reliable edge-stopping criterion in the Partial Differential Equation (PDE). In addition, the numerical calculation of curvature and other partial derivatives in the PDE is very sensitive to noise. In this paper, a new algorithm is developed to tackle such problems. Our idea is to first decompose the noisy image with the Orthogonal Wavelet Transform (OWT) and then we only filter the noisy wavelet coefficients at the three finest scales without touching the wavelet coefficients at higher levels for reducing noise while preserving edge-related coefficients. The level-set based curve evolution is finally performed on the less-noisy image reconstructed from the denoised wavelet coefficients. Thus, the PDE model can be optimized by removing the Gaussian smoothing component. Furthermore, the numerical calculation of all partial derivatives in the PDE is influenced by less noise and the selective denoising becomes more efficient. Experimental results show that the proposed algorithm outperforms the conventional level set methods and generates state-of-the-art denoising results in edge preservation and noise reduction.

Index Terms—orthogonal wavelet transform, level sets, mean curvature, image denoising

Cite: Junmei Zhong and Huifang Sun, "Edge-Preserving Image Denoising Based on Orthogonal Wavelet Transform and Level Sets," Journal of Image and Graphics, Vol. 6, No. 2, pp. 145-151, December 2018. doi: 10.18178/joig.6.2.145-151