A combined first-order and second-order variation approach for multiplicative noise removal

Le Jiang, Jin Huang, Jun Liu, Xiao-Guang Lv

Abstract


Denoising of images corrupted by multiplicative noise is an important task in various applications, such as laser imaging, synthetic aperture radar and ultrasound imaging. We propose a combined first-order and second-order variational model for removal of multiplicative noise. Our model substantially reduces the staircase effects while preserving edges in the restored images, since it combines advantages of the first-order and second-order total variation. The issues of existence and uniqueness of a minimizer for this variational model are analysed. Moreover, a gradient descent method is employed to solve the associated Euler–Lagrange equation, and several numerical experiments are given to show the efficiency of our model. In particular, a comparison with an existing model in terms of peak signal-to-noise ratio and structural similarity index is provided.



doi:10.1017/S1446181114000339

Keywords


multiplicative noise removal, denoising, total variation, Euler–Lagrange equation, structural similarity index



DOI: http://dx.doi.org/10.21914/anziamj.v56i0.7505



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.