Nonconvex regularization for blurred images with Cauchy noise

Abstract

<p style='text-indent:20px;'>In this paper, we propose a nonconvex regularization model for images damaged by Cauchy noise and blur. This model is based on the method of the total variational proposed by Federica, Dong and Zeng [SIAM J. Imaging Sci.(2015)], where a variational approach for restoring blurred images with Cauchy noise is used. Here we consider the nonconvex regularization, namely a weighted difference of <inline-formula><tex-math id="M1">\begin{document}$ l_1 $\end{document}</tex-math></inline-formula>-norm and <inline-formula><tex-math id="M2">\begin{document}$ l_2 $\end{document}</tex-math></inline-formula>-norm coupled with wavelet frame, the alternating direction method of multiplier is carried out for this minimization problem, we describe the details of the algorithm and prove its convergence. Numerical experiments are tested by adding different levels of noise and blur, results show that our method can denoise and deblur the image better.</p>