Modified algorithms for image inpainting in Fourier transform domain

Abstract

One of the aims of image inpainting is recovering an image some of which Fourier transform coefficients are lost. In this area, the algorithm of iterative coupled transform domain (ICTDI) has been given by Li and Zeng (SIAM J Imaging Sci 9:24–51, 2016). In this paper, we present some modified algorithms of ICTDI and prove their convergence. In fact, we consider the effect of spectrum and phase angle of the Fourier transform, separately. Therefore, in comparison with ICTDI, one more regularization parameter is generated, and hence, we have more degree of freedom, and therefore, in general, we expect a more appropriate solution.