One of the aims of 1 image inpainting is recovering an image some of which Fourier transform coefficients are lost. In this area, the algorithm of iterative coupled transform domain (ICT DI ) has been given by Li and Zeng (SIAM J Imaging Sci 9:24–51, 2016). In this paper, we present some modified algorithms of ICT DI and prove their convergence. In fact, we consider the effect of spectrum and phase angle of the Fourier transform, separately. Therefore, in comparison with ICT DI , one more regularization parameter is generated, and hence, we have more degree of freedom, and therefore, in general, we expect a more appropriate solution.
