Cai, Jian-Feng; Chan, Raymond H.; Shen, Lixin; Shen, Zuowei Simultaneously inpainting in image and transformed domains. (English) Zbl 1168.94312 Numer. Math. 112, No. 4, 509-533 (2009). Summary: We focus on the restoration of images that have incomplete data in either the image domain or the transformed domain or in both. The transform used can be any orthonormal or tight frame transforms such as orthonormal wavelets, tight framelets, the discrete Fourier transform, the Gabor transform, the discrete cosine transform, and the discrete local cosine transform. We propose an iterative algorithm that can restore the incomplete data in both domains simultaneously. We prove the convergence of the algorithm and derive the optimal properties of its limit. The algorithm generalizes, unifies, and simplifies the inpainting algorithm in image domains given in [J.-F. Cai et al., Appl. Comput. Harmon. 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