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A missing intensity interpolation method using a kernel principal component analysis (PCA)-based projection onto convex sets (POCS) algorithm and its applications are presented in this paper. In order to interpolate missing intensities within a target image, the proposed method reconstructs local textures containing the missing pixels by using the POCS algorithm. In this reconstruction process, a nonlinear eigenspace is constructed from each kind of texture, and the optimal subspace for the target local texture is introduced into the constraint of the POCS algorithm. In the proposed method, the optimal subspace can be selected by monitoring errors converged in the reconstruction process. This approach provides a solution to the problem in conventional methods of not being able to effectively perform adaptive reconstruction of the target textures due to missing intensities, and successful interpolation of the missing intensities by the proposed method can be realized. Furthermore, since our method can restore any images including arbitrary-shaped missing areas, its potential in two image reconstruction tasks, image enlargement and missing area restoration, is also shown in this paper.