Missing Intensity Interpolation Using a Kernel PCA-Based POCS Algorithm and its Applications

Abstract

Abstract-A missing intensity interpolation method using a kernel 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.

Adaptive Subspace-Based Inverse Projections via Division Into Multiple Sub-Problems for Missing Image Data Restoration

“…This method is called back projection for lost pixels (BPLP) method. Several methods using kernel PCA (KPCA) [22] for successfully representing nonlinear visual features have also been proposed [7], [23], [24]. In recent years, many restoration methods using subspaces obtained by sparse representation have been proposed [8], [11], [25]- [31].…”

“…This approach provides a solution to the conventional problem of degradation of image representation performance. The above idea has not been proposed so far, i.e., no previous methods (not only our previously reported methods [23], [24], [30], [54] but also other existing methods) did not perform the division of missing components into multiple sub-groups. Then, by iteratively solving each sub-problem with the constraints of other known components within the target patch, the whole missing components can be successfully reconstructed since higher-dimensional subspaces can be used for approximating the target patch.…”

“…This is the biggest contribution of our paper. Next, since target images generally consist of several kinds of textures, they should be adaptively restored by the subspaces of the same kinds of textures, and we have proposed adaptive restoration methods in [23], [24], [54] 1 . Furthermore, in different fields of image restoration such as image denoising, the idea of adaptive restoration has also been introduced by using optimal subspaces for target patches [66], [67].…”

“…Clustering using each cluster's subspace is based on the idea of our previously reported methods [23], [24], [54], and this section shows their generalized explanation for which subspaces are arbitrary, i.e., not limited to KPCAbased subspaces used in [23], [24], [54].…”

“…Then C k is the total sum of these mean square errors for all sub-known components U n (n = 1, 2, · · · , N). It has been reported that the use of errors caused in the estimation is effective for selecting the optimal cluster or the optimal bases [23], [24], [30]. Specifically, in [30], the use of errors caused in the inverse projection provides better bases, i.e., better subspaces for representing the target patch compared to the use of approximation errors calculated from only the known components.…”