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

This paper presents adaptive subspace-based inverse projections via division into multiple sub-problems (ASIP-DIMSs) for missing image data restoration. In the proposed method, a target problem for estimating missing image data is divided into multiple sub-problems, and each sub-problem is iteratively solved with the constraints of other known image data. By projection into a subspace model of image patches, the solution of each sub-problem is calculated, where we call this procedure “subspace-based inverse projection” for simplicity. The proposed method can use higher dimensional subspaces for finding unique solutions in each sub-problem, and successful restoration becomes feasible, since a high level of image representation performance can be preserved. This is the biggest contribution of this paper. Furthermore, the proposed method generates several subspaces from known training examples and enables derivation of a new criterion in the above framework to adaptively select the optimal subspace for each target patch. In this way, the proposed method realizes missing image data restoration using ASIP-DIMS. Since our method can estimate any kind of missing image data, its potential in two image restoration tasks, image inpainting and super-resolution, based on several methods for multivariate analysis is also shown in this paper.