A global approach for solving evolutive heat transfer for image denoising and inpainting

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.

Image inpainting on the basis of spectral structure from 2-D nonharmonic analysis

The restoration of images by digital inpainting is an active field of research and such algorithms are, in fact, now widely used. Conventional methods generally apply textures that are most similar to the areas around the missing region or use a large image database. However, this produces discontinuous textures and thus unsatisfactory results. Here, we propose a new technique to overcome this limitation by using signal prediction based on the nonharmonic analysis (NHA) technique proposed by the authors. NHA can be used to extract accurate spectra, irrespective of the window function, and its frequency resolution is less than that of the discrete Fourier transform. The proposed method sequentially generates new textures on the basis of the spectrum obtained by NHA. Missing regions from the spectrum are repaired using an improved cost function for 2D NHA. The proposed method is evaluated using the standard images Lena, Barbara, Airplane, Pepper, and Mandrill. The results show an improvement in MSE of about 10-20 compared with the examplar-based method and good subjective quality.