A PDE approach to image restoration problem with observation on a meager domain

We present here a new nonlinear PDE approach to image restoration (the inpainting problem) using a meager blurred image or a finite number of observation points. To this end, one uses a least square approach with the H⁻¹ distributional metric. Some important theoretical and numerical results are provided in this paper.     

Dictionary learning based sinogram inpainting for CT sparse reconstruction

In CT (computed tomography), reconstruction from undersampling projection data is often ill-posed and suffers from severe artifact in the reconstructed images. To overcome this problem, this paper proposes a sinogram inpainting method based on recently rising sparse representation technology. In this approach, a dictionary learning based inpainting is used to estimate the missing projection data. The final image can be reconstructed by the analytic filtered back projection (FBP) reconstruction. We conduct experiments using both simulated and real phantom data. Compared to the comparative interpolation method, visual and numerical results validate the clinical potential of the proposed method.     

Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA)

This paper describes a novel inpainting algorithm that is capable of filling in holes in overlapping texture and cartoon image layers. This algorithm is a direct extension of a recently developed sparse-representation-based image decomposition method called MCA (morphological component analysis), designed for the separation of linearly combined texture and cartoon layers in a given image (see [J.-L. Starck, M. Elad, D.L. Donoho, Image decomposition via the combination of sparse representations and a variational approach, IEEE Trans. Image Process. (2004), in press] and [J.-L. Starck, M. Elad, D.L. Donoho, Redundant multiscale transforms and their application for morphological component analysis, Adv. Imag. Electron Phys. (2004) 132]). In this extension, missing pixels fit naturally into the separation framework, producing separate layers as a by-product of the inpainting process. As opposed to the inpainting system proposed by Bertalmio et al., where image decomposition and filling-in stages were separated as two blocks in an overall system, the new approach considers separation, hole-filling, and denoising as one unified task. We demonstrate the performance of the new approach via several examples.