Image Inpainting and Enhancement using Fractional Order Variational Model

The intention of image inpainting is to complete or fill the corrupted or missing zones of an image by considering the knowledge from the source region. A novel fractional order variational image inpainting model in reference to Caputo definition is introduced in this article. First, the fractional differential, and its numerical methods are represented according to Caputo definition. Then, a fractional differential mask is represented in 8-directions. The complex diffusivity function is also defined to preserve the edges. Finally, the missing regions are filled by using variational model with fractional differentials of 8-directions. The simulation results and analysis display that the new model not only inpaints the missing regions, but also heightens the contrast of the image. The inpainted images have better visual quality than other fractional differential filters

Collaborative patch-based super-resolution for diffusion-weighted images

In this paper, a new single image acquisition super-resolution method is proposed to increase image resolution of diffusion weighted (DW) images. Based on a nonlocal patch-based strategy, the proposed method uses a non-diffusion image (b0) to constrain the reconstruction of DW images. An extensive validation is presented with a gold standard built on averaging 10 high-resolution DW acquis itions. A comparison with classical interpo- lation methods such as trilinear and B-spline demonstrates the competitive results of our proposed approach in termsofimprovementsonimagereconstruction,fractiona lanisotropy(FA)estimation,generalizedFAandangular reconstruction for tensor and high angular resolut ion diffusion imaging (HARDI) models. Besides, fi rst results of reconstructed ultra high resolution DW images are presented at 0.6 × 0.6 × 0.6 mm 3 and0.4×0.4×0.4mm 3 using our gold standard based on the average of 10 acquisitions, and on a single acquisition. Finally, fi ber tracking results show the potential of the proposed super-resolution approach to accurately analyze white matter brain architecture.We thank the reviewers for their useful comments that helped improve the paper. We also want to thank the Pr Louis Collins for proofreading this paper and his fruitful comments. Finally, we want to thank Martine Bordessoules for her help during image acquisition of DWI used to build the phantom. This work has been supported by the French grant "HR-DTI" ANR-10-LABX-57 funded by the TRAIL from the French Agence Nationale de la Recherche within the context of the Investments for the Future program. This work has been also partially supported by the French National Agency for Research (Project MultImAD; ANR-09-MNPS-015-01) and by the Spanish grant TIN2011-26727 from the Ministerio de Ciencia e Innovacion. This work benefited from the use of FSL (http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/), FiberNavigator (code.google.com/p/fibernavigator/), MRtrix software (http://www. brain.org.au/software/mrtrix/) and ITKsnap (www.itk.org).Coupé, P.; Manjón Herrera, JV.; Chamberland, M.; Descoteaux, M.; Hiba, B. (2013). Collaborative patch-based super-resolution for diffusion-weighted images. NeuroImage. 83:245-261. https://doi.org/10.1016/j.neuroimage.2013.06.030S2452618