ABSTRACT
Using the Fourier’s Heat Equation (HE) is the simplest way to diffuse information. However, this equation possesses only smooth solutions and, as such, it cannot preserve discontinuous image features. In order to address this shortcoming, nonlinear versions of the heat equation have been designed, as the ones relying on Total Variation (TV) flow, where the diffusivity constant depends upon the size of the image gradient (Shen & Chan 2002). Although clear improvements over the heat equation, these second-order PDEs still have some disadvantages as they do not perform well on edges spanning large gaps. As a result, a number of higher order PDEs for image inpainting have been proposed. For instance, Burger et al. (Burger, He, & Sch¨onlieb 2009) developed a new fourth-order variational equation that allows for isophotes connection across large distances and can be solved through very fast computational techniques: the TV-H-1 method. Although employed in other branches of image processing, this method has never been used to perform sinogram inpainting, at least to the best of our knowledge.
