On the well-posedness of a tensor-based second order PDE with bilateral term for image super-resolution

El Mourabit Idriss, MIMSC, EST Essaouira, Université Cadi Ayyad, Morocco, Abdelilah Hakim, Amine Laghrib, LAMAI, FST Marrakech, Université Cadi Ayyad, Morocco, EMI FST Béni-Mellal, Université Sultan Moulay Slimane, Maroc
2023 Evolution Equations and Control Theory  
In this paper, we introduce a second-order equation based on a diffusion tensor combined with a bilateral total variation (BTV) term that takes the benefit from the diffusion model of Perona-Malik in the homogeneous regions, the Weickert model near sharp edge and the BTV term in reducing blur. Compared to the other partial differential equations (PDE) used in the SR context, the proposed super-resolution (SR) PDE can efficiently preserve image components such as corners and flat regions with
more » ... s apparition of blur in homogeneous regions. Moreover, since the SR approaches are always illposed, a mathematical study of the existence and uniqueness of the solution is also checked in a Sobolev space. From the numerical experiments we can observe that the proposed PDE can efficiently improve the quality of the highresolution (HR) image. Surprisingly, the apparition of blur in the restored image is less compared to the other methods. In addition to visual evaluation, two-based metrics are computed to confirm the improvements offered by the proposed PDE.
doi:10.3934/eect.2022047 fatcat:2kfm476j2jcunh422ypwi3u3i4