An improved bilevel optimization approach for image super-resolution based on a fractional diffusion tensor

Abstract

Variational regularization techniques are widely used to improve the quality of the super-resolved image. However, the success of these methods depends on some sensitive parameters which have to be manually tuned. Recently, an improved strategy to avoid this illness is to learn these parameters from some available data. In this work we propose an improved super-resolution method with bilevel optimization technique to learn the spatially dependent parameter λ that controls the diffusivity of the fractional tensor of the Partial Differential Equation (PDE) to remove both Gaussian and speckle noises. Also, we elaborate a mathematical well-posedness of the optimal control problem and we introduce a projected quasi-Newton algorithm to compute the HR image X and the associated parameter λ. The numerical experiments cope with our theoretical part and show a significant improvement of the restored HR image compared to some state of art super-resolution.