An improved nonlinear anisotropic PDE with p(x)-growth conditions
applied to image restoration and enhancement
Abstract
This work proposes a novel nonlinear parabolic equation with p(x)-growth
conditions for image restoration and enhancement. Based on the
generalized Lebesgue and Sobolev spaces with variable exponent, we
demonstrate the well-posedness of the proposed model. As a first result,
we prove the existence of a weak solution to our model when the reaction
term is bounded by a suitable function. Secondly, we use the
approximations method to establish the existence of a nonnegative weak
SOLA solution (Solution Obtained as Limit of Approximations) to the
proposed model. Finally, numerical experiments illustrate that the
proposed model performs better for image enhancement and denoising.