On the existence and uniqueness of the weak solution to spatial fractional nonlinear diffusion equation related to image processing
DOI:
https://doi.org/10.7146/math.scand.a-152461Abstract
This work discusses the existence and uniqueness of the weak solution to a spatial fractional diffusion equation, which can be applied in image processing. The proposed model combines the advantages of both second- and fourth-order diffusion equations along with Gaussian filtering by employing spatial fractional derivatives and a Gaussian filter. This approach enhance edges preservation and robustness to noise. The existence and uniqueness of the weak solution for the model are proved by applying Schauder's fixed-point theorem.
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