| Summary: | The problem of interest in this paper is the mathematical and numerical analysis of a new non-variational model based on a high order non-linear PDE system resulting from image denoising. This model is motivated by involving the decomposition approach of $ H^{-1} $ norm suggested by Guo et al. <sup>[<xref ref-type="bibr" rid="b1">1</xref>,<xref ref-type="bibr" rid="b2">2</xref>]</sup> which is more appropriate to represent the small details in the textured image. Our model is based on a diffusion tensor that improves the behavior of the Perona-Malik diffusion directions in homogeneous regions and the Weickert model near tiny edges with a high diffusion order. A rigorous analysis of the existence and uniqueness of the weak solution of the proposed reaction-diffusion model is cheked in a suitable functional framework, using the Schauder fixed point theorem. Finally, we carry out a numerical result to show the effectiveness of our model by comparing the results obtained with some competitive models.
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