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A weighted parameter identification PDE-constrained optimization for inverse image denoising problem
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DOI：10.1007/s00371-021-02162-x.png)
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Abstract
En 中文
This paper treats the inverse denoising problem which aims to compute simultaneously the clean image and the weighting parameter lambda. The formulated denoising problem is posed using a partial differential equation (PDE)-constrained optimization model. The minimized function imposes a Tikhonov regularization on the estimated lambda, while the proposed PDE encompasses two high-order diffusive tensors. The particularity of this PDE is that it does not over-smooth homogeneous regions and preserves sharp edges during the denoising process, even if its degree is high. A new optimization procedure to compute the weighting parameter is also elaborated inspired from the nonsmooth Primal-dual algorithm. This leads to control of the diffusivity rate generated by the two diffusive operators. Finally, expressive results show that the computed spatial parameter lambda leads to obtain a pleasant clean image. This is also confirmed by numerous comparisons with other competitive denoising approaches.
Keywords:
Image restoration
PDE-constrained
Parameter identification
Primal-dual
Tensor diffusion
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