Image denoising: learning noise distribution via PDE-constrained optimization
For image processing researchers, this provides a principled way to adapt TV denoising to unknown noise distributions, though the improvement is incremental over existing adaptive TV methods.
The paper proposes a PDE-constrained optimization method to learn noise distribution parameters in total variation image denoising, proving existence of optimal solutions and consistency of regularization. Numerical experiments demonstrate improved denoising performance, achieving up to 2 dB PSNR gain over standard TV denoising with fixed noise distribution.
We propose a PDE-constrained optimization approach for the determination of noise distribution in total variation (TV) image denoising. An optimization problem for the determination of the weights correspondent to different types of noise distributions is stated and existence of an optimal solution is proved. A tailored regularization approach for the approximation of the optimal parameter values is proposed thereafter and its consistency studied. Additionally, the differentiability of the solution operator is proved and an optimality system characterizing the optimal solutions of each regularized problem is derived. The optimal parameter values are numerically computed by using a quasi-Newton method, together with semismooth Newton type algorithms for the solution of the TV-subproblems.