In this paper, we present a method of choice of an adaptative regularization parameter for data corrupted by Poisson noise based on a bilevel approach. The forward operator considered is nonlinear. The existence and unicity of the smoothed lower level problem, the differentiability properties of the constraint, and the adjoint method used to calculate the gradient of the reduced functional are studied in detail. The variance of the KL functional for Poisson noise is also investigated. The method is applied to the spectral CT inverse problem. Better reconstruction results are obtained with the bilevel method of choice than with a scalar regularization parameter.

中文翻译：

---

具有双水平方法的泊松噪声自适应正则化参数：在光谱计算机断层扫描中的应用

在本文中，我们提出了一种基于双水平方法为被泊松噪声破坏的数据选择自适应正则化参数的方法。所考虑的前向算子是非线性的。详细研究了平滑下层问题的存在性和唯一性，约束的可微性，以及用于计算约简泛函梯度的伴随方法。还研究了泊松噪声的 KL 泛函的方差。该方法应用于谱CT反问题。与使用标量正则化参数相比，选择双水平方法可以获得更好的重建结果。