Tikhonov regularization is an usual method to solve an ill-posed problem, recommended when the input data are contaminated with noise. However, in some cases, the use of this technique is not sufficient to provide good solutions. In this work, an improvement of the Tikhonov regularization method was proposed and tested in the inverse black body radiation problem. The method proposed consisted in including the norm of the fractional-order derivative of the solution in the original functional proposed by Tikhonov. In the present framework, the regularized solution depends on the regularization parameter, λ, and on the fractional derivative order, α. For α assuming real value between 0 and 2, the solution obtained is more precise than those from the usual Tikhonov regularization method.

中文翻译：

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用分数阶微分算子改进 Tikhonov 正则化方法求解逆黑体辐射问题

Tikhonov 正则化是解决不适定问题的常用方法，建议在输入数据受到噪声污染时使用。但是，在某些情况下，使用此技术不足以提供良好的解决方案。在这项工作中，提出了对 Tikhonov 正则化方法的改进，并在逆黑体辐射问题中进行了测试。提出的方法包括在 Tikhonov 提出的原始泛函中包含解的分数阶导数的范数。在本框架中，正则化解取决于正则化参数 λ 和分数阶导数 α。对于假设 0 和 2 之间的真实值的 α，获得的解比通常的 Tikhonov 正则化方法的解更精确。