This paper presents a new approach to construct regularizing operators for the inversion of noisy Laplace transforms known as a set of data points on the real axis. The effectiveness of the proposed approach is demonstrated through examples of noisy Laplace transform inversions and the deconvolution of nuclear magnetic resonance relaxation data, including experimentally measured data. The software implementation of this method allows for enforcing the positivity of the solution without requiring any additional information.

翻译：本文提出了一种新方法，用于构建含噪拉普拉斯变换（已知为实轴上的一组数据点）反演的正则化算子。通过含噪拉普拉斯变换反演以及核磁共振弛豫数据（包括实验测量数据）去卷积的实例，验证了所提方法的有效性。该方法的软件实现无需任何附加信息即可强制解的正性约束。