The probe and singular sources methods are two well-known classical direct reconstruction methods in inverse obstacle problems governed by partial differential equations. In this paper, by considering an inverse obstacle problem governed by the Laplace equation in a bounded domain as a prototype case, an integrated theory of the probe and singular sources methods is proposed. The theory consists of three parts: (i) introducing the singular sources method combined with the notion of the probe method; (ii) finding a third indicator function whose two ways decomposition yields the indicator functions in the probe and singular sources methods; (iii) finding the completely integrated version of the probe and singular sources methods.

翻译：探针法与奇异源法是偏微分方程反障碍问题中两种著名的经典直接重构方法。本文以有界域中拉普拉斯方程所描述的反障碍问题为原型案例，提出了一种探针法与奇异源法的融合理论。该理论包含三个部分：(i) 结合探针法的概念引入奇异源法；(ii) 寻找第三种指示函数，其两种分解方式分别产生探针法与奇异源法中的指示函数；(iii) 建立探针法与奇异源法的完全融合版本。