The probe and singular sources methods are well-known two 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 {\it 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：探测法与奇点源法是偏微分方程控制的反障碍问题中两种经典直接重建方法。本文以有界域内拉普拉斯方程控制的反障碍问题为原型案例，提出探测法与奇点源法的集成理论。该理论包含三部分：(i) 引入结合探测法思想的奇点源法；(ii) 寻求{\it 第三类指示函数}，其两种分解方式分别导出探测法与奇点源法中的指示函数；(iii) 建立探测法与奇点源法的完全集成版本。