A significant challenge in improving the regeneration process of jet engines is the reduction of engine down-time during inspection. As such, early defect detection without engine disassembly will speed up the regeneration process. Defects in the engines hot-gas path (HGP) influence the density distribution of the flow and lead to irregularities in the density distribution of the exhaust jet which can be detected with the optical background-oriented Schlieren (BOS) method in a tomographic setup. The present paper proposes a combination of tomographic BOS measurements and supervised learning algorithms to develop a methodology for an automatic defect detection system. In the first step, the methodology is tested by analyzing the exhaust jet of a swirl burner array with a nonuniform fuel-supply of single burners with tomographic BOS measurements. The measurements are used to implement a support vector machine (SVM) pattern recognition algorithm. It is shown that the reconstruction quality of tomographic BOS measurements is high enough to be combined with pattern recognition algorithms. The results strengthen the hypothesis that it is possible to automatically detect defects in jet engines with tomographic BOS measurements and pattern recognition algorithms.