In this book we investigate methods to solve certain inverse problems. According to Hadamard a problem is well-posed if a unique solution exists and the solution depends continuously on the data. If one of these properties is not fulfilled a problem is called ill-posed. Typically an inverse problem is ill-posed. In many applications it may not be necessary to solve the inverse problem in detail. One is only interested in determining areas, which differ in certain physical properties to a reference condition. For example in nondestructive material tests one is looking for holes, cracks or inclusions in a matter. Such partition of the domain in inclusion and surrounding area is called binary segmentation. In this work we study three different methods for solving such binary inverse problems.

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