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Time-dependent imaging problems have a broad range of applications and are a lively field of research. Classical tomographic techniques represent inverse problems that are stationary in the sense that neither the searched quantity, nor the data depend on time. So far solution methods for dynamic inverse problems seemed too time-consuming and demanded too much memory capacity to become interesting for real-world applications. However, imaging modalities with data and/or parameters that depend on time attracted much notice over the last years, demanding for innovative inversion and analysis techniques that particularly take into account the physical meaning of the additional temporal variable.