The seminar will start with a brief introduction to the theory of frames in Hilbert spaces. Then, the seminar will be devoted to the introduction and the study of the Gabor transform in time-frequency analysis which naturally fits into the theory of frames.Every participant will be assigned a paper covering a central result concerning the Gabor transform in signal processing.

Inverse problems arise in many applications in science & engineering. Typically, a physical model describes a forward problem and the task is to reconstruct from measurements, i.e. to perform inversion. In ill-posed problems, these inversions are troublesome as the inverse lacks e.g. stability. Regularization theory studies the controlled extraction of information from such systems.

While deep neural networks have been very successfully employed in classification problems, their stability properties remain still unclear. In particular, the presence of adversarial examples has demonstrated that state-of-the-art networks are vulnerable to small perturbations in the data. This course serves as an introduction to adversarial attacks and defenses for deep neural nework algorithms.

While deep neural networks have been very successfully employed in classification problems, their stability properties remain still unclear. In particular, the presence of so-called adversarial examples has demonstrated that state-of-the-art networks are extremely vulnerable to small perturbations in the data.

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