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Guest Editorial for Part 1 of the Special Issue on the Mathematics of Deep Learning [From the Guest Editors]

By
Laura Balzano, Joan Bruna Estrach, Gitta Kutyniok, Robert Nowak, and Jong Chul Ye

Signal processing (SP), in its essence, aims to extract useful information out of noisy and incomplete physical measurements. Classically, one might exploit known mathematical models of these measured signals, e.g., harmonics of a musical instrument or physics of a medical imaging device. Modern deep learning (DL) shares a similar goal, namely, to extract useful information out of complex high-dimensional observations, but in contrast, it replaces known physical models with vast datasets, signaling a transition from model-based to data-based algorithms.

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