Data structures in imaging

I have been working on various aspects of imaging for more than twenty years withseveral colleagues with whom it has been an honor and a pleasure to work: L. Borcea,T. Callaghan, A. Chai, J. Garnier, A. Kim, M. Leibovich, M. Moscoso, A. Novikov, L.Ryzhik, K. Solna, and C. Tsogka. Imaging is an interdisciplinary field that is deeplyimbedded into nearly all sciences and its emergence as mainstream applied mathematicsis relatively recent but accelerating and spreading broadly. My interests have been mostlyin image formation but this inevitably intersects with image precessing (and denoising) aswell as image identification.

After a brief overview of synthetic aperture imaging, an image formation method thathas been widely used for more than half a century (radar, sonar, ...), I will first describe thestructure of the recorded data and then the imaging algorithm and its performance. Onewould think that this is it. What more is there to do at a methodological level? It turnsout that there are a lot of very interesting things to do, such as imaging both stationaryand moving objects in a complex scene. I will present a way to deal with motion estimation(and other) issues by giving the data a tensor structure and then using tensor methodsthat are much more sensitive and flexible.

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