Super-Resolution of Positive Sources and One More Thing ...

The resolution of all microscopes is limited by diffraction. The observed data is a convolution of the emitted signal with a low-pass kernel, the point-spread function (PSF) of the microscope. The frequency cut-off of the PSF is inversely proportional to the wavelength of light. Hence, the features of the object that are smaller than the wavelength of light are difficult to observe. In single-molecule microscopy the emitted signal is a collection of point sources, produced by blinking molecules. The goal is to recover the location of these sources with precision that is much higher than the wavelength of light. This leads to the problem of super-resolution of positive sources in the presence of noise. I will show that the problem can be solved by using convex optimization in a stable fashion. The stability of reconstruction depends on Rayleigh-regularity of the signal support, i.e., on how many point sources can occur within an interval of one wavelength. The stability estimate is complemented by a converse result: the performance of the convex algorithm is nearly optimal. I will describe an application, developed in collaboration with the group of Prof. W.E. Moerner, where we use these theoretical ideas to improve data processing in modern microscopes.

Lastly, I will talk about the work I currently do as a senior researcher at Helm.AI, a young Silicon Valley startup. Using sophisticated mathematical modeling, we developed a state-of-the-art road lane detector for self-driving cars. The key innovation is that this system requires no human-labeled data for training, a very scalable semi-supervised learning approach. I will not go into proprietary details of the algorithms.

Veniamin is a senior researcher at Helm.AI, working on robust perception algorithms for self-driving cars. She specializes in extracting information from unlabeled video stream in order to build a reliable road lane detector. Her current research is multidisciplinary, using tools from computer vision, robust statistics, signal processing, and deep learning.

Before Helm.AI, Veniamin was a Postdoctoral scholar in the Statistics Department at Stanford University, where she developed and analyzed convex optimization algorithms for signal recovery problems in microscopy and in radar.

Veniamin studied mathematics and computer science at Saint-Petersburg State University, Russia, graduating with the Dipl. Math. degree with honors in 2004. She then joined the Communication Technology Laboratory at ETH Zurich, Switzerland, as a research assistant, where she worked on problems of information transmission in radio communication networks. Veniamin graduated from ETH Zurich in 2010, receiving the Dr. Sc. degree. Her Ph.D. thesis was awarded with an ETH Medal. From 2010 to 2012, she was a postdoctoral researcher at ETH Zurich.

In 2012, Veniamin received a two-year Fellowship for Advanced Researchers by the Swiss National Science Foundation. In 2015, the team that Veniamin led received a Second Prize in Thomson Reuters Eikon Text Tagging Challenge, a machine learning and natural language processing competition.