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Many machine learning and signal processing problems are traditionally cast as convex optimization problems where the objective function is a sum of many simple terms. In this situation, batch algorithms compute gradients of the objective function by summing all individual gradients at every iteration and exhibit a linear convergence rate for strongly-convex problems. Stochastic methods rather select a single function at random at every iteration, classically leading to cheaper iterations but with a convergence rate which decays only as the inverse of the number of iterations. In this talk, I will present the stochastic averaged gradient (SAG) algorithm which is dedicated to minimizing finite sums of smooth functions; it has a linear convergence rate for strongly-convex problems, but with an iteration cost similar to stochastic gradient descent, thus leading to faster convergence for machine learning and signal processing problems. I will also mention several extensions, in particular to saddle-point problems, showing that this new class of incremental algorithms applies more generally.
Raymond Chan obtained his PhD degree from The Courant Institute of Mathematical Sciences in 1985. He is now the Chairman of the Mathematics Department at The Chinese University of Hong Kong. He won a Leslie Fox Prize in 1989; a Feng Kang Prize in 1997; a Morningside Award in 1998; and 2011 Higher Education Outstanding Scientific Research Output Awards from the Ministry of Education in China. He was elected a SIAM Fellow in 2013. He has published 120 journal papers and has been in the ISI Science Citation List of Top 250 Highly-Cited Mathematicians in the world since 2004. Chan has served on the editorial boards of many journals, including: Journal of Mathematical Imaging and Vision, Journal of Scientific Computing, Numerical Linear Algebra with Applications, SIAM Journal on Imaging Sciences, and SIAM Journal on Scientific Computing.
The famous Shannon-Nyquist theorem has become a landmark in the development of digital signal processing. However, in many modern applications, the signal bandwidths have increased tremendously, while the acquisition capabilities have not scaled sufficiently fast. Consequently, conversion to digital has become a serious bottleneck. Furthermore, the resulting high rate digital data requires storage, communication and processing at very high rates which is computationally expensive and requires large amounts of power. In the context of medical imaging sampling at high rates often translates to high radiation dosages, increased scanning times, bulky medical devices, and limited resolution. In this talk, we present a framework for sampling and processing a wide class of wideband analog signals at rates far below Nyquist by exploiting signal structure and the processing task and show several demos of real-time sub-Nyquist prototypes. We then consider applications of these ideas to a variety of problems in medical and optical imaging including fast and quantitative MRI, wireless ultrasound, fast Doppler imaging, and correlation based super-resolution in microscopy and ultrasound which combines high spatial resolution with short integration time. We end by discussing several modern methods for structure-based phase retrieval which has applications in several areas of optical imaging.
Mrs Clarisse Manjary Mandridake received her PhD in Image and Signal Processing from the University of Bordeaux I, France, for her works on bi-dimensional signal decomposition applied to classification of textured images, done in Laboratoire Automatique Productique et Traitement du Signal, and in closed connection with ARIANA Project in INRIA Sophia-Antipolis. She joined the research team of Advestigo for her postdoc year in 2002. As a researcher at Advestigo and later at Hologram Industries (now renamed SURYS), she developed technologies for the representation, indexation and search of images and videos in large scale databases. She is now in charge of the coordination of the research project for the SURYS digital labs and animates the scientist partnerships with University labs. Her expertise covers Applied Mathematics, image characterization, fingerprinting and authentication on various physical supports, from ID documents to smartlabels. More recently, her area of interest is to contribute to technological innovation for use by poor countries or developing countries in order to help them put in place what is called "good governance". It is a sine qua non Condition for any future economic development.
Dr. Anna M. Michalak is a faculty member in the Department of Global Ecology of the Carnegie Institution for Science in Stanford, California, and an Associate Professor in the Department of Earth System Science at Stanford University. Prior to joining Carnegie, she was the Frank and Brooke Transue Faculty Scholar and Associate Professor at the University of Michigan, Ann Arbor. Her research interests primarily lie in two areas. She explores the impacts of climate change and extreme events on freshwater and coastal water quality via influences on nutrient delivery to, and on conditions within, water bodies. She also studies the cycling and emissions of greenhouse gases at the Earth surface at regional to global scales – scales directly relevant to informing climate science and policy – primarily through the use of atmospheric observations that provide the clearest constraints at these critical scales. She is the recipient of numerous awards, including the Presidential Early Career Award for Scientists and Engineers (nominated by NASA), the NSF CAREER award, the Association of Environmental Engineering and Science Professors Outstanding Educator Award, and the Leopold Fellowship in environmental leadership. Dr. Michalak holds a B.Sc. from the University of Guelph, Canada, and M.S. and Ph.D. degrees from Stanford.
Christoph Schnörr received his degrees from the Technical University of Karlsruhe (today: Karlsruhe Institute of Technology) and the University of Hamburg, respectively. He worked as a researcher at the Fraunhofer Institut of Information and Data Processing in Karlsruhe before moving to the University of Hamburg. In 1998, he became full professor at the University of Mannheim, where he set up and directed the Computer Vision and Pattern Recognition Group. He moved to the Heidelberg University in 2008 where he is heading the Image and Pattern Analysis Group at the Institute of Applied Mathematics, which also is member of the Interdisciplinary Center for Scientific Computing. Christoph Schnörr has been coordinating 2010-2018 a research training group focusing on probabilistic graphical models and its applications to image analysis, funded by the German Science Foundation. He is one of 4 directors of the Heidelberg Collaboratory for Image Processing that implements and explores novel ways of combining basic strategic research in academia and research labs in industry, as part of the excellence initiative of the Heidelberg University. He served 2005-2014 as co-editor in chief of the International Journal of Computer Vision and currently as associate editor for the Journal of Mathematical Imaging and Vision and the SIAM Journal of Imaging Science. His research interests include mathematical models of image analysis and numerical optimisation.