Sparse Representations, Numerical Linear Algebra, and Optimization (14w5003)


Gitta Kutyniok (LMU Munich)

(Stanford University)

(University of Wisconsin-Madison)

Ozgur Yilmaz (University of British Columbia)


The Banff International Research Station will host the "Sparse Representations, Numerical Linear Algebra, and Optimization" workshop from October 5th to October 10th, 2014.

The 21st century has been referred to as the Age of Data. Indeed,
scientists are facing a deluge of data---in astronomy, medicine,
seismology, meteorology, and many other areas---and need efficient
ways to analyze, compress, and extract meaning from this data. The
data processing paradigm of "sparse representation" makes the
observation that real-world data often is expressible in terms of just
a few elements of a suitable representation system. This fact has led
to important breakthroughs in data acquisition and processing
schemes. Anticipated social and scientific benefits include reduced
acquisition time for MRI images, higher-precision weather forecasting,
and improved subsurface imaging in geophysics, to name just a few.

Four research areas in mathematics are key to these developments:
compressed sensing, frame theory, numerical linear algebra, and
optimization. Compressed sensing studies efficient data acquisition
schemes; frame theory develops suitable representation systems; and
optimization and numerical linear algebra deliver efficient and stable
algorithms that use acquired data and representation systems to
recover vital information about the system being observed. Until now,
these four areas have interacted only in ad hoc ways in the service of
data analysis. This workshop brings together experts from all these
areas to initiate close and concerted interactions, to advance
research on the use of sparse representations in data processing and

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).