Keijo Ruotsalainen - University of Oulu, Faculty of Information Technology and Electrical Engineering, Department of Applied and Computational Mathematics - "Introduction to Compressed Sensing"
The basic problem in several practical problems of science and technology
is the task of inferring quantities of interest from measured information.
When the information retrieval is linear, the problem reduces to solving a
linear a system of equations
Ax = y,
where A 2 CmD is the linear information retrieval process, x 2 CD the signal
to be reconstructed and y 2 Cm the measured data. In Big Data application
then both m and D are Big Numbers. If we have random signals, then we
may include the noise n 2 Cm:
Ax + n = y.
In this talk, I will present some basic ideas of compressed sensing: per-
forming data collection and compression simultaneously. With some simple
examples it will be demonstrated that under certain conditions it is pos-
sible to reconstruct signals when the number of measurements is less than
the signal length, in contrary to Shannon's sampling theorem. The talk is
non-technical and quite non-formal.
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