How can a machine tell if a picture is an
image of a duck, a cloud, or a pair of dice? Millions of cameras have
been installed in buildings, streets, airports and cities around the
world. This has motivated the development of techniques on how to
acquire, compress, store, transmit and process massive amounts of
high-dimensional data. The Union of Subspace problem is easy to state,
has wide applications in computer vision and biomedical imaging, yet
there is a discrepancy between what we understand and what we can
implement. There are heuristic algorithms that work well in practice,
with no proofs on why they work. There is an ALGEBRAIC solution, but
there is no efficient way of implementing the solution. We will
carefully state and explain the problem, which originally arises in
harmonic analysis. We will look at a solution that uses modern algebra
at the undergraduate level. This problems brings together algebra and
analysis, thus the algebraists and the analysts are re-united under one
harmonious roof.
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