From Seismology to
Compressed Sensing and Back, a Brief History
this talk we provide an overview of the history of l1-norm
minimization applied to underdetermined inverse
problems. In the
70s and 80s geophysicists proposed using l1-norm minimization
for deconvolution from bandpass data in reflection seismography.
In the 2000s, inspired
by this approach and by magnetic resonance imaging, a method to provably recover sparse
signals from random projections, known as compressed
sensing, was developed. Theoretical insights used to
analyze compressed sensing have recently been adapted to
understand the potential and limitations of l1-norm
minimization for deterministic problems. These include
super-resolution from low-pass data and the deconvolution
problem that originally motivated the geophysicists.