On the Unreasonable Effectiveness of Compressive Imaging - Ben Adcock, Simon Fraser University

Explore the groundbreaking field of compressive imaging in this 41-minute conference talk by Ben Adcock from Simon Fraser University. Delve into the paradoxical effectiveness of compressed sensing and imaging techniques, examining their impact and theoretical foundations. Investigate the properties of matrices satisfying the Restricted Isometry Property (RIP) and challenge conventional wisdom about the inverse square law. Analyze practical sampling patterns, including the binary world and Fourier measurements in both 1D and dD cases. Discover optimal encoder-decoder pairs and near-optimal Fourier strategies. Gain valuable insights into sampling strategy design with four key recommendations. This talk, part of the Isaac Newton Institute's workshop on "Approximation, sampling and compression in data science," bridges various mathematical disciplines and fosters collaboration among researchers in data science, computational statistics, machine learning, optimization, information theory, and learning theory.

Main collaborators
Compressed sensing and imaging
Impact of compressive imaging
Compressed sensing theory
Matrices satisfying the RIP
Second paradox: the inverse square law is suboptimal
Which patterns are used in practice?
The binary world
Remainder of the talk
Setup
Fourier measurements: ID case
dD case: Dyadic Isotropic Sampling (DIS)
Optimal encoder-decoder pairs
Near-optimal Fourier encoder-decoders
Remarks
Idea behind the optimal strategy
Idea behind the Fourier strategy
Four recommendations for sampling strategy design