Transcript Slide 1

Optimization Issues in Compressed Sensing
• Algorithmic landscape for the most basic version
of signal recovery still unsettled
– Variety of approaches have been proposed; all have
drawbacks. New approaches needed!
• First-order vs. second-order methods?
• Combinatorial vs. linear vs. nonlinear methods?
• Important extensions needed
– No development to date of parallel/distributed
algorithms
• Very important for distributed sensor networks
– No development to date of algorithms that are stable
in the presence of noise in the measurements
Optimization Issues in Compressed Sensing
• Closely Related Issues
– How to optimally design set of measurements
• Theory says choose randomly, but is the best way to do it?
– How many measurements are needed?
• One can get by with much fewer measurements, but at the
expense of having to solve a tougher optimization problem.
What is the tradeoff?
• Tangential (but still important) Issues
– Extension of Compressed-Sensing Optimization to
Affine Rank Minimization
• Potentially very important in data mining