by Brian Busemeyer

# Compressed sensing

Compressed sensing is a way of extracting a full signal out of a sparse sampling. It's only requirement is that the signal has a sparse representation in some basis, which is actually true for most interesting signals that we encounter.

## Presentation Summary

In this presentation, I present:

- the basic problem this solves.
- why it makes sense to optimize for sparsity.
- results from my own implementation of the l-1 minimization approach.
- an exploration of the parameter space for which this method is successful.
- recent developments in the field, and it’s connection to physics.

## Examples

My compressed sensing notebook (html) and related python library.

## References

Original paper (I think? in some sense?):

IEEE Trans. Inf. Theory **52**, 1289 (2006)

Probabilistic seeding:

Phys. Rev. X **2**, 021005 (2012)

Simultaneous measurement of physical observables.:

Phys. Rev. Lett. **112**, 253602 (2014)

### All signal processing.

Yubo "Paul" Yang ALGORITHM

signal processing numerical method