- Homework for XMAS
- Light Field ++
- Compressing Imaging

- pick a paper
- tell me by Friday
- you can pick other papers you suggest, just ask me first
- SIGGRAPH Review Process
- writing technical reviews
- review instructions
- check suplementary material, videos, previous work.

- Presentation 10 minutes
- 5 minutes question
- send your presentation to me by the 11th

- read critically
- identify main contribution
- identify limitations
- justify your comments
- present the content

also compressive sampling

a novel sampling paradigm that asserts that one can recover certain signals from far fewer samplers than traditional methods

If a function x(t) contains no frequencies higher than B hertz, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart.

A sufficient sample-rate is therefore 2B samples/second, or anything larger. Equivalently, for a given sample rate fs, perfect reconstruction is guaranteed.

For some signals like images that are not naturally bandlimited, the sampling rate is dictated not by the Shannon theorem but by the desired temporal or spatial resolution.

many signals have some structure

incoherencesensing modality

images are sparse in some domain

images are sparse in some domain

images are sparse in some domain

compressed sensing, much less measurments

solving a Ax = b problem (b measurements, x unknown signal)

no in general

infinite x for the given y (linear subspace)

in the sparse case, yes!

easy! if you know the signal.

but we don't know the signal... :(

I want to design a $\phi$ matrix, that if I take K colums of it, they are full rank. (rank K)

And I want them to be close to orthogonal.

Restricted Isometry Property (RIP)

- k-sparse signal in space
- we want to find a $\phi$ that projects the signal into a lower dimensional space where it's still sparse
- dimensional reduction: we want to preserve distances

$\phi$ is still very large

check the rank of every possible selection of K

they found that this matrices are quite common, in fact random matrices usually work well

M is the number of samples, only grow logaritmically

plus l1 minimization

- measuring might me expensive
- takes long time
- exposure to radiation MRI
- 2013 Used for light fields

- many signals in nature are sparse
- we can take advantage of that when sampling
- taking random samples works with many signals
- given the correct basis
- and reconstructed with $l_1$ norm
- this is called compressed sensing

18.15 SALA 25

- Tell me the paper you choose: ASAP
- 5 minutes question
- send your presentation to me by the 12th

These slides have been prepared with materials, slides, and discussions from the following.

- Terence Tao
- Richard Baraniuk
- Gordon Wetzstein