With super-resolution compressive holography we try to address several persistent issues in enhanced image and volume reconstruction; these are: Ill-posed 2D-to-3D volume reconstruction, difficult regularization requiring tuning, super-resolution in the far-field, as well as bringing the computational requirements down towards real-time performance. We show examples of recent innovations and outline some of the challenges for the future.
3. Participatory Experiment
Who in the audience can name all the clips?
Assumptions:
1. Only a few of you
2. Random seating
Do I need to ask all of you or can I find out with
fewer ”measurements”?
Compressive sensing’s 1st cousin: Group testing
Highlight: 1st rule of compressive sensing:
Assumptions might fail, be careful!
6. Background
New measures:
Energy flow vector field
Energy source density
Energy dissipation
New hypothesis:
Energy flow reveals
neural network
causality patterns
phase-locked
average of
previous clip
9. Compressive Holography
Compressive holography can address all three issues!
Compressive holography is a contradiction in terms..
Compressive sensing raises the issue of prior knowledge or
assumptions about the signal, specifically about the
sparsity (which is a pretty weak assumption).
In general, finding the sparsest solution (ℓ0-optimization) is
NP-hard.
When the signal and measurement bases are uncorrelated
ℓ0 ℓ1, which is tractable, but still quite bad.
10. Compressive Holography
There is a wealth of ℓ1-optimization algorithms, but they
are all iterative, i.e. relatively slow.
Compressive sensing’s 2nd cousin: Tensor completion
Assumptions:
1. Approximate low (multilinear)-rank instead of sparsity
2. Data can be sensed in each mode separately
In the 2D case, that is:
IEEE Transactions on Signal Processing, Vol. 63, Jan. 2015
15. Super-resolution Compressive Holography
Challenges:
1. Combine the above solutions in a single framework
We can address all three issues, 2D-to-3D, regularization and far-field super-
resolution, as well as speed, but so far not at the same time.
2. Design and implement appropriate hardware sensors
?
16. Marcus Kaiser and Newcastle
Dynamic Connectome Lab
Miles Whittington and
York Oscillations Group
Gary Green and
York Neuroimaging Centre
Marco Manca and
CERN Medical Applications
Acknowledgements