1. SUPER-RESOLUTION COMPRESSIVE HOLOGRAPHY Henrik D. Kjeldsen
[email protected] CERN IDEASQUARE SEMINAR 20th of
February 2015
2. SUPER-RESOLUTION COMPRESSIVE HOLOGRAPHY Henrik D. Kjeldsen
[email protected] CERN IDEASQUARE SEMINAR 20th of
February 2015 Lets Enhance, Duncan Robson, Museum of the Moving
Image
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 sensings 1st cousin: Group testing Highlight: 1st rule
of compressive sensing: Assumptions might fail, be careful!
4. Background Implementation of an EM generalization of
acoustic holography Recent work in experimental neuroscience
5. Background SUPER-RESOLUTION: x3 in each spatial mode
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
8. Background Issues: 1. Ill-posed 2D-to-3D model 2. Difficult
regularization 3. No super-resolution in far-field Current work in
acoustic holography
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 (0-optimization) is NP-hard. When the signal and
measurement bases are uncorrelated 0 1, which is tractable, but
still quite bad.
10. Compressive Holography There is a wealth of 1-optimization
algorithms, but they are all iterative, i.e. relatively slow.
Compressive sensings 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
11. Compressive Holography Advantages: 1. Non-iterative
reconstruction 2. No assumption on sparse basis 3. Advantage of
higher dimensions 4. Tuning free regularization
12. Compressive Holography Example: Hardware realizations? !=
Compressive Sensing on a CMOS Separable-Transform Image Sensor,
Proceedings of the IEEE, 2010
13. 3D object 0 0.5 1 Compressive Holography Compressive
holographic tomography: Optimize sparsity on full 3D reconstruction
instead of individual 2D slices to overcome ill-posed 2D-to-3D
model. Rosen et.al., Optics Express, Vol. 19, Issue 7, 2011 Phase
of kernel -2 0 2 Numerical backpropagation 0.5 1 1.5 2 Compressive
reconstruction 0.2 0.4 0.6 0.8 Applied Optics, Vol. 50, 2011
Diffracted field 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
14. Compressive Holography Compressive holographic tomography:
Work in progress. Tool to render holograms of complex 3D scenes to
test detailed tomographic and volumetric reconstructions
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