1. 1. SUPER-RESOLUTION COMPRESSIVE HOLOGRAPHY Henrik D. Kjeldsen henrik.daniel.kjeldsen@cern.ch CERN IDEASQUARE SEMINAR 20th of February 2015
2. 2. SUPER-RESOLUTION COMPRESSIVE HOLOGRAPHY Henrik D. Kjeldsen henrik.daniel.kjeldsen@cern.ch CERN IDEASQUARE SEMINAR 20th of February 2015 Lets Enhance, Duncan Robson, Museum of the Moving Image
3. 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. 4. Background Implementation of an EM generalization of acoustic holography Recent work in experimental neuroscience
5. 5. Background SUPER-RESOLUTION: x3 in each spatial mode
6. 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
7. 7. Issues: 1. Ill-posed 2D-to-3D model, poor tomography 2. Difficult regularization, tuning required Tikhonov, Kyrlov, 2-regularization are resolution limited Background Rosen et.al., Optics Express, Vol. 19, Issue 7, 2011 Kjeldsen et. al., Journal of Neuroscience Methods, (in revision)
8. 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. 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. 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. 11. Compressive Holography Advantages: 1. Non-iterative reconstruction 2. No assumption on sparse basis 3. Advantage of higher dimensions 4. Tuning free regularization
12. 12. Compressive Holography Example: Hardware realizations? != Compressive Sensing on a CMOS Separable-Transform Image Sensor, Proceedings of the IEEE, 2010
13. 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. 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. 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. 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