Distributed Feature-Specific Imaging Jun Ke 1, Premchandra Shankar 1, and Mark A. Neifeld 1,2 Computational Optical Sensing and Imaging (COSI) Department of Electrical and Computer Engineering, 2 College of Optical Sciences University of Arizona

Outline  Motivation  Distributed feature-specific imaging system  System performance – reconstruction error & lifetime  Experimental result  Conclusion COSI2007

Conventional imaging : Feature-specific imaging (FSI) : Background COSI2007 measured image x+n noise n object x conventional imager collected irradiance post processing reconstruction object x estimated feature Fx+n noise n collected irradiance feature specific imager post processing reconstruction  Projections: PCA, DCT and Hadamard, etc.

Distributed feature-specific imaging (DFSI):  k > 1 → DFSI → m k = (F k G k -1 ) G k x + n k = F k x + n Motivation COSI2007 Distributed conventional imaging (DCI): n Imager K Imager 1 n Object: x n Imager 2 Base station # of measurement ←Large Small→ Complexity ←High Low→ Redundancy ←High Low→ Size/Weight/Power ←High Low→ Bandwidth ←High Low→ Lifetime ←Short Long→ Characteristics Object: x Base station n Imager 2 Imager 1 n n Imager K  k = 1 → FSI → m = F x + n  G k ~ geometric transform for the k th imager.

Parallel FS imager:  Imaging  -Optics Fixed Mask L – Detector Array m i = f i x + n, i=1, …, L n Noisy Measurements Object: x Feature-specific Imaging Architecture  Noise variance is proportional to σ 0 2 /T 0. Sequential FS imager:  Imaging Optics Light Collection Optics Programmable Mask Single Photo-Detector n Noisy Measurement Object: x m i = f i x + n i=1, …, L COSI2007  Noise variance is proportional to Lσ 0 2 /T 0.

System Performance – Reconstruction Error COSI2007 Object examples (32x32):  Wiener operator is used for reconstruction: where,  Reconstructed object:  RMSE:  Feature measurements: where,  For k imager DFSI, features are measured by each imager.  is the total # of features

System Performance – Reconstruction Error  There is a minimum RMSE for each curve.  Parallel FSI is better than sequential FSI in term of RMSE.  PCA reaches minimum using small number of features.  PCA has the best performance when # of features is small.  Hadamard has the best performance when # of features is large. COSI2007 M = total # of features

high noise moderate noise low noise As k increases,  System collected photons increases  # of features per imager decrease  Photons per feature increases  RMSE reduces Using more imagers will increase fidelity System Performance – Reconstruction Error COSI2007  When noise is high, PCA and Hadamard projections have similar performances  When noise is moderate or low, Hadamard produces the smallest minimum RMSE  Generally, Hadamard projection is the best candidate for noisy environment.

 Lifetime ~ total # of data transmitted before energy runs out / # of data in each transmission  Normalized lifetime in DFSI: ~ Lifetime of DFSI / Lifetime of conventional imaging system = N/(M/k)  Compression has not been considered in both systems System Performance – Lifetime COSI2007 n Imager K Imager 1 n Object: x n Imager 2 Base station M/k DFSI: N N N DCI: Object: x Base station n Imager 2 Imager 1 n n Imager K N N N

 Lifetime reduces as RMSE performance requirement is higher.  Lifetime is enlarged as more imagers are used.  With non-strict RMSE requirement, DFSI using PCA has the longest lifetime.  With strict requirement of RMSE, DFSI using Hadamard is the best option. Generally, DFSI with PCA present the best performance in term of lifetime. Normalized lifetime with different projections and different number of imagers k: System Performance – Lifetime COSI2007 k

Experiment  There is a minimum RMSE for each curve  RMSE reduces as K increases. COSI2007 σ 0 = Hadamard features original object k = 1,rmse=0.44k = 2,rmse=0.18 k = 3,rmse=0.12k = 4,rmse=0.10k = 5,rmse=0.09

Conclusion  DFSI preserves FSI properties.  DFSI has better performance compared with FSI  Hadamard is the best projection in term of reconstruction error.  PCA is the best projection in term of system lifetime. COSI2007

 Block-wise data testing  Random projection has the biggest RMSE  PCA achieves minimum RMSE quick  Hadamard performs better with more features Experiment - result COSI2007 σ 0 = 10 -4, Hadamard 600 features