Distributed Feature-Specific Imaging

Jun Ke1, Premchandra Shankar1, and Mark A. Neifeld1,2

Computational Optical Sensing and Imaging (COSI) 2007

1Department of Electrical and Computer Engineering, 2College of Optical Sciences

University of Arizona

Outline

Motivation

Distributed feature-specific imaging system

System performance – reconstruction error & lifetime

Experimental result

Conclusion

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Conventional imaging :

Feature-specific imaging (FSI) :

Background

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measured image

x+n

noise n

objectx

conventional imager

collected irradiance

post processing

reconstructionx̂

objectx

estimated featureFx+n

noise n

collected irradiance

feature specific imager

post processing

reconstructionx̂

Projections: PCA, DCT and Hadamard, etc.

Distributed feature-specific imaging (DFSI):

k > 1 → DFSI → mk = (FkGk-1) Gkx + nk = Fkx + n

Motivation

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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

Gk ~ geometric transform for the kth imager.

Parallel FS imager:

Imaging -Optics

Fixed Mask

L – Detector Array

mi = fi x + n, i=1, …, L

n

Noisy Measurements

Object: x

Feature-specific Imaging Architecture

Noise variance is proportional to σ02/T0.

Sequential FS imager:

Imaging Optics

Light Collection Optics

Programmable Mask

Single Photo-Detector

n

Noisy Measurement

Object: x

mi = fi x + n i=1, …, L

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Noise variance is proportional to Lσ02/T0 .

System Performance – Reconstruction Error

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Object examples (32x32):

T -1x x DW = R F(FR F +R )

{ }E TxR x x

Wiener operator is used for reconstruction:

where,: noise auto-correlation matrixDR

x̂ = Wy Reconstructed object:

2ˆ{|| || }/E N x - x RMSE:

m = Fx n Feature measurements: where, : 1 : : 1N M N M x F n

For k imager DFSI, features are measured by each imager./M k

is the total # of featuresM

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.

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M = total # of featuresM = 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

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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

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n

Imager K

Imager 1

n

Object: x

n

Imager 2

Base station

NN

M/k

M/k

M/k

M/k

M/k

M/k

DFSI:

NN

N

N

NDCI:

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

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k

Experiment

There is a minimum RMSE for each curve

RMSE reduces as K increases.

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σ0 = 10-3 1200 Hadamard features

original object k = 1,rmse=0.44 k = 2,rmse=0.18

k = 3,rmse=0.12 k = 4,rmse=0.10 k = 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.

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Block-wise data testing

Random projection has the biggest RMSE

PCA achieves minimum RMSE quick

Hadamard performs better with more features

Experiment - result

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σ0 = 10-4, Hadamard 600 features