Abstract

Static feature-specific imaging (SFSI), where the measurement basis remains fixed/static during the data measurement process, has been shown to be superior to conventional imaging for reconstruction tasks. Here, we describe an adaptive approach that utilizes past measurements to inform the choice of measurement basis for future measurements in an FSI system, with the goal of maximizing the reconstruction fidelity while employing the fewest measurements. An algorithm to implement this adaptive approach is developed for FSI systems, and the resulting systems are referred to as adaptive FSI (AFSI) systems. A simulation study is used to analyze the performance of the AFSI system for two choices of measurement basis: principal component (PC) and Hadamard. Here, the root mean squared error (RMSE) metric is employed to quantify the reconstruction fidelity. We observe that an AFSI system achieves as much as 30% lower RMSE compared to an SFSI system. The performance improvement of the AFSI systems is verified using an experimental setup employed using a digital micromirror device (DMD) array.

© 2010 Optical Society of America

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References

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2010 (1)

2009 (1)

J. Ke, P. M. Shankar, and M. A. Neifeld, “Distributed imaging using an array of compressive cameras,” Opt. Commun. 282, 185–197 (2009).
[CrossRef]

2008 (4)

E. J. Cand‘es and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25, 21–30 (2008).
[CrossRef]

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[CrossRef]

M. D’Urso, K. Belkebir, L. Crocco, T. Isernia, and A. Litman, “Phaseless imaging with experimental data: facts and challenges,” J. Opt. Soc. Am. A 25, 271–281 (2008).
[CrossRef]

M. Shankar, R. Willett, N. Pitsianis, T. Schulz, R. Gibbons, R. Te Kolste, J. Carriere, C. Chen, D. Prather, and D. Brady, “Thin infrared imaging systems through multichannel sampling,” Appl. Opt. 47, B1–B10 (2008).
[CrossRef] [PubMed]

2007 (4)

2006 (8)

P. K. Baheti and M. A. Neifeld, “Feature-specific structured imaging,” Appl. Opt. 45, 7382–7391 (2006).
[CrossRef] [PubMed]

O. Bucci, L. Crocco, M. D’Urso, and T. Isernia, “Inverse scattering from phaseless measurements of the total field on open lines,” J. Opt. Soc. Am. A 23, 2566–2577 (2006).
[CrossRef]

R. N. Jarvis Haupt, “Signal reconstruction from noisy random projections,” IEEE Trans. Inf. Theory 52, 4036–4048 (2006).
[CrossRef]

D. Takhar, J. Laska, M. Wakin, M. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).
[CrossRef]

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[CrossRef]

Y. Tsaig and D. Donoho, “Extensions of compressed sensing,” Signal Processing 86, 549–571 (2006).
[CrossRef]

N. Pitsianis, D. Brady, A. Portnoy, X. Sun, T. Suleski, M. Fiddy, M. Feldman, and R. TeKolste, “Compressive imaging sensors,” Proc. SPIE 6232, 62320A (2006).
[CrossRef]

2005 (1)

N. Pitsianis, D. Brady, and X. Sun, “Sensor-layer image compression based on the quantized cosine transform,” Proc. SPIE 5817, 250–257 (2005).
[CrossRef]

2003 (2)

S. Park, M. Park, and M. Kang, “Super-resolution image reconstruction: A technical overview,” IEEE Signal Process. Mag. 20, 21–36 (2003).
[CrossRef]

M. A. Neifeld and P. M. Shankar, “Feature specific imaging,” Appl. Opt. 42, 3379–3389 (2003).
[CrossRef] [PubMed]

1995 (1)

Agaian, S.

S. Agaian, Hadamard Matrices and Their Applications (Springer–Verlag, 1985).

Ashok, A.

Baheti, P. K.

Baraniuk, R.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[CrossRef]

D. Takhar, J. Laska, M. Wakin, M. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).
[CrossRef]

Baron, D.

D. Takhar, J. Laska, M. Wakin, M. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).
[CrossRef]

Belkebir, K.

Brady, D.

M. Shankar, R. Willett, N. Pitsianis, T. Schulz, R. Gibbons, R. Te Kolste, J. Carriere, C. Chen, D. Prather, and D. Brady, “Thin infrared imaging systems through multichannel sampling,” Appl. Opt. 47, B1–B10 (2008).
[CrossRef] [PubMed]

N. Pitsianis, D. Brady, A. Portnoy, X. Sun, T. Suleski, M. Fiddy, M. Feldman, and R. TeKolste, “Compressive imaging sensors,” Proc. SPIE 6232, 62320A (2006).
[CrossRef]

N. Pitsianis, D. Brady, and X. Sun, “Sensor-layer image compression based on the quantized cosine transform,” Proc. SPIE 5817, 250–257 (2005).
[CrossRef]

Bucci, O.

Cand‘es, E. J.

E. J. Cand‘es and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25, 21–30 (2008).
[CrossRef]

Candès, E.

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

Carriere, J.

Cathey, W. T.

Chen, C.

Crocco, L.

D’Urso, M.

Davenport, M.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[CrossRef]

Donoho, D.

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[CrossRef]

Y. Tsaig and D. Donoho, “Extensions of compressed sensing,” Signal Processing 86, 549–571 (2006).
[CrossRef]

Dowski, E. R.

Duarte, M.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[CrossRef]

D. Takhar, J. Laska, M. Wakin, M. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).
[CrossRef]

Feldman, M.

N. Pitsianis, D. Brady, A. Portnoy, X. Sun, T. Suleski, M. Fiddy, M. Feldman, and R. TeKolste, “Compressive imaging sensors,” Proc. SPIE 6232, 62320A (2006).
[CrossRef]

Fiddy, M.

N. Pitsianis, D. Brady, A. Portnoy, X. Sun, T. Suleski, M. Fiddy, M. Feldman, and R. TeKolste, “Compressive imaging sensors,” Proc. SPIE 6232, 62320A (2006).
[CrossRef]

Gibbons, R.

Isernia, T.

Jarvis Haupt, R. N.

R. N. Jarvis Haupt, “Signal reconstruction from noisy random projections,” IEEE Trans. Inf. Theory 52, 4036–4048 (2006).
[CrossRef]

Jolliffe, I.

I. Jolliffe, Principle Component Analysis (Springer, 2002).

Kang, M.

S. Park, M. Park, and M. Kang, “Super-resolution image reconstruction: A technical overview,” IEEE Signal Process. Mag. 20, 21–36 (2003).
[CrossRef]

Ke, J.

J. Ke, P. M. Shankar, and M. A. Neifeld, “Distributed imaging using an array of compressive cameras,” Opt. Commun. 282, 185–197 (2009).
[CrossRef]

J. Ke and M. A. Neifeld, “Optical architectures for compressive imaging,” Appl. Opt. 46, 5293–5303 (2007).
[CrossRef] [PubMed]

Kelly, K.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[CrossRef]

D. Takhar, J. Laska, M. Wakin, M. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).
[CrossRef]

Laska, J.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[CrossRef]

D. Takhar, J. Laska, M. Wakin, M. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).
[CrossRef]

Litman, A.

Neifeld, M. A.

Park, M.

S. Park, M. Park, and M. Kang, “Super-resolution image reconstruction: A technical overview,” IEEE Signal Process. Mag. 20, 21–36 (2003).
[CrossRef]

Park, S.

S. Park, M. Park, and M. Kang, “Super-resolution image reconstruction: A technical overview,” IEEE Signal Process. Mag. 20, 21–36 (2003).
[CrossRef]

Pitsianis, N.

M. Shankar, R. Willett, N. Pitsianis, T. Schulz, R. Gibbons, R. Te Kolste, J. Carriere, C. Chen, D. Prather, and D. Brady, “Thin infrared imaging systems through multichannel sampling,” Appl. Opt. 47, B1–B10 (2008).
[CrossRef] [PubMed]

N. Pitsianis, D. Brady, A. Portnoy, X. Sun, T. Suleski, M. Fiddy, M. Feldman, and R. TeKolste, “Compressive imaging sensors,” Proc. SPIE 6232, 62320A (2006).
[CrossRef]

N. Pitsianis, D. Brady, and X. Sun, “Sensor-layer image compression based on the quantized cosine transform,” Proc. SPIE 5817, 250–257 (2005).
[CrossRef]

Portnoy, A.

N. Pitsianis, D. Brady, A. Portnoy, X. Sun, T. Suleski, M. Fiddy, M. Feldman, and R. TeKolste, “Compressive imaging sensors,” Proc. SPIE 6232, 62320A (2006).
[CrossRef]

Prasad, S.

Prather, D.

Romberg, J.

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

Sarvotham, S.

D. Takhar, J. Laska, M. Wakin, M. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).
[CrossRef]

Schulz, T.

Shankar, M.

Shankar, P. M.

J. Ke, P. M. Shankar, and M. A. Neifeld, “Distributed imaging using an array of compressive cameras,” Opt. Commun. 282, 185–197 (2009).
[CrossRef]

M. A. Neifeld and P. M. Shankar, “Feature specific imaging,” Appl. Opt. 42, 3379–3389 (2003).
[CrossRef] [PubMed]

Suleski, T.

N. Pitsianis, D. Brady, A. Portnoy, X. Sun, T. Suleski, M. Fiddy, M. Feldman, and R. TeKolste, “Compressive imaging sensors,” Proc. SPIE 6232, 62320A (2006).
[CrossRef]

Sun, T.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[CrossRef]

Sun, X.

N. Pitsianis, D. Brady, A. Portnoy, X. Sun, T. Suleski, M. Fiddy, M. Feldman, and R. TeKolste, “Compressive imaging sensors,” Proc. SPIE 6232, 62320A (2006).
[CrossRef]

N. Pitsianis, D. Brady, and X. Sun, “Sensor-layer image compression based on the quantized cosine transform,” Proc. SPIE 5817, 250–257 (2005).
[CrossRef]

Takhar, D.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[CrossRef]

D. Takhar, J. Laska, M. Wakin, M. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).
[CrossRef]

Tao, T.

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

Te Kolste, R.

TeKolste, R.

N. Pitsianis, D. Brady, A. Portnoy, X. Sun, T. Suleski, M. Fiddy, M. Feldman, and R. TeKolste, “Compressive imaging sensors,” Proc. SPIE 6232, 62320A (2006).
[CrossRef]

Tsaig, Y.

Y. Tsaig and D. Donoho, “Extensions of compressed sensing,” Signal Processing 86, 549–571 (2006).
[CrossRef]

Wakin, M.

D. Takhar, J. Laska, M. Wakin, M. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).
[CrossRef]

Wakin, M. B.

E. J. Cand‘es and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25, 21–30 (2008).
[CrossRef]

Willett, R.

Appl. Opt. (7)

IEEE Signal Process. Mag. (3)

E. J. Cand‘es and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25, 21–30 (2008).
[CrossRef]

S. Park, M. Park, and M. Kang, “Super-resolution image reconstruction: A technical overview,” IEEE Signal Process. Mag. 20, 21–36 (2003).
[CrossRef]

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[CrossRef]

IEEE Trans. Inf. Theory (3)

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[CrossRef]

R. N. Jarvis Haupt, “Signal reconstruction from noisy random projections,” IEEE Trans. Inf. Theory 52, 4036–4048 (2006).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Commun. (1)

J. Ke, P. M. Shankar, and M. A. Neifeld, “Distributed imaging using an array of compressive cameras,” Opt. Commun. 282, 185–197 (2009).
[CrossRef]

Opt. Express (1)

Proc. SPIE (3)

D. Takhar, J. Laska, M. Wakin, M. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).
[CrossRef]

N. Pitsianis, D. Brady, A. Portnoy, X. Sun, T. Suleski, M. Fiddy, M. Feldman, and R. TeKolste, “Compressive imaging sensors,” Proc. SPIE 6232, 62320A (2006).
[CrossRef]

N. Pitsianis, D. Brady, and X. Sun, “Sensor-layer image compression based on the quantized cosine transform,” Proc. SPIE 5817, 250–257 (2005).
[CrossRef]

Signal Processing (1)

Y. Tsaig and D. Donoho, “Extensions of compressed sensing,” Signal Processing 86, 549–571 (2006).
[CrossRef]

Other (4)

I. Jolliffe, Principle Component Analysis (Springer, 2002).

Pico projector, http://focus.ti.com/dlpdmd/docs/dlpdiscovery.tsp?sectionId=60&tabId=2234.

Beagle Board, http://beagleboard.org/.

S. Agaian, Hadamard Matrices and Their Applications (Springer–Verlag, 1985).

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Figures (16)

Fig. 1
Fig. 1

Block diagram for SFSI using PC bases.

Fig. 2
Fig. 2

Hadamard bases (a) sorted in Sylvester’s order, (b) sorted in energy collection order, (c-I) object example; object reconstruction example using 200 Hadamard bases (c-II) sorted in Sylvester’s order, (c-III) sorted in energy collection order.

Fig. 3
Fig. 3

Block diagram for AFSI using a PC basis, where * indicates the blocks distinguishing FASI using a PC basis from those using a Hadamard basis.

Fig. 4
Fig. 4

Image samples from a (a) high- and (b) low-diversity training set.

Fig. 5
Fig. 5

RMSE versus M in PCA-based SFSI systems and AFSI systems for L = 1 , 10, and 20 using (a) high- and (b) low-diversity training sets.

Fig. 6
Fig. 6

Examples of (a) object reconstruction using a PCA-based system; (b) using an SFSI system for M = 100 , (c) using an SFSI system for M = 260 , (d) using an AFSI system for M = 100 , and (e) using an AFSI system for M = 260 with a high-diversity training set A H .

Fig. 7
Fig. 7

RMSE versus M in an H-AFSI system for L = 1 , 10 using (a) a high- and (b) low-diversity training sets.

Fig. 8
Fig. 8

Object examples (top row) and their noisy measurements (bottom row) when σ 2 = 1 / T 0 with T 0 = 0.02 s .

Fig. 9
Fig. 9

RMSE versus M using (a) a PC and Hadamard AFSI system for L = 4 when T 0 = 0.02 s , (b) PC, and (c) Hadamard AFSI system for different L using high-diversity training set.

Fig. 10
Fig. 10

RMSE versus M for different T 0 ( s ) in a PC-based AFSI system using a high-diversity training set when L = 32 .

Fig. 11
Fig. 11

T total versus T 0 for (a) L = 1 , (b) L = 4 , and (c) L = 16 , PC-based; and (d) L = 1 , (e) L = 4 , and (f) L = 16 , Hadamard-based SFSI and AFSI systems using a high-diversity training set.

Fig. 12
Fig. 12

Experiment setup diagram.

Fig. 13
Fig. 13

Testing samples in experiment.

Fig. 14
Fig. 14

Reconstructions from (a) 128 PCA, and (b) 128 Hadamard experimental feature measurements in SFSI and AFSI systems for a 32 × 32 object when L = 1 .

Fig. 15
Fig. 15

Reconstructions from 160 Hadamard experimental feature measurements in SFSI and AFSI systems when L = 1 .

Fig. 16
Fig. 16

First five PC vectors in SFSI and AFSI system for face object 1 when L = 1 .

Tables (7)

Tables Icon

Table 1 RMSE in PC-SFSI and PC-AFSI Systems for L = 1 , 10, with M = 250 Using High- and Low-Diversity Training Sets

Tables Icon

Table 2 RMSE in H-SFSI and H-AFSI Systems for L = 1 , 10 with M = 250 Using High- and Low-Diversity Training Sets

Tables Icon

Table 3 Minimum T total in PC-based SFSI and AFSI Systems for L = 1 , 4, and 16 Using A H

Tables Icon

Table 4 Minimum T total in Hadamard-Based SFSI and AFSI Systems for L = 1 , 4, and 16 Using A H

Tables Icon

Table 5 RMSE in Experimental SFSI and AFSI Systems for L = 1 with M = 128 Using High-Diversity Training Sets

Tables Icon

Table 6 RMSE for Face and Tank Reconstructions from 128 PC and Hadamard Experimental, Simulated Feature Values in SFSI and AFSI Systems for L = 1 Using A H

Tables Icon

Table 7 System Performance Improvement in Terms of RMSE for Face and Tank Reconstructions from 128 PC and Hadamard Simulated Feature Values in SFSI and AFSI Systems for L = 1 Using A H

Equations (7)

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y = Fx + n ,
W = R x F T [ F R x F T + R n ] 1
y ^ ( i ) = W y ( i ) y ( i ) ,
W y ( i ) = R y ( i ) [ R y ( i ) + R n ] 1
R y ( i ) = E { [ F ( i ) x ] [ F ( i ) x ] T }
= F ( i ) R B ( i ) F ( i ) T .
y = c + * y + c - * y - = f T x + c + * n + c - * n - .

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