Abstract

Compressive imagers acquire images, or other optical scene information, by a series of spatially filtered intensity measurements, where the total number of measurements required depends on the desired image quality. Compressive imaging (CI) offers a versatile approach to optical sensing which can improve size, weight, and performance (SWaP) for multispectral imaging or feature-based optical sensing. Here we report the first (to our knowledge) systematic performance comparison of a CI system to a conventional focal plane imager for binary, grayscale, and natural light (visible color and infrared) scenes. We generate 1024×1024 images from a range of measurements (0.1%–100%) acquired using digital (Hadamard), grayscale (discrete cosine transform), and random (Noiselet) CI basis sets. Comparing the outcome of the compressive images to conventionally acquired images, each made using 1% of full sampling, we conclude that the Hadamard Transform offered the best performance and yielded images with comparable aesthetic quality and slightly higher spatial resolution than conventionally acquired images.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. E. J. Candès and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies?” IEEE Trans. Inf. Theory 52, 5406–5425 (2006).
    [CrossRef]
  4. D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).
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    [CrossRef]
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2012 (1)

L. McMackin, M. A. Herman, B. Chatterjee, and M. Weldon, “A high-resolution SWIR camera via compressed sensing,” Proc. SPIE 8353, 835303 (2012).
[CrossRef]

2011 (1)

S. Becker, J. Bobin, and E. Candès, “NESTA: a fast and accurate first-order method for sparse recovery,” SIAM J. Imaging Sci. 4, 1–39 (2011).

2009 (2)

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

P. K. Baheti and M. A. Neifeld, “Recognition using information-optimal adaptive feature-specific imaging,” J. Opt. Soc. Am. A 26, 1055–1070 (2009).
[CrossRef]

2008 (2)

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

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

2007 (2)

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

R. G. Baraniuk, “Compressive sensing [Lecture Notes],” IEEE Signal Process. Mag. 24, 118–121 (2007).
[CrossRef]

2006 (6)

G. Frenkel, E. Katzav, M. Schwartz, and N. Sochen, “Distribution of anomalous exponents of natural images,” Phys. Rev. Lett. 97, 103902 (2006).
[CrossRef]

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

E. J. 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]

E. J. Candès and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies?” IEEE Trans. Inf. Theory 52, 5406–5425 (2006).
[CrossRef]

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

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

2005 (2)

2003 (1)

1998 (1)

D. Doherty and G. Hewlett, “10.4: phased reset timing for improved digital micromirror device (DMD) brightness,” Soc. Inf. Disp. Symp. Dig. Tech. Pap. 29, 125–128 (1998).
[CrossRef]

1997 (1)

D. L. Ruderman, “Origins of scaling in natural images,” Vis. Res. 37, 3385–3398 (1997).
[CrossRef]

Alzaidi, S.

R. P. Millane, S. Alzaidi, and W. H. Hsiao, “Scaling and power spectra of natural images,” in Proceedings of Image and Vision Computing New Zealand, D. G. Bailey, ed. (Massey University, 2003), pp. 148–153.

Anderson, D.

R. Robucci, L. K. Chiu, J. Gray, J. Romberg, P. Hasler, and D. Anderson, “Compressive sensing on a CMOS separable transform image sensor,” in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2008 (IEEE, 2008), pp. 5125–5128.

Baheti, P. K.

Baraniuk, R. G.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

R. G. Baraniuk, “Compressive sensing [Lecture Notes],” IEEE Signal Process. Mag. 24, 118–121 (2007).
[CrossRef]

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

M. B. Wakin, J. N. Laska, M. F. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. F. Kelly, and R. G. Baraniuk, “An architecture for compressive imaging,” in 2006 IEEE International Conference on Image Processing (IEEE, 2006) pp. 1273–1276.

Baron, D.

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

M. B. Wakin, J. N. Laska, M. F. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. F. Kelly, and R. G. Baraniuk, “An architecture for compressive imaging,” in 2006 IEEE International Conference on Image Processing (IEEE, 2006) pp. 1273–1276.

Becker, S.

S. Becker, J. Bobin, and E. Candès, “NESTA: a fast and accurate first-order method for sparse recovery,” SIAM J. Imaging Sci. 4, 1–39 (2011).

Bobin, J.

S. Becker, J. Bobin, and E. Candès, “NESTA: a fast and accurate first-order method for sparse recovery,” SIAM J. Imaging Sci. 4, 1–39 (2011).

Boyd, S.

S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University, 2004).

Candès, E.

S. Becker, J. Bobin, and E. Candès, “NESTA: a fast and accurate first-order method for sparse recovery,” SIAM J. Imaging Sci. 4, 1–39 (2011).

Candès, E. J.

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

E. J. 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]

E. J. Candès and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies?” IEEE Trans. Inf. Theory 52, 5406–5425 (2006).
[CrossRef]

Chatterjee, B.

L. McMackin, M. A. Herman, B. Chatterjee, and M. Weldon, “A high-resolution SWIR camera via compressed sensing,” Proc. SPIE 8353, 835303 (2012).
[CrossRef]

Chiu, L. K.

R. Robucci, L. K. Chiu, J. Gray, J. Romberg, P. Hasler, and D. Anderson, “Compressive sensing on a CMOS separable transform image sensor,” in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2008 (IEEE, 2008), pp. 5125–5128.

Davenport, M. A.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

Doherty, D.

D. Doherty and G. Hewlett, “10.4: phased reset timing for improved digital micromirror device (DMD) brightness,” Soc. Inf. Disp. Symp. Dig. Tech. Pap. 29, 125–128 (1998).
[CrossRef]

Donoho, D. L.

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

Duarte, M. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

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

M. B. Wakin, J. N. Laska, M. F. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. F. Kelly, and R. G. Baraniuk, “An architecture for compressive imaging,” in 2006 IEEE International Conference on Image Processing (IEEE, 2006) pp. 1273–1276.

Frenkel, G.

G. Frenkel, E. Katzav, M. Schwartz, and N. Sochen, “Distribution of anomalous exponents of natural images,” Phys. Rev. Lett. 97, 103902 (2006).
[CrossRef]

Gamal, A. E.

Y. Oike and A. E. Gamal, “A 256×256 CMOS image sensor with ΔΣ-based single-shot compressed sensing,” in Solid-State Circuits Conference Digest of Technical Papers (ISSCC) (IEEE, 2012), pp. 386–388.

Ganotra, D.

Gonzalez, R. C.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. (Prentice-Hall, 2006).

Gray, J.

R. Robucci, L. K. Chiu, J. Gray, J. Romberg, P. Hasler, and D. Anderson, “Compressive sensing on a CMOS separable transform image sensor,” in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2008 (IEEE, 2008), pp. 5125–5128.

Hasler, P.

R. Robucci, L. K. Chiu, J. Gray, J. Romberg, P. Hasler, and D. Anderson, “Compressive sensing on a CMOS separable transform image sensor,” in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2008 (IEEE, 2008), pp. 5125–5128.

Herman, M. A.

L. McMackin, M. A. Herman, B. Chatterjee, and M. Weldon, “A high-resolution SWIR camera via compressed sensing,” Proc. SPIE 8353, 835303 (2012).
[CrossRef]

Hewlett, G.

D. Doherty and G. Hewlett, “10.4: phased reset timing for improved digital micromirror device (DMD) brightness,” Soc. Inf. Disp. Symp. Dig. Tech. Pap. 29, 125–128 (1998).
[CrossRef]

Hornbeck, L. J.

L. J. Hornbeck, “Digital light processing: a new MEMS-based display technology,” in Technical Digest of the Institute of Electrical Engineers of Japan 14th Sensor Symposium (IEEJ, Kawasaki, Japan, 1996), pp. 297–304.

Hsiao, W. H.

W. H. Hsiao and R. P. Millane, “Effects of occlusion, edges, and scaling on the power spectra of natural images,” J. Opt. Soc. Am. A 22, 1789–1797 (2005).
[CrossRef]

R. P. Millane, S. Alzaidi, and W. H. Hsiao, “Scaling and power spectra of natural images,” in Proceedings of Image and Vision Computing New Zealand, D. G. Bailey, ed. (Massey University, 2003), pp. 148–153.

Katzav, E.

G. Frenkel, E. Katzav, M. Schwartz, and N. Sochen, “Distribution of anomalous exponents of natural images,” Phys. Rev. Lett. 97, 103902 (2006).
[CrossRef]

Ke, J.

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

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

Kelly, K. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

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

M. B. Wakin, J. N. Laska, M. F. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. F. Kelly, and R. G. Baraniuk, “An architecture for compressive imaging,” in 2006 IEEE International Conference on Image Processing (IEEE, 2006) pp. 1273–1276.

Laska, J. N.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

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

M. B. Wakin, J. N. Laska, M. F. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. F. Kelly, and R. G. Baraniuk, “An architecture for compressive imaging,” in 2006 IEEE International Conference on Image Processing (IEEE, 2006) pp. 1273–1276.

McMackin, L.

L. McMackin, M. A. Herman, B. Chatterjee, and M. Weldon, “A high-resolution SWIR camera via compressed sensing,” Proc. SPIE 8353, 835303 (2012).
[CrossRef]

Millane, R. P.

W. H. Hsiao and R. P. Millane, “Effects of occlusion, edges, and scaling on the power spectra of natural images,” J. Opt. Soc. Am. A 22, 1789–1797 (2005).
[CrossRef]

R. P. Millane, S. Alzaidi, and W. H. Hsiao, “Scaling and power spectra of natural images,” in Proceedings of Image and Vision Computing New Zealand, D. G. Bailey, ed. (Massey University, 2003), pp. 148–153.

Neifeld, M. A.

Oike, Y.

Y. Oike and A. E. Gamal, “A 256×256 CMOS image sensor with ΔΣ-based single-shot compressed sensing,” in Solid-State Circuits Conference Digest of Technical Papers (ISSCC) (IEEE, 2012), pp. 386–388.

Pal, H. S.

Robucci, R.

R. Robucci, L. K. Chiu, J. Gray, J. Romberg, P. Hasler, and D. Anderson, “Compressive sensing on a CMOS separable transform image sensor,” in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2008 (IEEE, 2008), pp. 5125–5128.

Romberg, J.

E. J. 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]

R. Robucci, L. K. Chiu, J. Gray, J. Romberg, P. Hasler, and D. Anderson, “Compressive sensing on a CMOS separable transform image sensor,” in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2008 (IEEE, 2008), pp. 5125–5128.

Ruderman, D. L.

D. L. Ruderman, “Origins of scaling in natural images,” Vis. Res. 37, 3385–3398 (1997).
[CrossRef]

Sarvotham, S.

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

M. B. Wakin, J. N. Laska, M. F. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. F. Kelly, and R. G. Baraniuk, “An architecture for compressive imaging,” in 2006 IEEE International Conference on Image Processing (IEEE, 2006) pp. 1273–1276.

Schwartz, M.

G. Frenkel, E. Katzav, M. Schwartz, and N. Sochen, “Distribution of anomalous exponents of natural images,” Phys. Rev. Lett. 97, 103902 (2006).
[CrossRef]

Shankar, P.

J. Ke, P. 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. Shankar, “Feature-specific imaging,” Appl. Opt. 42, 3379–3389 (2003).
[CrossRef]

Sochen, N.

G. Frenkel, E. Katzav, M. Schwartz, and N. Sochen, “Distribution of anomalous exponents of natural images,” Phys. Rev. Lett. 97, 103902 (2006).
[CrossRef]

Sun, T.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

Takhar, D.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

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

M. B. Wakin, J. N. Laska, M. F. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. F. Kelly, and R. G. Baraniuk, “An architecture for compressive imaging,” in 2006 IEEE International Conference on Image Processing (IEEE, 2006) pp. 1273–1276.

Tao, T.

E. J. 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]

E. J. Candès and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies?” IEEE Trans. Inf. Theory 52, 5406–5425 (2006).
[CrossRef]

Vandenberghe, L.

S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University, 2004).

Wakin, M. B.

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

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

M. B. Wakin, J. N. Laska, M. F. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. F. Kelly, and R. G. Baraniuk, “An architecture for compressive imaging,” in 2006 IEEE International Conference on Image Processing (IEEE, 2006) pp. 1273–1276.

Weldon, M.

L. McMackin, M. A. Herman, B. Chatterjee, and M. Weldon, “A high-resolution SWIR camera via compressed sensing,” Proc. SPIE 8353, 835303 (2012).
[CrossRef]

Woods, R. E.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. (Prentice-Hall, 2006).

Appl. Opt. (4)

IEEE Signal Process. Mag. (3)

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

R. G. Baraniuk, “Compressive sensing [Lecture Notes],” IEEE Signal Process. Mag. 24, 118–121 (2007).
[CrossRef]

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

IEEE Trans. Inf. Theory (3)

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

E. J. 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]

E. J. Candès and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies?” IEEE Trans. Inf. Theory 52, 5406–5425 (2006).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

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

Phys. Rev. Lett. (1)

G. Frenkel, E. Katzav, M. Schwartz, and N. Sochen, “Distribution of anomalous exponents of natural images,” Phys. Rev. Lett. 97, 103902 (2006).
[CrossRef]

Proc. SPIE (2)

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

L. McMackin, M. A. Herman, B. Chatterjee, and M. Weldon, “A high-resolution SWIR camera via compressed sensing,” Proc. SPIE 8353, 835303 (2012).
[CrossRef]

SIAM J. Imaging Sci. (1)

S. Becker, J. Bobin, and E. Candès, “NESTA: a fast and accurate first-order method for sparse recovery,” SIAM J. Imaging Sci. 4, 1–39 (2011).

Soc. Inf. Disp. Symp. Dig. Tech. Pap. (1)

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Figures (14)

Fig. 1.
Fig. 1.

Schematic of CI system. A scene is imaged onto a digital micromirror device (DMD), which serves as a SLM. A sequence of specific basis patterns are emulated by the DMD mirrors, and the filtered signals are collected by a second lens onto a single photodetector. A sink blocks undesired deflected stray light.

Fig. 2.
Fig. 2.

Photo of experimental CI system. A scene is imaged onto the DMD which directs a portion of the imaged scene to a condenser lens, which then directs the optical energy to a single photodetector. A focusing scope helps the user to position the imaging lens. Filters can be used to capture multispectral images. The enclosure and light sink are not shown.

Fig. 3.
Fig. 3.

Grayscale representation through the use of TDM of the DMD. An 8 bit PNG image loaded into the D4100 controller board is converted into eight 1 bit image files, each of which is displayed for a different time duration. The dataset of a single frame shows a test case where all the values of the input 8 bit PNG are set to 85decimal which, when converted to binary, alternate between zeros and ones. Some samples are taken during the mirror transition reset time.

Fig. 4.
Fig. 4.

Two methods of sampling the CI system patterns are compared in order to improve 8 bit system performance. To perform the comparison, 256 PNG files are run through the system, each containing uniform intensity ranging from 0 to 255. (a) Data taken by averaging samples within a subframe and scaling by their place value. (b) Data taken by averaging all values within the entire frame. Errors associated with (a) and (b) are shown in (c) and (d), respectively. Periodic fluctuations in (c) are dominated by the 2524 place value transition. Averaging over the entire frame introduces less significant error.

Fig. 5.
Fig. 5.

Sixteen of the basis patterns depicting the (b) Noiselet, (c) Hadamard, and (d) DCT basis transform sets. The colorbar is shown in (a).

Fig. 6.
Fig. 6.

Ground truth images taken with a Canon 5D Mark II DSLR camera. The scenes include (a) and (b), back-illuminated chrome on glass transparencies in a lab setting, and (c) a daylight illuminated building.

Fig. 7.
Fig. 7.

Spectral data of the outdoor image scene [Fig. 6(c)] taken using an Ocean Optics Spectrometer with and without color filters in place.

Fig. 8.
Fig. 8.

Experimentally acquired (a), (d) Noiselet, (b), (e) Hadamard, and (c), (f) DCT complete datasets from lab-imaged, back-illuminated chrome on glass transparencies of a 1951 USAF resolution target (a)–(c) and a grayscale Lena portrait (d)–(f). Each sample corresponds to a basis pattern and produces a basis coefficient. The ground truths of the corresponding images are shown in Figs. 6(a) and 6(b). As opposed to Noiselet transform, highly spatially structured patterns, such as Hadamard and DCT, interact with the image, making certain coefficients stand out.

Fig. 9.
Fig. 9.

(a)–(d) Noiselet, (e)–(h) Hadamard, and (i)–(l) DCT reconstructed images of a 1951 USAF resolution target using 0.1, 1, 10, 100% of samples recorded in a lab setting. Error is calculated with reference to the respective 100% reconstruction.

Fig. 10.
Fig. 10.

(a)–(c) Noiselet, (d)–(f) Hadamard, and (g)–(i) DCT reconstructions of a grayscale image using 1%, 10%, 100% of samples recorded in a lab setting. Error is calculated with reference to the respective 100% reconstruction.

Fig. 11.
Fig. 11.

Plot of the RMSD error versus the number of measurements used in the reconstruction of the two lab scenes using the three basis sets. Measurements are taken from Fig. 9 (solid line) and Fig. 10 (dashed line) and are normalized to the number of functions in the complete basis set. The Hadamard transform has the least error followed closely by the Noiselet and last the DCT.

Fig. 12.
Fig. 12.

Reconstructed images with the red, green, and blue bandpass filters were combined to form outdoor color images. Reconstructions were made using 1% of the (a) Noiselet, (b) Hadamard, and (c) DCT transforms. Daylight changed during the image acquisition, resulting in variations in color and illumination.

Fig. 13.
Fig. 13.

Infrared reconstructed images using 1% of samples recorded outdoors using an IR bandpass filter.

Fig. 14.
Fig. 14.

Comparison of the compressive imager with a conventional camera. (a) Images taken by a Canon 5D Mark II where the pixel data has been binned to 1% of its original 1.04 MPix size, namely 10,404 pixels. (b) Shows the images in (a) upsampled to the same resolution (1.04 MPix) as the compressive imager. (c) Shows the CI result using 1% (10,404 samples) of the lowest spatial frequency Hadamard data.

Tables (2)

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Table 1. Texas Instruments High Definition 0.95 1080p DMD Specifications

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Table 2. Speed and Memory Requirements of Encoding Algorithms for Acquiring 1% of the Samples (10,486 Basis Patterns and Coefficients) of the Corresponding 1.04 MPix Image

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