Abstract

In this paper we present the design and implementation of a Compressive Sensing Microscopy (CSM) imaging system, which uses the Compressive Sensing (CS) method to realize optical-sectioning imaging. The theoretical aspect of the proposed system is investigated using the mathematical model of the CS method and an experimental prototype is constructed to verify the CSM design. Compared to conventional optical-sectioning microscopes (such as Laser Scanning Confocal Microscopes (LSCMs) or Programmable Array Microscopes (PAMs)), the CSM system realizes optical-sectioning imaging using a single-pixel photo detector and without any mechanical scanning process. The complete information of the imaging scene is reconstructed from the CS measurements numerically.

© 2010 OSA

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  1. J. A. Conchello and J. W. Lichtman, “Optical sectioning microscopy,” Nat. Methods 2(12), 920–931 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. Q. S. Hanley, D. Verveer, and T. M. Jovin, “Optical-sectioning fluorescence spectroscopy in a programmable array microscope,” Appl. Spectrosc. 52(6), 783–792 (1998).
    [CrossRef]
  5. E. Candès and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
    [CrossRef]
  6. E. Candès, “Compressive sampling,” Proc. Int. Congress of Mathematics 3, 1433–1452, Madrid, Spain, (2006).
  7. M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58(6), 1182–1195 (2007).
    [CrossRef] [PubMed]
  8. R. G. Baraniuk, “Compressive Sensing,” IEEE Signal Process. Mag. 24(4), 118–121 (2007).
    [CrossRef]
  9. M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-Pixel Imaging via Compressive Sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
    [CrossRef]
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  11. P. Ye, J. L. Paredes, Y. Wu, C. Chen, G. R. Arce, and D. W. Prather, “Compressive confocal microscopy: 3D reconstruction algorithms,” Proc. SPIE 7210, 72100G (2009).
  12. S. J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “A method for large-scale l1- regularized least squares,” IEEE J. STSP 1(4), 606–617 (2007).
  13. D. Dudley, W. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proc. SPIE 4985, 14 (2003).
  14. J. W. Goodman, Introduction to Fourier Optics, 3rd Edition (Roberts & Company Publishers, 2004), Chap. 6.

2010

Y. Wu, P. Ye, Z. Wang, G. R. Arce, and D. W. Prather, “A Single-Pixel Optical Sectioning Programmable Array Microscope (SP-PAM),” Proc. SPIE 7596, 75960D (2010).

2009

P. Ye, J. L. Paredes, Y. Wu, C. Chen, G. R. Arce, and D. W. Prather, “Compressive confocal microscopy: 3D reconstruction algorithms,” Proc. SPIE 7210, 72100G (2009).

2008

E. Candès and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[CrossRef]

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-Pixel Imaging via Compressive Sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

2007

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58(6), 1182–1195 (2007).
[CrossRef] [PubMed]

R. G. Baraniuk, “Compressive Sensing,” IEEE Signal Process. Mag. 24(4), 118–121 (2007).
[CrossRef]

S. J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “A method for large-scale l1- regularized least squares,” IEEE J. STSP 1(4), 606–617 (2007).

2005

J. A. Conchello and J. W. Lichtman, “Optical sectioning microscopy,” Nat. Methods 2(12), 920–931 (2005).
[CrossRef] [PubMed]

2003

D. Dudley, W. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proc. SPIE 4985, 14 (2003).

1999

Q. S. Hanley, P. J. Verveer, M. J. Gemkow, D. Arndt-Jovin, and T. M. Jovin, “An optical sectioning programmable array microscope implemented with a digital micromirror device,” J. Microsc. 196(3), 317–331 (1999).
[CrossRef] [PubMed]

1998

1997

Arce, G. R.

Y. Wu, P. Ye, Z. Wang, G. R. Arce, and D. W. Prather, “A Single-Pixel Optical Sectioning Programmable Array Microscope (SP-PAM),” Proc. SPIE 7596, 75960D (2010).

P. Ye, J. L. Paredes, Y. Wu, C. Chen, G. R. Arce, and D. W. Prather, “Compressive confocal microscopy: 3D reconstruction algorithms,” Proc. SPIE 7210, 72100G (2009).

Arndt-Jovin, D.

Q. S. Hanley, P. J. Verveer, M. J. Gemkow, D. Arndt-Jovin, and T. M. Jovin, “An optical sectioning programmable array microscope implemented with a digital micromirror device,” J. Microsc. 196(3), 317–331 (1999).
[CrossRef] [PubMed]

Baraniuk, R. G.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, 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,” IEEE Signal Process. Mag. 24(4), 118–121 (2007).
[CrossRef]

Boyd, S.

S. J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “A method for large-scale l1- regularized least squares,” IEEE J. STSP 1(4), 606–617 (2007).

Candès, E.

E. Candès and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[CrossRef]

Chen, C.

P. Ye, J. L. Paredes, Y. Wu, C. Chen, G. R. Arce, and D. W. Prather, “Compressive confocal microscopy: 3D reconstruction algorithms,” Proc. SPIE 7210, 72100G (2009).

Conchello, J. A.

J. A. Conchello and J. W. Lichtman, “Optical sectioning microscopy,” Nat. Methods 2(12), 920–931 (2005).
[CrossRef] [PubMed]

Davenport, M. A.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-Pixel Imaging via Compressive Sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

Donoho, D.

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58(6), 1182–1195 (2007).
[CrossRef] [PubMed]

Duarte, M. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-Pixel Imaging via Compressive Sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

Dudley, D.

D. Dudley, W. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proc. SPIE 4985, 14 (2003).

Duncan, W.

D. Dudley, W. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proc. SPIE 4985, 14 (2003).

Gemkow, M. J.

Q. S. Hanley, P. J. Verveer, M. J. Gemkow, D. Arndt-Jovin, and T. M. Jovin, “An optical sectioning programmable array microscope implemented with a digital micromirror device,” J. Microsc. 196(3), 317–331 (1999).
[CrossRef] [PubMed]

Gorinevsky, D.

S. J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “A method for large-scale l1- regularized least squares,” IEEE J. STSP 1(4), 606–617 (2007).

Hanley, Q. S.

Q. S. Hanley, P. J. Verveer, M. J. Gemkow, D. Arndt-Jovin, and T. M. Jovin, “An optical sectioning programmable array microscope implemented with a digital micromirror device,” J. Microsc. 196(3), 317–331 (1999).
[CrossRef] [PubMed]

Q. S. Hanley, D. Verveer, and T. M. Jovin, “Optical-sectioning fluorescence spectroscopy in a programmable array microscope,” Appl. Spectrosc. 52(6), 783–792 (1998).
[CrossRef]

Jovin, T. M.

Q. S. Hanley, P. J. Verveer, M. J. Gemkow, D. Arndt-Jovin, and T. M. Jovin, “An optical sectioning programmable array microscope implemented with a digital micromirror device,” J. Microsc. 196(3), 317–331 (1999).
[CrossRef] [PubMed]

Q. S. Hanley, D. Verveer, and T. M. Jovin, “Optical-sectioning fluorescence spectroscopy in a programmable array microscope,” Appl. Spectrosc. 52(6), 783–792 (1998).
[CrossRef]

Kelly,

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-Pixel Imaging via Compressive Sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

Kim, S. J.

S. J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “A method for large-scale l1- regularized least squares,” IEEE J. STSP 1(4), 606–617 (2007).

Koh, K.

S. J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “A method for large-scale l1- regularized least squares,” IEEE J. STSP 1(4), 606–617 (2007).

Krause, A. W.

Laska, J. N.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-Pixel Imaging via Compressive Sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

Liang, M.

Lichtman, J. W.

J. A. Conchello and J. W. Lichtman, “Optical sectioning microscopy,” Nat. Methods 2(12), 920–931 (2005).
[CrossRef] [PubMed]

Lustig, M.

S. J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “A method for large-scale l1- regularized least squares,” IEEE J. STSP 1(4), 606–617 (2007).

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58(6), 1182–1195 (2007).
[CrossRef] [PubMed]

Paredes, J. L.

P. Ye, J. L. Paredes, Y. Wu, C. Chen, G. R. Arce, and D. W. Prather, “Compressive confocal microscopy: 3D reconstruction algorithms,” Proc. SPIE 7210, 72100G (2009).

Pauly, J. M.

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58(6), 1182–1195 (2007).
[CrossRef] [PubMed]

Prather, D. W.

Y. Wu, P. Ye, Z. Wang, G. R. Arce, and D. W. Prather, “A Single-Pixel Optical Sectioning Programmable Array Microscope (SP-PAM),” Proc. SPIE 7596, 75960D (2010).

P. Ye, J. L. Paredes, Y. Wu, C. Chen, G. R. Arce, and D. W. Prather, “Compressive confocal microscopy: 3D reconstruction algorithms,” Proc. SPIE 7210, 72100G (2009).

Slaughter, J.

D. Dudley, W. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proc. SPIE 4985, 14 (2003).

Stehr, R. L.

Takhar, D.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-Pixel Imaging via Compressive Sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

Ting Sun, K. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-Pixel Imaging via Compressive Sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

Verveer, D.

Verveer, P. J.

Q. S. Hanley, P. J. Verveer, M. J. Gemkow, D. Arndt-Jovin, and T. M. Jovin, “An optical sectioning programmable array microscope implemented with a digital micromirror device,” J. Microsc. 196(3), 317–331 (1999).
[CrossRef] [PubMed]

Wakin, M.

E. Candès and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[CrossRef]

Wang, Z.

Y. Wu, P. Ye, Z. Wang, G. R. Arce, and D. W. Prather, “A Single-Pixel Optical Sectioning Programmable Array Microscope (SP-PAM),” Proc. SPIE 7596, 75960D (2010).

Wu, Y.

Y. Wu, P. Ye, Z. Wang, G. R. Arce, and D. W. Prather, “A Single-Pixel Optical Sectioning Programmable Array Microscope (SP-PAM),” Proc. SPIE 7596, 75960D (2010).

P. Ye, J. L. Paredes, Y. Wu, C. Chen, G. R. Arce, and D. W. Prather, “Compressive confocal microscopy: 3D reconstruction algorithms,” Proc. SPIE 7210, 72100G (2009).

Ye, P.

Y. Wu, P. Ye, Z. Wang, G. R. Arce, and D. W. Prather, “A Single-Pixel Optical Sectioning Programmable Array Microscope (SP-PAM),” Proc. SPIE 7596, 75960D (2010).

P. Ye, J. L. Paredes, Y. Wu, C. Chen, G. R. Arce, and D. W. Prather, “Compressive confocal microscopy: 3D reconstruction algorithms,” Proc. SPIE 7210, 72100G (2009).

Appl. Spectrosc.

IEEE J. STSP

S. J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “A method for large-scale l1- regularized least squares,” IEEE J. STSP 1(4), 606–617 (2007).

IEEE Signal Process. Mag.

E. Candès and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[CrossRef]

R. G. Baraniuk, “Compressive Sensing,” IEEE Signal Process. Mag. 24(4), 118–121 (2007).
[CrossRef]

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Ting Sun, Kelly, and R. G. Baraniuk, “Single-Pixel Imaging via Compressive Sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

J. Microsc.

Q. S. Hanley, P. J. Verveer, M. J. Gemkow, D. Arndt-Jovin, and T. M. Jovin, “An optical sectioning programmable array microscope implemented with a digital micromirror device,” J. Microsc. 196(3), 317–331 (1999).
[CrossRef] [PubMed]

Magn. Reson. Med.

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58(6), 1182–1195 (2007).
[CrossRef] [PubMed]

Nat. Methods

J. A. Conchello and J. W. Lichtman, “Optical sectioning microscopy,” Nat. Methods 2(12), 920–931 (2005).
[CrossRef] [PubMed]

Opt. Lett.

Proc. SPIE

Y. Wu, P. Ye, Z. Wang, G. R. Arce, and D. W. Prather, “A Single-Pixel Optical Sectioning Programmable Array Microscope (SP-PAM),” Proc. SPIE 7596, 75960D (2010).

P. Ye, J. L. Paredes, Y. Wu, C. Chen, G. R. Arce, and D. W. Prather, “Compressive confocal microscopy: 3D reconstruction algorithms,” Proc. SPIE 7210, 72100G (2009).

D. Dudley, W. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proc. SPIE 4985, 14 (2003).

Other

J. W. Goodman, Introduction to Fourier Optics, 3rd Edition (Roberts & Company Publishers, 2004), Chap. 6.

E. Candès, “Compressive sampling,” Proc. Int. Congress of Mathematics 3, 1433–1452, Madrid, Spain, (2006).

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