Abstract

This paper presents the Static Computational Optical Undersampled Tracker (SCOUT), an architecture for compressive motion tracking systems. The architecture uses compressive sensing techniques to track moving targets at significantly higher resolution than the detector array, allowing for low cost, low weight design and a significant reduction in data storage and bandwidth requirements. Using two amplitude masks and a standard focal plane array, the system captures many projections simultaneously, avoiding the need for time-sequential measurements of a single scene. Scenes with few moving targets on static backgrounds have frame differences that can be reconstructed using sparse signal reconstruction techniques in order to track moving targets. Simulations demonstrate theoretical performance and help to inform the choice of design parameters. We use the coherence parameter of the system matrix as an efficient predictor of reconstruction error to avoid performing computationally intensive reconstructions over the entire design space. An experimental SCOUT system demonstrates excellent reconstruction performance with 16X compression tracking movers on scenes with zero and nonzero backgrounds.

© 2012 OSA

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  1. M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, “An architecture for compressive imaging,” in Proceedings of IEEE Intl. Conference on Image Processing, (IEEE, 2006), pp. 1273–1276.
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  9. H. Rauhut, “Circulant and Toeplitz matrices in compressed sensing,” http://arxiv.org/abs/0902.4394 .
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    [CrossRef]
  11. F. Sebert, Y. Zou, and L. Ying, “Toeplitz block matrices in compressed sensing and their applications in imaging,” in Proceedings of IEEE International Conference on Information Technology and Applications in Biomedicine, (IEEE, 2008), pp. 47–50.
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  13. S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Sig. Proc.1, 606–617 (2007).
    [CrossRef]
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    [CrossRef]

2012

2011

R. Willett, R. Marcia, and J. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng.50, 072601 (2011).
[CrossRef]

2010

2009

J. Romberg, “Compressive sensing by random convolution,” SIAM J. Imaging Sci.2, 1098–1128 (2009).
[CrossRef]

2008

B. Liu, F. Sebert, Y. Zou, and L. Ying, “SparseSENSE: randomly-sampled parallel imaging using compressed sensing,” in Proceedings of the 16th Annual Meeting of ISMRM3154 (2008).

2007

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Sig. Proc.1, 606–617 (2007).
[CrossRef]

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

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

2006

J. Tropp, “Just relax: Convex programming methods for identifying sparse signals in noise,” IEEE Trans. Inf. Theory52, 1030–1051 (2006).
[CrossRef]

Bajwa, W.

W. Bajwa, J. Haupt, G. Raz, S. Wright, and R. Nowak, “Toeplitz-structured compressed sensing matrices,” in Proceedings of IEEE Workshop on Statistical Signal Processing, (IEEE, 2007), pp. 294–298.

Baraniuk, R.

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

Baron, D.

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

Boyd, S.

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Sig. Proc.1, 606–617 (2007).
[CrossRef]

Donoho, D.

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

Duarte, M.

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

Gehm, M.

M. Stenner, D. Townsend, and M. Gehm, “Static architecture for compressive motion detection in persistent, pervasive surveillance applications,” in Imaging Systems, OSA Technical Digest Series (Optical Society of America, 2010), paper IMB2.

Gorinevsky, D.

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Sig. Proc.1, 606–617 (2007).
[CrossRef]

Haupt, J.

W. Bajwa, J. Haupt, G. Raz, S. Wright, and R. Nowak, “Toeplitz-structured compressed sensing matrices,” in Proceedings of IEEE Workshop on Statistical Signal Processing, (IEEE, 2007), pp. 294–298.

Javidi, B.

Kashter, Y.

Ke, J.

Kelly, K.

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

Kim, S.

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Sig. Proc.1, 606–617 (2007).
[CrossRef]

Koh, K.

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Sig. Proc.1, 606–617 (2007).
[CrossRef]

Laska, J.

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

Levi, O.

Liu, B.

B. Liu, F. Sebert, Y. Zou, and L. Ying, “SparseSENSE: randomly-sampled parallel imaging using compressed sensing,” in Proceedings of the 16th Annual Meeting of ISMRM3154 (2008).

Lustig, M.

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Sig. Proc.1, 606–617 (2007).
[CrossRef]

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

Marcia, R.

R. Willett, R. Marcia, and J. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng.50, 072601 (2011).
[CrossRef]

Neifeld, M.

Nichols, J.

R. Willett, R. Marcia, and J. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng.50, 072601 (2011).
[CrossRef]

Nowak, R.

W. Bajwa, J. Haupt, G. Raz, S. Wright, and R. Nowak, “Toeplitz-structured compressed sensing matrices,” in Proceedings of IEEE Workshop on Statistical Signal Processing, (IEEE, 2007), pp. 294–298.

Pauly, J.

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

Raz, G.

W. Bajwa, J. Haupt, G. Raz, S. Wright, and R. Nowak, “Toeplitz-structured compressed sensing matrices,” in Proceedings of IEEE Workshop on Statistical Signal Processing, (IEEE, 2007), pp. 294–298.

Rivenson, Y.

Romberg, J.

J. Romberg, “Compressive sensing by random convolution,” SIAM J. Imaging Sci.2, 1098–1128 (2009).
[CrossRef]

Sarvotham, S.

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

Sebert, F.

B. Liu, F. Sebert, Y. Zou, and L. Ying, “SparseSENSE: randomly-sampled parallel imaging using compressed sensing,” in Proceedings of the 16th Annual Meeting of ISMRM3154 (2008).

F. Sebert, Y. Zou, and L. Ying, “Toeplitz block matrices in compressed sensing and their applications in imaging,” in Proceedings of IEEE International Conference on Information Technology and Applications in Biomedicine, (IEEE, 2008), pp. 47–50.

Stenner, M.

M. Stenner, D. Townsend, and M. Gehm, “Static architecture for compressive motion detection in persistent, pervasive surveillance applications,” in Imaging Systems, OSA Technical Digest Series (Optical Society of America, 2010), paper IMB2.

Stern, A.

Takhar, D.

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

Townsend, D.

M. Stenner, D. Townsend, and M. Gehm, “Static architecture for compressive motion detection in persistent, pervasive surveillance applications,” in Imaging Systems, OSA Technical Digest Series (Optical Society of America, 2010), paper IMB2.

Tropp, J.

J. Tropp, “Just relax: Convex programming methods for identifying sparse signals in noise,” IEEE Trans. Inf. Theory52, 1030–1051 (2006).
[CrossRef]

Wakin, M.

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

Willett, R.

R. Willett, R. Marcia, and J. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng.50, 072601 (2011).
[CrossRef]

Wright, S.

W. Bajwa, J. Haupt, G. Raz, S. Wright, and R. Nowak, “Toeplitz-structured compressed sensing matrices,” in Proceedings of IEEE Workshop on Statistical Signal Processing, (IEEE, 2007), pp. 294–298.

Ying, L.

B. Liu, F. Sebert, Y. Zou, and L. Ying, “SparseSENSE: randomly-sampled parallel imaging using compressed sensing,” in Proceedings of the 16th Annual Meeting of ISMRM3154 (2008).

F. Sebert, Y. Zou, and L. Ying, “Toeplitz block matrices in compressed sensing and their applications in imaging,” in Proceedings of IEEE International Conference on Information Technology and Applications in Biomedicine, (IEEE, 2008), pp. 47–50.

Zou, Y.

B. Liu, F. Sebert, Y. Zou, and L. Ying, “SparseSENSE: randomly-sampled parallel imaging using compressed sensing,” in Proceedings of the 16th Annual Meeting of ISMRM3154 (2008).

F. Sebert, Y. Zou, and L. Ying, “Toeplitz block matrices in compressed sensing and their applications in imaging,” in Proceedings of IEEE International Conference on Information Technology and Applications in Biomedicine, (IEEE, 2008), pp. 47–50.

Appl. Opt.

IEEE J. Sel. Top. Sig. Proc.

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Sig. Proc.1, 606–617 (2007).
[CrossRef]

IEEE Trans. Inf. Theory

J. Tropp, “Just relax: Convex programming methods for identifying sparse signals in noise,” IEEE Trans. Inf. Theory52, 1030–1051 (2006).
[CrossRef]

Magn. Reson. Med.

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

Opt. Eng.

R. Willett, R. Marcia, and J. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng.50, 072601 (2011).
[CrossRef]

Opt. Express

Proceedings of the 16th Annual Meeting of ISMRM

B. Liu, F. Sebert, Y. Zou, and L. Ying, “SparseSENSE: randomly-sampled parallel imaging using compressed sensing,” in Proceedings of the 16th Annual Meeting of ISMRM3154 (2008).

SIAM J. Imaging Sci.

J. Romberg, “Compressive sensing by random convolution,” SIAM J. Imaging Sci.2, 1098–1128 (2009).
[CrossRef]

Other

F. Sebert, Y. Zou, and L. Ying, “Toeplitz block matrices in compressed sensing and their applications in imaging,” in Proceedings of IEEE International Conference on Information Technology and Applications in Biomedicine, (IEEE, 2008), pp. 47–50.

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

W. Bajwa, J. Haupt, G. Raz, S. Wright, and R. Nowak, “Toeplitz-structured compressed sensing matrices,” in Proceedings of IEEE Workshop on Statistical Signal Processing, (IEEE, 2007), pp. 294–298.

H. Rauhut, “Circulant and Toeplitz matrices in compressed sensing,” http://arxiv.org/abs/0902.4394 .

M. Stenner, D. Townsend, and M. Gehm, “Static architecture for compressive motion detection in persistent, pervasive surveillance applications,” in Imaging Systems, OSA Technical Digest Series (Optical Society of America, 2010), paper IMB2.

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