Compressive Imaging

   

Recently a great deal of attention has been directed toward the new theory of compressed sensing (CS); which aims to reduce the overall complexity required by a large variety of measurement systems by introducing signal compression into the measurement process [1][2] [3]. This theory states that “sparse signal statistics can be recovered from a small number of non-adaptive linear measurements”. In more general terms, CS refers to any measurement process in which the total number of measurements is smaller than the dimensionality of the signals of interest. The sparse nature of most signals of interest allows high-fidelity reconstructions to be made using this approach.

The field of digital imaging is a good candidate for CS due to the large amount of raw data acquired by conventional image sensors. It is often required that this data be immediately compressed for the sake of efficiently storing or transmitting the data [4]. Compared to conventional imaging, compressive imaging (CI) offers improved performance with reduced system complexity. This reduced complexity can be important for example in mid-wave infrared (MWIR) image systems where photodetecting array technology is less developed and much more expensive than the photodetector array technology used in visible imaging. CI also holds an advantage in detector-noise-limited measurement fidelity (SNR) over conventional imaging because the total number of photons can be measured using fewer photodetectors [5][6].

Rather than spatial sampling an image by collecting the individual pixel data, a CI system measures linear projections of the object space. The resulting projections can then be processed for applications such as image reconstruction [5][7] or recognition [8]. A large number of candidate linear projections such as wavelets, principal components, Hadamard, discrete-cosine and pseudo-random projections have been studied in the context of CI [6][9][10][11][12][13]. Linear and nonlinear reconstruction methods have also been investigated in detail including linear minimum mean square error (LMMSE) using large training sets [6]; and a variety of nonlinear reconstruction methods [14][15][16][17] based on the CS theory of Candes, Romberg, and Tao [1], and Donoho [2].

We have built an experimental setup incorporating a modified arc-sectioned eight-reflection lens in conjunction with a Texas Instruments DLP® DMD for use as a CI test bed. The purposes of this system are to (a) demonstrate a novel reflective CI system based on a CMR lens as a first step toward an all-reflective MWIR compressive camera, and (b) investigate the performance of different CI hardware architectures available (position and number of detectors etc.) and algorithms.

Collaborators: Jun Ke, Pawan Baheti and Mark Neifeld at the University of Arizona.

Additional Information:
Selected Presentation Slides

References:

1. E. Candès, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inform. Theory, 52, 489-509, (2006).
2. D. L. Donoho, "Compressed sensing," Information Theory, IEEE Transactions on , 52, 1289-1306 (2006).
3. E. Candès and T. Tao, "Near optimal signal recovery from random projections: Universal encoding strategies?" IEEE Trans. Inform. Theory, vol. 52, 5406-5425, (2006).
4. D.S. Taubman and M.W. Marcellin, JPEG 2000: Image Compression Fundamentals, Standards and Practice. (Norwell, MA: Kluwer, 2001).
5. M. A. Neifeld and P. Shankar, "Feature-Specific Imaging," Appl. Opt., vol. 42, 3379-3389 (2003).
6. M. A. Neifeld and J. Ke, "Optical architectures for compressive imaging," Appl. Opt., vol. 46, 5293-5303 (2007).
7. H. Pal and M. Neifeld, "Multispectral principal component imaging," Opt. Express, vol. 11, 2118-2125 (2003).
8. H. S. Pal, D. Ganotra, and M. A. Neifeld, "Face recognition by using feature-specific imaging," Appl. Opt., vol. 44, 3784-3794 (2005).
9. P. Baheti, and M. A. Neifeld, “Feature-specific structured imaging,” Appl. Opt., vol. 45, 7382-7391 (2006).
10. J. Ke, M. Stenner, and M. A. Neifeld, “Minimum reconstruction error in feature-specific imaging,” in Proc. SPIE, Visual Information Processing XIV, vol. 5817, (2005).
11. J. Ke, P. Shankar, and M. A. Neifeld, “Distributed imaging using and array of compressive cameras,” Opt. Comm. Preprint, (2008).
12. D. J. Brady, N. P. Pitsianis, and X. Sun, “Sensor-layer image compression based on the quantized cosine transform,” in Proc. SPIE, Visual Information Processing XIV, vol. 5817, (2005).
13. A. Portnoy, X. Sun, T. Suleski, M. A. Fiddy, M. R. Feldman, N. P. Pitsianis, D. J. Brady, and R. D. TeKolste, “Compressive imaging sensors,” in Proc. SPIE, Intelligent Integrated Microsystems, vol. 6232, (2006).
14. J. Haupt and R. Nowak, "Signal reconstruction from noisy random projections," IEEE Trans. Info. Theory 52, 4036-4048 (2006).
15. M. F. Duarte, M. A. Davenport, M. B. Wakin, and R. G. Baraniuk, "Sparse signal detection from incoherent projections," in IEEE International Conference on Acoustics, Speech and Signal Processing, 2006. ICASSP 2006 Proceedings, Vol. 3 (IEEE, 2006).
16. E. Candes, J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pure Appl. Mathematics 59, 1207-1223 (2006).
17. S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM Soc. Ind. Appl. Math. J. Numer. Anal. 43, 129-159 (2001).