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Terahertz Imaging with Compressed Sensing and Phase Retrieval

Terahertz Imaging with Compressed Sensing and Phase Retrieval. Wai Lam Chan Matthew Moravec Daniel Mittleman Richard Baraniuk. Department of Electrical and Computer Engineering Rice University, Houston, Texas, USA. THz Time-domain Imaging. THz Transmitter.

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Terahertz Imaging with Compressed Sensing and Phase Retrieval

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  1. Terahertz Imaging with Compressed Sensing and Phase Retrieval • Wai Lam Chan Matthew Moravec • Daniel Mittleman Richard Baraniuk Department of Electrical and Computer Engineering Rice University, Houston, Texas, USA

  2. THz Time-domain Imaging THz Transmitter THz Receiver Object

  3. THz Transmitter THz Receiver Object THz Time-domain Imaging Chocolate bar (food) Automobile dashboard (foam layer) Suitcase (weapons) (Karpowicz, et al., Appl. Phys. Lett. vol. 86, 054105 (2005)) (Mittleman, et al., Appl. Phys. B, vol. 68, 1085-1094 (1999))

  4. THz Transmitter THz Receiver Object THz Time-domain Imaging • Pixel-by-pixel scanning • Limitations: acquisition time vs. resolution • Faster imaging method

  5. R “sparse” signal / image (K-sparse) Measurements (random projections) Measurement Matrix (e.g., random Fourier) information rate High-speed THz Imaging with Compressed Sensing (CS) • Take fewer ( ) measurements • Reconstruct via nonlinear processing(optimization) (Donoho, IEEE Trans. on Information Theory, 52(4), pp. 1289 - 1306, April 2006)

  6. Compressed Sensing (CS) Example: Single-Pixel Camera R DSP imagereconstruction DMD DMD Random pattern on DMD array (Baraniuk, Kelly, et al. Proc. of Computational Imaging IV at SPIE Electronic Imaging, Jan 2006)

  7. THz Fourier Imaging Setup THz transmitter (fiber-coupled PC antenna) object mask THz receiver aperture R 6cm 6cm 12cm 12cm 12cm automated translation stage

  8. pick only random measurements for Compressed Sensing THz Fourier Imaging Setup Fourier plane object mask N Fourier samples THz transmitter R 6cm 6cm 12cm 12cm 12cm

  9. THz Fourier Imaging Setup THz receiver automated translation stage object mask “R” (3.5cm x 3.5cm) polyethlene lens

  10. Fourier Imaging Results 8 cm 6 cm R 6 cm 8 cm Resolution: 3mm Inverse Fourier Transform Reconstruction (zoomed-in) Fourier Transform of object (Magnitude)

  11. R R Imaging Results with Compressed Sensing (CS) 6 cm 6 cm Inverse Fourier Transform Reconstruction (6400 measurements) CS Reconstruction (1000 measurements)

  12. Imaging Using the Fourier Magnitude object mask THz receiver THz transmitter aperture R 6cm 12cm variable object position translation stage

  13. Reconstruction with Phase Retrieval (PR) • Reconstruct signal from only the magnitude of its Fourier transform • Iterative algorithm based on prior knowledge of signal: • positivity • real-valued • finite support • Hybrid Input-Output (HIO) algorithm (Fienup, Appl. Optics., 21(15), pp. 2758 - 2769, August 1982)

  14. Imaging Results with PR 8 cm 6.4 cm R 6.4 cm 8 cm Resolution: 3.2mm Fourier Transform of object (Magnitude) PR Reconstruction (6400 measurements)

  15. R R Compressed Sensing Phase Retrieval (CSPR) Results • Modified PR algorithm with CS 8 cm 6.4 cm 6.4 cm 8 cm Fourier Transform of object (Magnitude) PR Reconstruction (6400 measurements) CSPR Reconstruction (1000 measurements)

  16. Summary of CSPR Imaging System • Novel THz imaging method with compressed sensing (CS) and phase retrieval (PR) • Improved acquisition speed • Processing time • Resolution in reconstructed image

  17. Acknowledgements National Science Foundation National Aeronautics and Space Administration Defense Advanced Research Projects Agency

  18. ….001010…. Measurement matrix (e.g., random) Compressed Sensing (CS) Theory R sparsesignal (image) information rate

  19. measurements Compressed Sensing (CS) Theory R sparsesignal (image) Measurement matrix (e.g., random) information rate

  20. THz Tomography • Other imaging methods: • Pulsed THz Tomography (S. Wang & X.C. Zhang) • WART (J. Pearce & D. Mittleman) • Interferometric and synthetic aperture imaging (A. Bandyopadhyay & J. Federici) • Limitations in speed and resolution

  21. Future Improvements • Higher imaging resolution • Higher SNR • Using Broad spectral information • Reconstruction of “complex” objects • CS and CSPR detection

  22. 2-D Wavelet Transform (Sparsity)

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