Transcript Terahertz Imaging with Compressed Sensing and Phase Retrieval Wai Lam Chan Matthew Moravec

Terahertz Imaging with Compressed
Sensing and Phase Retrieval
Wai Lam Chan
Daniel Mittleman
Matthew Moravec
Richard Baraniuk
Department of Electrical and Computer Engineering
Rice University, Houston, Texas, USA
THz Time-domain Imaging
THz Transmitter
THz Receiver
Object
THz Time-domain Imaging
THz Transmitter
THz Receiver
Object
Suitcase (weapons)
Automobile dashboard
(foam layer)
(Karpowicz, et al., Appl. Phys.
Lett. vol. 86, 054105 (2005))
Chocolate bar (food)
(Mittleman, et al., Appl. Phys. B,
vol. 68, 1085-1094 (1999))
THz Time-domain Imaging
THz Transmitter
THz Receiver
Object
• Pixel-by-pixel scanning
• Limitations: acquisition time vs. resolution
• Faster imaging method
High-speed THz Imaging with
Compressed Sensing (CS)
• Take fewer (
Measurements
(random projections)
) measurements
Measurement
Matrix (e.g.,
random Fourier)
“sparse” signal / image
(K-sparse)
information rate
• Reconstruct via nonlinear processing (optimization)
(Donoho, IEEE Trans. on Information Theory, 52(4), pp. 1289 - 1306, April 2006)
Compressed Sensing (CS)
Example: Single-Pixel Camera
DSP
DMD
DMD
image
reconstruction
Random pattern on
DMD array
(Baraniuk, Kelly, et al. Proc. of Computational
Imaging IV at SPIE Electronic Imaging, Jan 2006)
THz Fourier Imaging Setup
THz transmitter
(fiber-coupled
PC antenna)
object
mask
THz receiver
aperture
6cm
12cm
12cm
automated
translation stage
THz Fourier Imaging Setup
Fourier plane
object
mask
THz transmitter
6cm
N Fourier
samples
12cm
12cm
pick only
random
measurements for
Compressed Sensing
THz Fourier Imaging Setup
THz receiver
object mask “R”
(3.5cm x 3.5cm)
automated
translation
stage
polyethlene
lens
Fourier Imaging Results
8 cm
6 cm
8 cm
6 cm
Resolution: 3mm
Fourier Transform of
object (Magnitude)
Inverse Fourier Transform
Reconstruction (zoomed-in)
Imaging Results with Compressed
Sensing (CS)
6 cm
6 cm
Inverse Fourier Transform
Reconstruction
(6400 measurements)
CS Reconstruction
(1000 measurements)
Imaging Using the Fourier
Magnitude
object
mask
THz transmitter
THz receiver
aperture
6cm
variable object
position
12cm
translation
stage
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)
Imaging Results with PR
8 cm
6.4 cm
8 cm
6.4 cm
Resolution: 3.2mm
Fourier Transform of
object (Magnitude)
PR Reconstruction
(6400 measurements)
Compressed Sensing Phase
Retrieval (CSPR) Results
• Modified PR algorithm with CS
6.4 cm
8 cm
6.4 cm
8 cm
Fourier Transform of
object (Magnitude)
PR Reconstruction
CSPR Reconstruction
(6400 measurements) (1000 measurements)
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
Acknowledgements
National Science Foundation
National Aeronautics and Space
Administration
Defense Advanced Research
Projects Agency
Compressed Sensing (CS) Theory
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sparse
signal (image)
Measurement matrix
(e.g., random)
information
rate
Compressed Sensing (CS) Theory
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measurements
sparse
signal (image)
Measurement matrix
(e.g., random)
information
rate
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
Future Improvements
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Higher imaging resolution
Higher SNR
Using Broad spectral information
Reconstruction of “complex” objects
CS and CSPR detection
2-D Wavelet Transform
(Sparsity)