Transcript Document 7537478

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 / object
(K-sparse)
M << N
• 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
6cm
metal
aperture
12cm
THz receiver
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
7.2 cm
7.2 cm
6.4 cm
6.4 cm
Resolution: 1.125 mm
Fourier Transform of
object (Magnitude)
Inverse Fourier Transform
Reconstruction (zoomed-in)
Imaging Results with Compressed
Sensing (CS)
7.2 cm
7.2 cm
Inverse Fourier Transform
Reconstruction
(4096 measurements)
CS Reconstruction
(2000 measurements)
Imaging Using the Fourier
Magnitude
object
mask
THz transmitter
6cm
variable object
position
metal
aperture
THz receiver
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:
– real-valued
– positivity
– finite support
• Hybrid Input-Output (HIO) algorithm
(Fienup, Appl. Optics., 21(15), pp. 2758 - 2769, August 1982)
Imaging Results with Phase
Retrieval (PR)
8 cm
6.4 cm
8 cm
6.4 cm
Resolution: 3.2mm
Fourier Transform of
object (Magnitude-only)
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-only)
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
2-D Wavelet Transform
(Sparsity)
Imaging Results with Phase
Retrieval (PR)
6.4 cm
4.8 cm
6.4 cm
4.8 cm
Resolution: 1.5mm
Fourier Transform of
object (Magnitude-only)
PR Reconstruction
(4096 measurements)