terahertz imaging with compressed sensing and phase retrieval
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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
Object
THz TransmitterTHz Receiver
THz Time-domain Imaging
Object
THz TransmitterTHz Receiver
Suitcase (weapons) Automobile dashboard (foam layer)
Chocolate bar (food)
(Mittleman, et al., Appl. Phys. B, vol. 68, 1085-1094 (1999))
(Karpowicz, et al., Appl. Phys. Lett. vol. 86, 054105 (2005))
THz Time-domain Imaging
Object
THz TransmitterTHz Receiver
• Pixel-by-pixel scanning
• Limitations: acquisition time vs. resolution
• Faster imaging method
• Reconstruct via nonlinear processing (optimization)
• Take fewer ( ) measurements
High-speed THz Imaging with Compressed Sensing (CS)
Measurements(random projections)
(Donoho, IEEE Trans. on Information Theory, 52(4), pp. 1289 - 1306, April 2006)
“sparse” signal / object(K-sparse)
MeasurementMatrix (e.g.,
random Fourier)
M << N
Compressed Sensing (CS) Example: Single-Pixel Camera
DMD
Random pattern onDMD array
(Baraniuk, Kelly, et al. Proc. of Computational Imaging IV at SPIE Electronic Imaging, Jan 2006)
imagereconstruction
DSP
DMD
THz Fourier Imaging Setup
12cm6cm 12cm 12cm
objectmask
THz transmitter (fiber-coupled PC antenna)
THz receiver
6cm
metal aperture
automated translation stage
N Fourier samples
THz Fourier Imaging Setup
12cm6cm 12cm 12cm
objectmask
THz transmitter
6cm
Fourier plane
pick only random measurements for
Compressed Sensing
THz Fourier Imaging Setup
automated translation
stage
polyethlene lens
object mask “R”(3.5cm x 3.5cm)
THz receiver
Fourier Imaging Results
Fourier Transform of object (Magnitude)
Inverse Fourier Transform Reconstruction (zoomed-in)
6.4 cm 7.2 cm
6.4
cm
7.2
cm
Resolution: 1.125 mm
Imaging Results with Compressed Sensing (CS)
Inverse Fourier Transform Reconstruction
(4096 measurements)
CS Reconstruction (2000 measurements)
7.2 cm
7.2
cm
Imaging Using the Fourier Magnitude
12cm
objectmask
THz transmitterTHz receiver
6cm
metalaperture
translationstage
variable objectposition
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
8
cm
6.4 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
Fourier Transform of object
(Magnitude-only)
PR Reconstruction (6400 measurements)
CSPR Reconstruction (1000 measurements)
8 cm
8
cm
6.4 cm
6.4
cm
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
6.4
cm
4.8 cm
4.8
cm
Resolution: 1.5mm
Fourier Transform of object (Magnitude-only)
PR Reconstruction(4096 measurements)