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)