A Spatial Terahertz Modulator for high-speed Terahertz imaging
W. L. Chan, H.-T. Chen, A. J. Taylor, I. Brener, M. J. Cich, D. M. Mittleman

We have developed a compressed sensing terahertz imaging system that uses a single pixel detector to enable high-speed image acquisition. A high-speed spatial THz modulator is the crucial component for encoding random spatial patterns into the wave front of a terahertz beam.

Our first-generation device consists of a 4 x 4 pixel array, where each pixel is an array of subwavelength-sized split-ring resonator elements fabricated on a semiconductor substrate, and is independently controlled by applying an external voltage. Through terahertz transmission experiments, we show that the spatial modulator has a uniform modulation depth of around 40% across all pixels, and negligible crosstalk, at the resonant frequency. This device can operate under small voltage levels, at room temperature, with low power consumption and reasonably high switching speed. Our next step is to build a similar device with higher resolution.

Terahertz imaging with Compressed Sensing and Phase Retrieval
W. L. Chan, M. Moravec, R. Baraniuk, D. M. Mittleman

Over the past several years, the wide applicability of terahertz (THz) imaging in areas such as detection of foam insulation defects, illicit drug detection and package inspection has driven the development of novel, high-speed THz imaging systems. We developed two THz imaging systems based on the theory of compressed sensing (CS). The theory of CS enables reconstruction of an image using a number of measurements that is fewer than the number of pixels. In general, an infinite number of signals can be found that match these few measurements; CS uses an optimization procedure to find the "best" solution. This notion of "best" is based on assumptions of the objects' spatial structure, e.g., the sparsest solution in terms of some basis. The reduction in sampling required for CS image recovery can significantly speed up the image acquisition process. We demonstrate the advantage of our approach with two examples: (1) the single-pixel THz camera, and (2) THz Fourier imaging with compressed sensing (CS) and phase retrieval (PR). The former uses only a single-pixel detector and random patterns, and requires no raster scanning of objects, nor detection using a focal-plane array. The latter uses a limited and randomly chosen subset of a Fourier image, and allows image reconstruction based on only the Fourier magnitude. (Here is a copy of the powerpoint presentation about this research: PPT)

Directional Hypercomplex Wavelets for Multidimensional Signal Analysis and Processing
W. L. Chan, H. Choi, R. G. Baraniuk

We extend the wavelet transform to handle multi-dimensional signals that are smooth save for singularities along lower-dimensional manifolds. We first generalize the complex wavelet transform to higher dimensions using a multi-dimensional Hilbert transform. Then, using the resulting hypercomplex wavelet transform (HWT) as a building block, we construct new classes of nearly shift-invariant wavelet frames that are oriented along lower-dimensional subspaces. The HWT can be computed efficiently using a 1-D dual-tree complex wavelet transform along each signal axis. We demonstrate how the HWT can be used for fast line detection in 3-D. (Here is a copy of the powerpoint presentation about this approach: PPT)