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Using the concepts of two-dimensional Hubert transform and analytic signal, we construct a new quaternion wavelet transform (QWT). The QWT forms a tight frame and can be efficiently computed using a-2-D dual-tree filter bank. The QWT and the 2-D complex wavelet transform (CWT) are related by a unitary transformation, but the former inherits the quaternion… (More)

The dual-tree quaternion wavelet transform (QWT) is a new multiscale analysis tool for geometric image features. The QWT is a near shift-invariant tight frame representation whose coefficients sport a magnitude and three phases: two phases encode local image shifts while the third contains image texture information. The QWT is based on an alternative theory… (More)

We develop a quaternion wavelet transform (QWT) as a new multiscale analysis tool for geometric image features. The QWT is a near shift-invariant, tight frame representation whose coefficients sport a magnitude and three phase values, two of which are directly proportional to local image shifts. The QWT can be efficiently computed using a dual-tree filter… (More)

We describe a terahertz imaging system that uses a single pixel detector in combination with a series of random masks to enable high-speed image acquisition. The image formation is based on the theory of compressed sensing, which permits the reconstruction of a N-by-N pixel image using much fewer than N 2 measurements. This approach eliminates the need for… (More)

We describe a novel, high-speed pulsed terahertz (THz) Fourier imaging system based on compressed sensing (CS), a new signal processing theory, which allows image reconstruction with fewer samples than traditionally required. Using CS, we successfully reconstruct a 64 x 64 image of an object with pixel size 1.4 mm using a randomly chosen subset of the 4096… (More)

Within the last several years, the field of terahertz science and technology has changed dramatically. Many new advances in the technology for generation, manipulation, and detection of terahertz radiation have revolutionized the field. Much of this interest has been inspired by the promise of valuable new applications for terahertz imaging and sensing.… (More)

We extend the wavelet transform to handle multidimensional signals that are smooth save for singularities along lower-dimensional manifolds. We first generalize the complex wavelet transform to higher dimensions using a multidimensional Hilbert transform. Then, using the resulting hypercomplex wavelet transform (HWT) as a building block, we construct new… (More)

We design and implement a multipixel spatial modulator for terahertz beams using active terahertz metamaterials. Our first-generation device consists of a 4 ϫ 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… (More)

In reconstructing complex signals, many existing methods apply regularization on the magnitude only. We show that by adding control on the phase, the quality of the reconstruction can be improved. This is demonstrated in a compressed sensing terahertz imaging system.

- Lin Shu, Kai Ying Mai, Xiaoming Tao, Ying Li, Wing Cheung Wong, Ka Fai Lee +4 others
- ICCH
- 2012