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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)

- Wai Lam Chan, Kriti Charan, Dharmpal Takhar, Kevin F Kelly, Richard G Baraniuk, Daniel M Mittleman
- 2008

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)

- Wai Lam Chan, Matthew L Moravec, Richard G Baraniuk, Daniel M Mittleman
- Optics letters
- 2008

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)

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)

Using the conccptn of two-dimensionnl Hilbert transform and analytic signal, we construct a new qriutenrimz wavrler rrunsfunn (QWT). The QWT forms a tight frame and can be efficiently computed using a 2-D dual-tree tilter hank. The QWT and the 2-D complex wavclet transform (CWT) are related by a unitary transformation. but the former inhcrits the quaternion… (More)

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

We propose an efficient multiscale image disparity estimation algorithm that estimates the local translations needed to align different regions in two images. The algorithm is based on the dual-tree quaternion wavelet transform (QWT). Each QWT coefficient features a magnitude and three phase angles; we exploit the fact that two of the phase angles are… (More)

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