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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)
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)
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)
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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