Browsing by Author "Chan, Wai Lam"
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Item Coherent Image Processing using Quaternion Wavelets(2005-08-01) Chan, Wai Lam; Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)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 bank and is based on a 2-D Hilbert transform. We demonstrate how the QWT's magnitude and phase can be used to accurately analyze local geometric structure in images. We also develop a multiscale flow/motion estimation algorithm that computes a disparity flow map between two images with respect to local object motion.Item Coherent Multiscale Image Processing using Quaternion Wavelets(2006-10-01) Chan, Wai Lam; Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)The 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 for the 2-D Hilbert transform and can be computed using a dual-tree filter bank with linear computational complexity. To demonstrate the properties of the QWT's coherent magnitude/phase representation, we develop an efficient and accurate procedure for estimating the local geometrical structure of an image. We also develop a new multiscale algorithm for estimating the disparity between a pair of images that is promising for image registration and flow estimation applications. The algorithm features multiscale phase unwrapping, linear complexity, and sub-pixel estimation accuracy.Item Coherent multiscale image processing using quaternion wavelets(2006) Chan, Wai Lam; Baraniuk, Richard G.This thesis develops 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 phases: two phases encode local image shifts while the third contains textural information. The QWT can be computed using a dual-tree filter bank with linear computational complexity. We develop the QWT by applying an alternative theory of 2-D Hilbert transforms and analytic signals to the 1-D complex wavelet transform. To demonstrate the properties of the QWT's coherent magnitude/phase representation, we develop a efficient and accurate algorithm for estimating the local geometrical structure of images and a multiscale algorithm for estimating the disparity between a pair of images. The latter algorithm has potentials for various applications in image registration and flow estimation. It uses an interesting multiscale phase unwrapping procedure and features linear complexity and sub-pixel accuracy.Item Directional Hypercomplex Wavelets for Multidimensional Signal Analysis and Processing(2004-05-01) Chan, Wai Lam; Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)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 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.Item Quaternion Wavelets for Image Analysis and Processing(2004-10-01) Chan, Wai Lam; Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)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 Fourier-transform (QFT) phase properties, which are desirable for image analysis. The quaternion magnitude-phase representation of the QWT directly leads to near shift-invariance and the ability to encode phase shifts in an absolute x-y-coordinate system, which we can use for applications such as edge estimation and statistical image modeling.Item Terahertz imaging with compressive sensing(2010) Chan, Wai Lam; Mittleman, Daniel M.Most existing terahertz imaging systems are generally limited by slow image acquisition due to mechanical raster scanning. Other systems using focal plane detector arrays can acquire images in real time, but are either too costly or limited by low sensitivity in the terahertz frequency range. To design faster and more cost-effective terahertz imaging systems, the first part of this thesis proposes two new terahertz imaging schemes based on compressive sensing (CS). Both schemes can acquire amplitude and phase-contrast images efficiently with a single-pixel detector, thanks to the powerful CS algorithms which enable the reconstruction of N-by- N pixel images with much fewer than N2 measurements. The first CS Fourier imaging approach successfully reconstructs a 64x64 image of an object with pixel size 1.4 mm using a randomly chosen subset of the 4096 pixels which defines the image in the Fourier plane. Only about 12% of the pixels are required for reassembling the image of a selected object, equivalent to a 2/3 reduction in acquisition time. The second approach is single-pixel CS imaging, which uses a series of random masks for acquisition. Besides speeding up acquisition with a reduced number of measurements, the single-pixel system can further cut down acquisition time by electrical or optical spatial modulation of random patterns. In order to switch between random patterns at high speed in the single-pixel imaging system, the second part of this thesis implements a multi-pixel electrical spatial modulator for terahertz beams using active terahertz metamaterials. The first generation of this device consists of a 4x4 pixel array, where each pixel is an array of sub-wavelength-sized split-ring resonator elements fabricated on a semiconductor substrate, and is independently controlled by applying an external voltage. The spatial modulator has a uniform modulation depth of around 40 percent across all pixels, and negligible crosstalk, at the resonant frequency. The second-generation spatial terahertz modulator, also based on metamaterials with a higher resolution (32x32), is under development. A FPGA-based circuit is designed to control the large number of modulator pixels. Once fully implemented, this second-generation device will enable fast terahertz imaging with both pulsed and continuous-wave terahertz sources.