Browsing by Author "Choi, Hyeokho"
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Item Analysis of Multiscale Texture Segmentation using Wavelet-Domain Hidden Markov Trees(1999-10-01) Choi, Hyeokho; Hendricks, Brent; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)This paper describes a technique for estimating the Kullback-Leibler (KL) distance between two Hidden Markov Models (HMMs), and for measuring the quality of the estimator. It also provides some results based on applying the technique to wavelet domain Hidden Markov Tree (HMT) models used in image segmentation. The technique is easily applied, because in most situations the necessary tools (data generation and likelihood calculation) are already in place.Item Analysis of Wavelet domain Wiener Filters(1998-10-01) Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)We investigate Wiener filtering of wavelet coefficients for signal denoising. Empirically designed wavelet-domain Wiener filters outperform many other denoising algorithms based on wavelet thresholding. However, up to now, it has not been clear how to choose the signal model used to design the filter, because the effect of model selection on the filter performance is difficult to understand. By analyzing the error involved in the Wiener filter designed with an empirically obtained signal model, we show that hard thresholding is typically outperformed by a Wiener filter designed in an alternate wavelet domain. Our analysis furthermore provides a method for selecting the various parameters involved in a wavelet-domain Wiener filtering scheme.Item Bayesian Tree-Structured Image Modeling(2000-04-01) Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Wavelet-domain hidden Markov models have proven to be useful tools for statistical signal and image processing. The hidden Markov tree (HMT) model captures the key features of the joint statistics of the wavelet coefficients of real-world data. One potential drawback to the HMT framework is the need for computationally expensive iterative training (using the EM algorithm, for example). In this paper, we propose two reduced-parameter HMT models that capture the general structure of a broad class of grayscale images. The image HMT (iHMT) model leverages the fact that for a large class of images the structure of the HMT is self-similar across scale. This allows us to reduce the complexity of the iHMT to just nine easily trained parameters (independent of the size of the image and the number of wavelet scales). In the universal HMT (uHMT) we take a Bayesian approach and fix these nine parameters. The uHMT requires no training of any kind. While simple, we show using a series of image estimation/denoising experiments that these two new models retain nearly all of the key structures modeled by the full HMT. Based on these new models, we develop a shift-invariant wavelet denoising scheme that outperforms all algorithms in the current literature.Item Bayesian Tree-Structured Image Modeling using Wavelet-domain Hidden Markov Models(1999-07-20) Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G.; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)Wavelet-domain hidden Markov models have proven to be useful tools for statistical signal and image processing. The hidden Markov tree (HMT) model captures the key features of the joint probability density of the wavelet coefficients of real-world data. One potential drawback to the HMT framework is the need for computationally expensive iterative training to fit an HMT model to a given data set (using the Expectation-Maximization algorithm, for example). In this paper, we greatly simplify the HMT model by exploiting the inherent self-similarity of real-world images. This simplified model specifies the HMT parameters with just nine meta-parameters (independent of the size of the image and the number of wavelet scales). We also introduce a Bayesian universal HMT (uHMT) that mixes these nine parameters. The uHMT requires no training of any kind. While extremely simple, we show using a series of image estimation/denoising experiments that these two new models retain nearly all of the key structure modeled by the full HMT. Finally, we propose a fast shift-invariant HMT estimation algorithm that outperforms other wavelet-based estimators in the current literature, both in mean-square error and visual metrics.Item Bayesian Tree-Structured Image Modeling using Wavelet-domain Hidden Markov Models(2001-07-01) Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G.; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)Wavelet-domain hidden Markov models have proven to be useful tools for statistical signal and image processing. The hidden Markov tree (HMT) model captures the key features of the joint probability density of the wavelet coefficients of real-world data. One potential drawback to the HMT framework is the need for computationally expensive iterative training to fit an HMT model to a given data set (using the Expectation-Maximization algorithm, for example). In this paper, we greatly simplify the HMT model by exploiting the inherent self-similarity of real-world images. This simplified model specifies the HMT parameters with just nine meta-parameters (independent of the size of the image and the number of wavelet scales). We also introduce a Bayesian universal HMT (uHMT) that fixes these nine parameters. The uHMT requires no training of any kind. While extremely simple, we show using a series of image estimation/denoising experiments that these new models retain nearly all of the key image structure modeled by the full HMT. Finally, we propose a fast shift-invariant HMT estimation algorithm that outperforms other wavelet-based estimators in the current literature, both visually and in mean-square error.Item Bayesian Wavelet Domain Image Modeling using Hidden Markov Trees(1999-10-01) Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Wavelet-domain hidden Markov models have proven to be useful tools for statiscal signal and image processing. The hidden Markov tree (HMT) model captures the key features o teh join statistics of the wavelet coefficients of real-world data. One potential drawback to the HMT framework is the need for computationally expensive iterative training (using the EM algorithm, for example). In this paper, we propose two reduced-parameter HMT models that capture the general structure of a broad class of grayscale images. The image HMT (iHMT) model leverages the fact that for a large class of images the structure of the HMT is self-similar across scale. This allows us to reduce the complexity of teh iHMT to just nine easily trained parameters (independent of the size of teh image and the number of wavelet scales). In the universal HMT (uHMT) we take a Bayesian approach and fix these nine parameters. The uHMT requires no training of any kind. While simple, we show using a series of image estimation/denoising experiments that these two new models retain nearly all of the key structures modeled by the full HMT. Based on these new models, we develop a shift-invariant wavelet denoising scheme that outperforms all algorithms in the current literature.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 Community Driven Digital Signal Processing Laboratories in Connexions(2004-06-01) Baraniuk, Richard G.; Choi, Hyeokho; Jones, Douglas L.; Potter, Lee; Digital Signal Processing (http://dsp.rice.edu/)The conventional textbook is largely inadequate for digital signal processing (DSP) laboratory education due to inherent factors such as a small and fragmented market and rapid hardware obsolescence. Freely available open-content materials that enable and promote both local customization and further development by a community of educators offers a fresh approach to lab text development that can surmount these barriers. In this paper, we overview a joint effort organized by the Connexions Project to develop a large pool of DSP lab modules sufficient to serve as the complete, stand-alone text for several types of DSP lab courses.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 Distributed Camera Network Localization(2004-11-01) Mantzel, William; Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Localization, estimating the positions and orientations of a set of cameras, is a critical first step in camera-based sensor network applications such as geometric estimation, scene reconstruction, and motion tracking. We propose a new distributed localization algorithm for networks of cameras with sparse overlapping view structure that is energy efficient and copes well with networking dynamics. The distributed nature of the localization computations can result in order-of magnitude savings in communication energy over centralized approaches.Item Distributed Multiscale Data Analysis and Processing for Sensor Networks(2005-02-01) Wagner, Raymond; Sarvotham, Shriram; Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)While multiresolution data analysis, processing, and compression hold considerable promise for sensor network applications, progress has been confounded by two factors. First, typical sensor data are irregularly spaced, which is incompatible with standard wavelet techniques. Second, the communication overhead of multiscale algorithms can become prohibitive. In this paper, we take a first step in addressing both shortcomings by introducing two new distributed multiresolution transforms. Our irregularly sampled Haar wavelet pyramid and telescoping Haar orthonormal wavelet basis provide efficient piecewise-constant approximations of sensor data. We illustrate with examples from distributed data compression and in-network wavelet de-noising.Item Distributed Wavelet Transform for Irregular Sensor Network Grids(2005-07-01) Wagner, Raymond; Choi, Hyeokho; Baraniuk, Richard G.; Delouille, Veronique; Digital Signal Processing (http://dsp.rice.edu/)Wavelet-based distributed data processing holds much promise for sensor networks; however, irregular sensor node placement precludes the direct application of standard wavelet techniques. In this paper, we develop a new distributed wavelet transform based on lifting that takes into account irregular sampling and provides a piecewise-planar multiresolution representation of the sensed data. We develop the transform theory; outline how to implement it in a multi-hop, wireless sensor network; and illustrate with several simulations. The new transform performs on par with conventional wavelet methods in a head-to-head comparison on a regular grid of sensor nodes.Item DSP Education At Rice University(2003-09-01) Frantz, Patrick; Choi, Hyeokho; Baraniuk, Richard G.; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)Rice University has a decades-long tradition of both digital signal processing (DSP) research and education, beginning in 1968. Since that time, Rice University has become a world leader and continued to be a pioneer in the DSP field. This paper will focus on the following three areas of activity at Rice. First, a brief history of DSP education and research at Rice will be presented, along with the current state of DSP research and education (Section 2). Second, a DSP Lab course will be presented, which utilizes Riceâ s Texas Instruments Elite DSP Laboratory and the C6x series of DSPs to educate students in the practical art of DSP (Section 3). This course is a 1-semester long series of labs, with a larger DSP project to be completed at the end of the course. Third, a brief overview of the Connexions project will be given, a tool originally developed to advance DSP education at Rice and other institutions (Sections 4 - 8). Connexions is a collaborative, community-driven approach to authoring, teaching, and learning that seeks to provide a cohesive body of high-quality educational content to anyone in the world, for free.Item Edge Localized Image Sharpening via Reassignment with Application to Computed Tomography(2000-07-01) Dorney, Timothy D.; Bhashyam, Srikrishna; Doran, Andrew; Choi, Hyeokho; Flandrin, Patrick; Baraniuk, Richard G.; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)Traditional filtering methods operate on the entire signal or image. In some applications, however, errors are concentrated in specific regions or features. A prime example is images generated using computed tomography. Practical implementations limit the amount of high frequency content in the reconstructed image, and consequently, edges are blurred. We introduce a new post-reconstruction edge enhancement algorithm, based on the reassignment principle and wavelets, that localizes its sharpening exclusively to edge features. Our method enhances edges without disturbing the low frequency textural details.Item Estimation-Quantization Geometry Coding Using Normal Meshes(2003-03-01) Lavu, Sridhar; Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)We propose a new algorithm for compressing three-dimensional triangular mesh data used for representing surfaces. We apply the Estimation-Quantization (EQ) algorithm originally designed for still image compression to the normal mesh wavelet coefficients. The EQ algorithm models the wavelet coefficients as a Gaussian random field with slowly varying standard deviation. By designing the quantizers in a rate-distortion optimal fashion, we improve upon the recently proposed zerotree normal mesh compression algorithm by 0.5 to 1 dB in distortion.Item Item ForWaRD: Fourier-Wavelet Regularized Deconvolution for Ill-Conditioned Systems(2004-02-01) Neelamani, Ramesh; Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)We propose an efficient, hybrid Fourier-Wavelet Regularized Deconvolution (ForWaRD) algorithm that performs noise regularization via scalar shrinkage in both the Fourier and wavelet domains. The Fourier shrinkage exploits the Fourier transform's sparse representation of the colored noise inherent in deconvolution, while the wavelet shrinkage exploits the wavelet domain's sparse representation of piecewise smooth signals and images. We derive the optimal balance between the amount of Fourier and wavelet regularization by optimizing an approximate mean-squared-error (MSE) metric and find that signals with sparser wavelet representations require less Fourier shrinkage. ForWaRD is applicable to all ill-conditioned deconvolution problems, unlike the purely wavelet-based Wavelet-Vaguelette Deconvolution (WVD), and its estimate features minimal ringing, unlike purely Fourier-based Wiener deconvolution. We analyze ForWaRD's MSE decay rate as the number of samples increases and demonstrate its improved performance compared to the optimal WVD over a wide range of practical sample-lengths.Item An FPGA-based Daughtercard for TIs C6000 family of DSKs(2005-06-01) Gadhiok, Manik; Hardy, Ricky; Murphy, Patrick; Frantz, Patrick; Choi, Hyeokho; Cavallaro, Joseph R.; Digital Signal Processing (http://dsp.rice.edu/)In this paper we present an FPGA-based daughtercard designed for TIs C6000 family of DSP Starter Kits (DSKs). The hardware, initially designed for a course project, provides a platform for studying heterogeneous systems and hardware software co-design. Students will leverage the DSK-FPGA system for rapid prototyping of signal processing algorithms and to study task-partitioning and system integration. These techniques are becoming increasingly important for system designers as we move to system-on-chip (SOC) devices. The daughtercard hardware is fully functional, and a software package is being developed to provide a seamless communication interface between the DSK and FPGA.Item A Geometric Hidden Markov Tree Wavelet Model(2003-08-01) Romberg, Justin; Wakin, Michael; Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)In the last few years, it has become apparent that traditional wavelet-based image processing algorithms and models have significant shortcomings in their treatment of edge contours. The standard modeling paradigm exploits the fact that wavelet coefficients representing smooth regions in images tend to have small magnitude, and that the multiscale nature of the wavelet transform implies that these small coefficients will persist across scale (the canonical example is the venerable zero-tree coder). The edge contours in the image, however, cause more and more large magnitude wavelet coefficients as we move down through scale to finer resolutions. But if the contours are smooth, they become simple as we zoom in on them, and are well approximated by straight lines at fine scales. Standard wavelet models exploit the grayscale regularity of the smooth regions of the image, but not the geometric regularity of the contours. In this paper, we build a model that accounts for this geometric regularity by capturing the dependencies between complex wavelet coefficients along a contour. The Geometric Hidden Markov Tree (GHMT) assigns each wavelet coefficient (or spatial cluster of wavelet coefficients) a hidden state corresponding to a linear approximation of the local contour structure. The shift and rotational-invariance properties of the complex wavelet transform allow the GHMT to model the behavior of each coefficient given the presence of a linear edge at a specified orientation --- the behavior of the wavelet coefficient given the state. By connecting the states together in a quadtree, the GHMT ties together wavelet coefficients along a contour, and also models how the contour itself behaves across scale. We demonstrate the effectiveness of the model by applying it to feature extraction.
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