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Browsing DSP Publications by Author "Baraniuk, Richard G."
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Item An Adaptive Optimal-Kernel Time-Frequency Representation(1995-10-01) Jones, Douglas L.; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Time-frequency representations with fixed windows or kernels figure prominently in many applications, but perform well only for limited classes of signals. Representations with signal- dependent kernels can overcome this limitation. However, while they often perform well, most existing schemes are block-oriented techniques unsuitable for on-line implementation or for tracking signal components with characteristics that change with time. The time-frequency representation developed here, based on a signal-dependent radially Gaussian kernel that adapts over time, overcomes these limitations. The method employs a short-time ambiguity function both for kernel optimization and as an intermediate step in computing constant-time slices of the representation. Careful algorithm design provides reasonably efficient computation and allows on-line implementation. Certain enhancements, such as cone-kernel constraints and approximate retention of marginals, are easily incorporated with little additional computation. While somewhat more expensive than fixed-kernel representations, this new technique often provides much better performance. Several examples illustrate its behavior on synthetic and real-world signals.Item Adaptive Wavelet Transforms for Image Coding(1997-11-01) Claypoole, Roger L.; Davis, Geoffrey; Sweldens, Wim; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)We introduce a new adaptive transform for wavelet-based image coding. The lifting framework for wavelet construction motivates our analysis and provides new insight into the problem. Since the adaptive transform is non-linear, we examine the central issues of invertibility, stability, and artifacts in its construction. We describe a new type of non-linearity: a set of linear predictors are chosen adaptively using a non-linear selection function. We also describe how earlier families of non-linear filter banks can be extended through the use of prediction functions operating on a causal neighborhood. We present preliminary results for a synthetic test image.Item Adaptive Wavelet Transforms for Image Coding(1997-11-01) Claypoole, Roger L.; Davis, Geoffrey; Sweldens, Wim; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)We introduce a new adaptive transform for wavelet-based image coding. The lifting framework for wavelet construction motivates our analysis and provides new insight into the problem. Since the adaptive transform is non-linear, we examine the central issues of invertibility, stability, and artifacts in its construction. We describe a new type of non-linearity: a set of linear predictors are chosen adaptively using a non-linear selection function. We also describe how earlier families of non-linear filter banks can be extended through the use of prediction functions operating on a causal neighborhood. We present preliminary results for a synthetic test image.Item Adaptive Wavelet Transforms for Image Coding using Lifting(1998-03-01) Claypoole, Roger L.; Davis, Geoffrey; Sweldens, Wim; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Summary form only given. Image compression relies on efficient representations of images, and within smooth image regions, the wavelet transform provides such a representation. However, near edges, wavelet coefficients decay slowly and are expensive to code. We focus on improving the transform by incorporating adaptivity. Construction of nonlinear filter banks has been discussed, but the question of how to utilize the nonlinearities remained. We answer this question by describing our transform via lifting. Lifting provides a spatial domain framework for the wavelet transform. In the lifting formalism, wavelet coefficients are seen as prediction residuals from a linear prediction operation. Wavelet coefficients are large near edges because the linear predictors are built to interpolate low order polynomials. Our goal is to avoid this problem by adapting the predictor based on local image properties. In smooth regions of the image, we use high order polynomial predictors. We adaptively reduce the prediction order to avoid attempting to predict values across discontinuities.Item Adaptive Wavelet Transforms via Lifting(1998) Claypoole, Roger L.; Baraniuk, Richard G.; Nowak, Robert David; Digital Signal Processing (http://dsp.rice.edu/)This paper develops new algorithms for adapted multiscale analysis and signal adaptive wavelet transforms. We construct our adaptive transforms with the lifting scheme, which decomposes the wavelet transform into prediction and update stages. We adapt the prediction stage to the signal structure and design the update stage to preserve the desirable properties of the wavelet transform. We incorporate this adaptivity into the redundant and non-redundant transforms; the resulting transforms are scale and spatially adaptive. We study applications to signal estimation; our new transforms show improved denoising performance over existing (non-adaptive) orthogonal transforms.Item Adaptive Wavelet Transforms via Lifting(1999-01-15) Claypoole, Roger L.; Baraniuk, Richard G.; Nowak, Robert David; Digital Signal Processing (http://dsp.rice.edu/)This paper develops new algorithms for adapted multiscale analysis and signal adaptive wavelet transforms. We construct our adaptive transforms with the lifting scheme, which decomposes the wavelet transform into prediction and update stages. We adapt the prediction stage to the signal structure and design the update stage to preserve the desirable properties of the wavelet transform. We incorporate this adaptivity into the redundant and non-redundant transforms; the resulting transforms are scale and spatially adaptive. We study applications to signal estimation; our new transforms show improved denoising performance over existing (non-adaptive) orthogonal transforms.Item Adaptive Wavelet Transforms via Lifting(1998-05-01) Claypoole, Roger L.; Baraniuk, Richard G.; Nowak, Robert David; Digital Signal Processing (http://dsp.rice.edu/)This paper develops two new adaptive wavelet transforms based on the lifting scheme. The lifting construction exploits a spatial-domain, prediction-error interpretation of the wavelet transform and provides a powerful framework for designing customized transforms. We use the lifting construction to adaptively tune a wavelet transform to a desired signal by optimizing data-based prediction error criteria. The performances of the new transforms are compared to existing wavelet transforms, and applications to signal denoising are investigated.Item Adaptive Weighted Highpass Filters Using Multiscale Analysis(1998-07-01) Nowak, Robert David; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)In this paper, we propose a general framework for studying a class of weighted highpass filters. Our framework, based on a multiscale signal decomposition, allows us to study a wide class of filters and to assess the merits of each. We derive an automatic procedure to tune a filter to the local structure of the image under consideration. The entire algorithm is fully automatic and requires no parameter specification from the user. Several simulations demonstrate the efficacy of the method.Item Additive and Multiplicative Mixture Trees for Network Traffic Modeling(2002-05-01) Sarvotham, Shriram; Wang, Xuguang; Riedi, Rudolf H.; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Network traffic exhibits drastically different statistics, ranging from nearly Gaussian marginals and long range dependence at very large time scales to highly non-Gaussian marginals and multifractal scaling on small scales. This behavior can be explained by forming two components of the traffic according to the speed of connections, one component absorbing most traffic and being mostly Gaussian, the other constituting virtually all the small scale bursts. Towards a better understanding of this phenomenon, we propose a novel tree-based model which is flexible enough to accommodate Gaussian as well as bursty behavior on different scales in a parsimonious way.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 the DCS one-stage Greedy Algorothm for Common Sparse Supports(2005-11-01) Baron, Dror; Duarte, Marco F.; Wakin, Michael; Sarvotham, Shriram; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Analysis of the DCS one-stage Greedy Algorothm for Common Sparse SupportsItem 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 Applications of Adaptive Time Frequency Representations to Underwater Acoustic Signal Processing(1991-11-01) Baraniuk, Richard G.; Jones, Douglas L.; Tom, Brotherton; Larry, Marple; Digital Signal Processing (http://dsp.rice.edu/)The authors describe the application of an adaptive optimal kernel (AOK) time-frequency representation to the processing of underwater acoustic data. The optimal kernel is a signal-dependent radially Gaussian function. Examples are given which demonstrate the effectiveness of the approach for simulated and real sonar data. The simulations indicate that the technique should work well for a larger set of signal classes than any current fixed-kernel representation. The technique has excellent performance even in the presence of substantial additive noise; this property may be exploited for signal detection. The AOK technique appears to offer unique features that can be used to characterize and automatically classify signals of interest, particularly when compared to other processing techniques.Item Applications of Terahertz Imaging(1998-08-01) Mittleman, Daniel M.; Neelamani, Ramesh; Baraniuk, Richard G.; Nuss, Martin C.; Digital Signal Processing (http://dsp.rice.edu/)The recent advances involving imaging with sub-picosecond terahertz pulses have opened up a wide range of possibilities in the applications of far-infrared technology. For the first time, a commercially viable terahertz imaging spectrometer seems a realizable prospect. However, several substantial engineering research challenges remain to be overcome before this goal can be achieved. One of these involves the necessity for a femtosecond laser system, required for gating the emitter and receiver antennas used in the THz-TDS system. The demonstration experiments performed to date have employed rather crude signal processing algorithms. The shortcomings of these are evident in some of the results presented here, highlighting the need for a more sophisticated treatment.Item Approximation and Compression of Piecewise Smooth Images Using a Wavelet/Wedgelet Geometric Model(2003-09-01) Romberg, Justin; Wakin, Michael; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Inherent to photograph-like images are two types of structures: large smooth regions and geometrically smooth edge contours separating those regions. Over the past years, efficient representations and algorithms have been developed that take advantage of each of these types of structure independently: quadtree models for 2D wavelets are well-suited for uniformly smooth images (C² everywhere), while quadtree-organized wedgelet approximations are appropriate for purely geometrical images (containing nothing but C² contours). This paper shows how to combine the wavelet and wedgelet representations in order to take advantage of both types of structure simultaneously. We show that the asymptotic approximation and rate-distortion performance of a wavelet-wedgelet representation on piecewise smooth images mirrors the performance of both wavelets (for uniformly smooth images) and wedgelets (for purely geometrical images). We also discuss an efficient algorithm for fitting the wavelet-wedgelet representation to an image; the convenient quadtree structure of the combined representation enables new algorithms such as the recent WSFQ geometric image coder.Item An Architecture for Distributed Wavelet Analysis and Processing in Sensor Networks(2006-04-01) Wagner, Raymond; Baraniuk, Richard G.; Du, Shu; Johnson, David B.; Cohen, AlbertDistributed wavelet processing within sensor networks holds promise for reducing communication energy and wireless bandwidth usage at sensor nodes. Local collaboration among nodes de-correlates measurements, yielding a sparser data set with significant values at far fewer nodes. Sparsity can then be leveraged for subsequent processing such as measurement compression, de-noising, and query routing. A number of factors complicate realizing such a transform in real-world deployments, including irregular spatial placement of nodes and a potentially prohibitive energy cost associated with calculating the transform in-network. In this paper, we address these concerns head-on; our contributions are fourfold. First, we propose a simple interpolatory wavelet transform for irregular sampling grids. Second, using ns-2 simulations of network traffic generated by the transform, we establish for a variety of network configurations break-even points in network size beyond which multiscale data processing provides energy savings. Distributed lossy compression of network measurements provides a representative application for this study. Third, we develop a new protocol for extracting approximations given only a vague notion of source statistics and analyze its energy savings over a more intuitive but naive approach. Finally, we extend the 2-dimensional (2-D) spatial irregular grid transform to a 3-D spatio-temporal transform, demonstrating the substantial gain of distributed 3-D compression over repeated 2-D compression.Item Asymptotic Performance of Transmit Diversity via OFDM for Multipath Channels(2002-11-01) Ahmed, Nadeem; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Many wireless systems exploit transmit diversity for more reliable detection of signals at the receiver. To accomplish this, coding is spread across multiple transmit antennas. An example of this is the well known "Alamouti transmit diversity", where a very simple coding scheme across multiple transmit antennas allows systems to attain performance similar to systems with multiple receive antennas. The major drawback is that this system only works when a "flat-fading" model for the channel is assumed; when used in a multipath environment, the system breaks down. Here we show that when the Alamouti code is placed within an OFDM structure, using adjacent frequency bands rather than consecutive symbol intervals, it can asymptotically achieve the same performance in multipath fading as the Alamouti code in flat-fading.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.