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Item The 2nu-SVM: A Cost-Sensitive Extension of the nu-SVM(2005-12-01) Davenport, Mark A.; Digital Signal Processing (http://dsp.rice.edu/)Standard classification algorithms aim to minimize the probability of making an incorrect classification. In many important applications, however, some kinds of errors are more important than others. In this report we review cost-sensitive extensions of standard support vector machines (SVMs). In particular, we describe cost-sensitive extensions of the C-SVM and the nu-SVM, which we denote the 2C-SVM and 2nu-SVM respectively. The C-SVM and the nu-SVM are known to be closely related, and we prove that the 2C-SVM and 2nu-SVM share a similar relationship. This demonstrates that the 2C-SVM and 2nu-SVM explore the same space of possible classifiers, and gives us a clear understanding of the parameter space for both versions.Item 3-D Local Radon Power Spectra for Seismic Attribute Extraction(1998-01-15) Steeghs, Philippe; Fokkema, Jacob T; Diephuis, Gerhard; Digital Signal Processing (http://dsp.rice.edu/)In this paper we discuss a method for volume attribute extraction that is based on a new type of local Radon power spectrum. The new algorithm results in robust and geologically meaningful volume attributes, such as volume dip and azimuth. Seismic volume attribute analysis greatly facilitates the interpretation of large 3-D seismic data volumes. However, horizon attribute maps are generally more easy to interpret than volume attribute images, which are usually time slices or cross-sections. We show that, for dip estimation, the volume attribute image is very similar to the horizon dip map.Item 3D Geometry Coding using Mixture Models and the Estimation Quantization Algorithm(2002-09-01) Lavu, Sridhar; Lavu, Sridhar; Digital Signal Processing (http://dsp.rice.edu/)3D surfaces are used in applications such as animations, 3D object modeling and visualization. The geometries of such surfaces are often approximated using polygonal meshes. This thesis aims to compress 3D geometry meshes by using an algorithm based on normal meshes and the Estimation-Quantization (EQ) algorithm. Normal meshes are multilevel representations where finer level vertices lie in a direction normal to the local surface and therefore compress the vertex data to one scalar value per vertex. A mixture distribution model is used for the wavelet coefficients. The EQ algorithm uses the local neighborhood information and Rate-Distortion optimization to encode the wavelet coefficients. We achieve performance gains of 0.5-1dB compared to the zerotree coder for normal meshes.Item A HIGH RESOLUTION DATA-ADAPTIVE TIME-FREQUENCY REPRESENTATION(1987) JONES, DOUGLAS LLEWELLYN; Parks, ThomasThe short-time Fourier transform and the Wigner distribution are the time-frequency representations that have received the most attention. The Wigner distribution has a number of desirable properties, but it introduces nonlinearities called cross-terms that make it difficult to interpret when applied to real multi-component signals. The short-time Fourier transform has achieved widespread use in applications, but it often has poor resolution of signal components and can bias the estimate of signal parameters. A need exists for a time-frequency representation without the shortcomings of the current techniques. This dissertation develops a data-adaptive time-frequency representation that overcomes the often poor resolution of the traditional short-time Fourier transform, while avoiding the nonlinearities that make the Wigner distribution and other bilinear representations difficult to interpret and use. The new method uses an adaptive Gaussian basis, with the basis parameters varying at different time-frequency locations to maximize the local signal concentration in time-frequency. Two methods for selecting the Gaussian parameters are presented: a method that maximizes a measure of local signal concentration, and a parameter estimation approach. The new representation provides much better performance than any of the currently known techniques in the analysis of multi-modal dispersive waveforms.Item A MIXED FLAT AND EQUAL-RIPPLE CRITERION FOR FILTER DESIGN(1970) SOUTO, FERNANDO SIMOESItem A NOVEL FRAMEWORK FOR SURFACE RECONSTRUCTION FROM 3-DIMENSIONAL CONTOURS(1986) KEHTARNAVAZ, NASSERIn many applications, such as computer vision, medical imaging, scene forming, and motion animation, surface data is available in the form of two-dimensional (2D) or three-dimensional (3D) contours. Reconstruction of the surface integrates this information into a three-dimensional format. A good surface reconstruction framework must be able to include the surface characteristics inherited in the local structures of the contours. In order to achieve this goal, we have developed a novel surface reconstruction framework which consists of the formulation and solution of three separate subproblems: First, a new scheme for segmenting 3D contours into a set of 3D curve segments is developed. This scheme uses the norm of the Darboux vector, also called generalized curvature, as the segmentation criterion. The Darboux vector includes, as its components, the conventional curvature and the second curvature or torsion of the contour. Hence, it gives a complete representation of the structural characteristics of the contour. We use distributional derivatives in our formulation in order to combat the noise in contour data. The final result of the segmentation process is the representation of a 3D contour in the form of a string of 3D curve segments separated by a number of breakpoints. Second, having represented 3D contours by strings as above, one-to-one correspondences between breakpoints of adjacent strings are found. This correspondence problem is converted into a matching procedure by searching for the best possible match between the set of all homomorphic images of one contour and the adjacent one. An attribute vector, called a 3D-C-descriptor, is assigned to each curve segment. 3D-C-descriptors are then used as a cost function to locate this best match via the branch-and-bound search technique. This search is conducted with dynamic-programming which reduces the otherwise exponential-time complexity problem to one with polynomial-time complexity. Finally, once the curve segments are matched on all contours, parametric surface patches are created between the matched curve segments. Surface patch formation is carried out by blending the curve segments using novel spline and sinc blending functions. These blending functions interpolate simultaneously several contours and are chosen such that the boundary conditions are satisfied, and the shape of a curve segment is propagated along the surface beyond neighboring contours.Item A STUDY OF WINDOWS FOR THE SHORT-TIME FOURIER TRANSFORM (WIGNER, TIME, FREQUENCY, MATCHED)(1986) JONES, DOUGLAS LLEWELLYNItem Adaptive Iterative Reqeighted Least Squares Design of LP FIR Filters(IEEE, 1999-03-01) Vargas, Ricardo; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)This paper presents an efficient adaptive algorithm for designing FIR digital filters that are efficient according to an Lp error criteria. The algorithm is an extension of Burrus' iterative reweighted least-squares (IRLS) method for approximating Lp filters. Such algorithm will converge for most significant cases in a few iterations. In some cases however, the transition bandwidth is such that the number of iterations increases significantly. The proposed algorithm controls such problem and drastically reduces the number of iterations required.Item ADAPTIVE NONLINEAR IMAGE RESTORATION BY A MODIFIED KALMAN FILTERING APPROACH(1980) RAJALA, SARAH ANNAn adaptive nonlinear Kalman-type filter is presented in this dissertation for the restoration of two-dimensional images degraded by general image formation system degradations and additive white noise. A vector difference equation model is used to model the degradation process. The object plane distribution function is partitioned into disjoint regions based on the amount of spatial activity in the image, and difference equation models are used to characterize the object plane distribution function. It is shown that each of the regions can be uniquely characterized by their second order statistics. The autocorrelation function for each region is then used to determine the coefficients of the difference equation model for each region. Recursive estimation techniques are applied to a composite difference equation model. If the images are to be restored for human viewing it is desirable to account for the response of the human visual system as part of the receiver characteristics. This is done by weighting the variance (sigma)('2) of the additive noise by a visibility function, where the visibility function is a subjective measure of the visibility of additive noise in an image by the human visual system. As a consequence, the resulting effective variance depends nonlinearly on the state. Two additional features are added to the new restoration filter to solve problems arising in the implementation phase. A nearest neighbor algorithm is proposed for the selection of a previously processed pixel for providing the previous state vector for the state of pixel (i,j). Secondly, a two-dimensional interpolation scheme is proposed to improve the estimates of the initial states for each region.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 Representation of JPEG 2000 Images Using Header-based Processing(2002-09-20) Neelamani, Ramesh; Berkner, Kathrin; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/); CML (http://cml.rice.edu/); CITI (http://citi.rice.edu/)To bridge the mismatch between the sizes of images and display devices, we present an efficient and automatic algorithm to create an adaptive image representation called SmartNail. Given a digital image and rectangular display frame smaller than the image, we define the SmartNail as an appropriately cropped part of a suitably scaled-down image. We choose the SmartNail-defining parameters - down-scaling factor and cropping location - to maximize a bit-allocation-based cost function that quantifies the visual importance of the image content in the SmartNail. For JPEG 2000-encoded images, the SmartNail parameters can be determined using just the header information available in the encoded file. Hence only the wavelet coefficients required to reconstruct the SmartNail need to be decoded from the entire JPEG 2000 code stream. Consequently, the SmartNail construction requires minimal computations and memory requirements. Simulations demonstrate the effectiveness of SmartNail representations.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 Adding Linguistic Constraints to Document Image Decoding: Comparing the Iterated Complete Path and Stack Algorithms(2001-01-20) Popat, Kris; Greene, Dan; Romberg, Justin; Bloomberg, DanBeginning with an observed document image and a model of how the image has been degraded, Document Image Decoding recognizes printed text by attempting to find a most probable path through a hypothesized Markov source. The incorporation of linguistic constraints, which are expressed by a sequential predictive probabilistic language model, can improve recognition accuracy significantly in the case of moderately to severely corrupted documents. Two methods of incorporating linguistic constraints in the best-path search are described, analyzed and compared. The first, called the iterated complete path algorithm, involves iteratively rescoring complete paths using conditional language model probability distributions of increasing order, expanding state only as necessary with each iteration. A property of this approach is that it results in a solution that is exactly optimal with respect to the specified source, degradation, and language models; no approximation is necessary. The second approach considered is the Stack algorithm, which is often used in speech recognition and in the decoding of convolutional codes. Experimental results are presented in which text line images that have been corrupted in a known way are recognized using both the ICP and Stack algorithms. This controlled experimental setting preserves many of the essential features and challenges of real text line decoding, while highlighting the important algorithmic issues.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.