Browsing by Author "Odegard, Jan E."
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Item 2008-'09 Open Education Cup: High Performance Computing(Rice University, 2012-06-04) Odegard, Jan E.This collection provides an overview of the 2008-'09 Open Education Cup competition. Contest rules, author resources, and example content are provided. This competition is intended to encourage development of original educational content in the field of parallel computing, with cash prizes awarded to contest winners. Selected modules will be included as part of a new collection available through Connexions.Item Constrained FIR Filter Design for 2-band Filter Banks and Orthonormal Wavelets(1994-10-20) Markus, Lang; Selesnick, Ivan W.; Odegard, Jan E.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)2-band paraunitary FIR filter banks can be used to generate a multiresolution analysis with compactly supported orthonormal (ON) wavelets. The filter design problem is formulated and solved (a) as a constrained LÂ â ¡ optimization problem and (b) as a constrained L2 optimization problem which allows arbitrary compromises between an L2 and an LÂ â ¡ approach with both of them as special cases. Additional flatness constraints can also be easily included. The L2 and the LÂ â ¡ design are based on the Kuhn-Tucker (KT) conditions and the alternation theorem, respectively. Therefore, optimality of the solution is guaranteed. The method (a) is a simpler alternative to a known method. The method (b) solves a more general problem than the approaches known in the literature including all of them as special cases.Item Design of Linear Phase Cosine Modulated Filter Banks for Subband Image Compression(1994-01-15) Odegard, Jan E.; Gopinath, Ramesh A.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/); CML (http://cml.rice.edu/)Wavelet methods give a flexible alternative to Fourier methods in non-stationary signal analysis. The concept of band-limitedness plays a fundamental role in Fourier analysis. Since wavelet theory replaces frequency with scale, a natural question is whether there exists a useful concept of scale-limitedness. Obvious definitions of scale-limitedness are too restrictive, in that there would be few or no useful scale-limited signals. This paper introduces a viable definition for scale-limited signals, and shows that the class is rich enough to include bandlimited signals, and impulse trains, among others. Moreover, for a wide choice of criteria, we show how to design the optimal wavelet for representing a given signal, and how to design robust wavelets that optimally represent certain classes of signals.Item Discrete finite variation: A new measure of smoothness for the design of wavelet basis(1996-05-20) Odegard, Jan E.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)A new method for measuring and designing smooth wavelet basis which dispenses with the need for having a large number of zero moments of the wavelet is given. The method is based on minimizing the "discrete finite variation", and is a measure of the local "roughness" of a sampled version of the scaling function giving rise to "visually smooth" wavelet basis. Smooth wavelet basis are deemed to be important for several applications and in particularly for image compression where the goal is to limit spurious artifacts due to non-smooth basis functions in the presence of quantization of the individual subbands. The definition of smoothness introduced here gives rise to new algorithms for designing smooth wavelet basis with only one vanishing moment leaving free parameters, otherwise used for setting moments to zero, for optimization.Item Enhancement of Decompressed Images at Low Bit Rates(1994-07-20) Gopinath, Ramesh A.; Lang, Markus; Guo, Haitao; Odegard, Jan E.; Digital Signal Processing (http://dsp.rice.edu/)Transform coding at low bit rates introduces artifacts associated with the basis functions of the transform. For example, decompressed images based on the DCT (discrete cosine transform)- like JPEG16 - exhibit blocking artifacts at low bit rates. This paper proposes a post-processing scheme to enhance decompressed images that is potentially applicable in several situations. In particular, the method works remarkable well in "deblocking" of DCT compressed images. The method is non-linear, computationally efficient, and spatially adaptive - and has the distint feature that it removes artifacts while yet retaining sharp features in the images. An important implication of this result is that images coded using the JPEG standard can be efficiently post-processed to give significantly improved visual quality in the images.Item Image enhancement by nonlinear wavelet processing(1994-10-20) Odegard, Jan E.; Digital Signal Processing (http://dsp.rice.edu/)In this paper we describe how the theory of wavelet thresholding introduced by Donoho and Johnstone can successfully be applied to two distinct problems in image processing where traditional linear filtering techniques are insufficient. The first application is related to speckle reduction in coherent imaging systems. We show that the proposed method works well for reducing speckle in SAR images while maintaining bright reflections for subsequent processing and detection. Secondly we apply the wavelet based method for reducing blocking artifacts associated with most DCT based image coders (e.g., most notably the Joint Photographic Experts Group (JPEG) standard at high compression ratios). In particular we demonstrate an algorithm for post-processing decoded images without the need for a novel coder/decoder. By applying this algorithm we are able to obtain perceptually superior images at high compression ratios using the JPEG coding standard. For both applications we have developed methods for estimating the required threshold parameter and we have applied these to large number of images to study the effect of the wavelet thresholding. Our main goal with this paper is to illustrate how the recent theory of wavelet denoising can be applied to a wide range of practical problems which does not necessarily satisfy all the assumptions of the developed theory.Item Instantaneous Frequency Estimation using the Reassignment method(1998-01-15) Odegard, Jan E.; Baraniuk, Richard G.; Oehler, Kurt L; Digital Signal Processing (http://dsp.rice.edu/)This paper explores the method of reassignment for extracting instantaneous frequency attributes from seismic data. The reassignment method was first applied to the spectrogram by Kodera, Gendrin and de Villedary and later generalized to any bilinear time-frequency or time-scale representation by Auger and Flandrin. Key to the method is a nonlinear convolution where the value of the convolution is not placed at the center of the convolution kernel but rather reassigned to the center of mass of the function within the kernel. The resulting reassigned representation yields significantly improved component localization. In this paper we will study the impact of the reassigned time-frequency representation on our ability to reliably estimate instantaneous frequency for a given seismic signal.Item Joint Compression and Speckle Reduction of SAR Images using Embedded Zerotree Models(1996-03-01) Odegard, Jan E.; Guo, Haitao; Burrus, C. Sidney; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)We propose a new method for speckle reduction in synthetic aperture radar (SAR) imagery based on the embedded zerotree image compression algorithm. This new approach to denoising is inspired by the realization that the wavelet transform domain and the zero-tree image model are natural for both compression and denoising. We illustrate the proposed scheme using fully polarimetric SAR images and a variety of compression ratios.Item New class of wavelets for signal approximation(1996-05-20) Odegard, Jan E.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)This paper develops a new class of wavelets for which the classical Daubechies zero moment property has been relaxed. The advantages of relaxing higher order wavelet moment constraints is that within the framework of compact support and perfect reconstruction (orthogonal and biorthogonal) one can obtain wavelet basis with new and interesting approximation properties. This paper investigates a new class of wavelets that is obtained by setting a few lower order moments to zero and using the remaining degrees of freedom to minimize a larger number of higher order moments. The resulting wavelets are shown to be robust for representing a large classes of inputs. Robustness is achieved at the cost of exact representation of low order polynomials but with the advantage that higher order polynomials can be represented with less error compared to the maximally regular solution of the same support.Item Noise Reduction Using an Undecimated Discrete Wavelet Transform(1995-01-15) Lang, Markus; Guo, Haitao; Odegard, Jan E.; Burrus, C. Sidney; Wells, R.O.; Digital Signal Processing (http://dsp.rice.edu/)A new nonlinear noise reduction method is presented that uses the discrete wavelet transform. Similar to Donoho and Johnstone, we employ thresholding in the wavelet transform domain but, following a suggestion by Coifman, we use an undecimated, shift-invariant, nonorthogonal wavelet transform instead of the usual orthogonal one. This new approach can be interpreted as a repeated application of the original Donoho and Johnstone method for different shifts. The main feature of the new algorithm is a significantly improved noise reduction compared to the original wavelet based approach, both the l2 error and visually, for a large class of signals. This is shown both theoretically as well as by experimental results.Item Nonlinear Processing of a Shift Invariant DWT for Noise Reduction(1995-04-20) Lang, Markus; Guo, Haitao; Odegard, Jan E.; Burrus, C. Sidney; Wells, R.O.; Digital Signal Processing (http://dsp.rice.edu/); CML (http://cml.rice.edu/)A novel approach for noise reduction is presented. Similar to Donoho, we employ thresholding in some wavelet transform domain but use a nondecimated and consequently redundant wavelet transform instead of the usual orthogonal one. Another difference is the shift invariance as opposed to the traditional orthogonal wavelet transform. We show that this new approach can be interpreted as a repeated application of Donoho's original method. The main feature is, however, a dramatically improved noise reduction compared to Donoho's approach, both in terms of the l2 error and visually, for a large class of signals. This is shown by theoretical and experimental results, including synthetic aperture radar (SAR) images.Item Nonlinear Processing of a Shift Invariant DWT for Noise Reduction(1995-03-20) Lang, Markus; Guo, Haitao; Odegard, Jan E.; Burrus, C. Sidney; Wells, R.O.; Digital Signal Processing (http://dsp.rice.edu/); CML (http://cml.rice.edu/)A novel approach for noise reduction is presented. Similar to Donoho, we employ thresholding in some wavelet transform domain but use a nondecimated and consequently redundant wavelet transform instead of the usual orthogonal one. Another difference is the shift invariance as opposed to the traditional orthogonal wavelet transform. We show that this new approach can be interpreted as a repeated application of Donoho's original method. The main feature is, however, a dramatically improved noise reduction compared to Donoho's approach, both in terms of the l2 error and visually, for a large class of signals. This is shown by theoretical and experimental results, including synthetic aperture radar (SAR) images.Item Nonlinear Wavelet Processing for Enhancement of Images(1994-05-20) Odegard, Jan E.; Lang, Markus; Guo, Haitao; Gopinath, Ramesh A.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)In this note we apply some recent results on nonlinear wavelet analysis to image processing. In particular we illustrate how the (soft) thresholding algorithm due to Donoho and Johnstone can successfully be used to remove speckle in SAR imagery. Furthermore, we also show that transform coding artifacts, such as blocking in the JPEG algorithm, can be removed to achieve a perceptually improved image by post-processing the decompressed image.Item On the Correlation Structure of Multiplicity M Scaling Functions and Wavelets(1992-05-20) Gopinath, Ramesh A.; Odegard, Jan E.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/); CML (http://cml.rice.edu/)NoneItem On the Correlation Structure of Multiplicity M Scaling Functions and Wavelets(1992-01-15) Gopinath, Ramesh A.; Odegard, Jan E.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/); CML (http://cml.rice.edu/)In this paper we study the auto-correlation and cross-correlation structure of the scaling and wavelet functions associated with compactly supported orthonormal wavelet basis. These correlation structures play an important role in both wavelet-based interpolation and in answering the question of existence of scale-limited signals. Our investigations into their nature, gives us a fairly complete account of all the zeros of the correlation functions and also give efficient algorithms for their computation. An interesting fact that arises from the analysis is that all the correlations possible have infinitely many zeros in their support.Item Optimal wavelets for signal decomposition and the existence of scale limited signals(1992-05-20) Odegard, Jan E.; Gopinath, Ramesh A.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/); CML (http://cml.rice.edu/)Wavelet methods give a flexible alternative to Fourier methods in non-stationary signal analysis. The concept of band-limitedness plays a fundamental role in Fourier analysis. Since wavelet theory replaces frequency with scale, a natural question is whether there exists a useful concept of scale-limitedness. Obvious definitions of scale-limitedness are too restrictive, in that there would be few or no useful scale-limited signals. This paper introduces a viable definition for scale-limited signals, and shows that the class is rich enough to include bandlimited signals, and impulse trains, among others. Moreover, for a wide choice of criteria, we show how to design the optimal wavelet for representing a given signal, and how to design robust wavelets that optimally represent certain classes of signals.Item Optimal wavelets for signal decomposition and the existence of scale limited signals(1992-01-15) Odegard, Jan E.; Gopinath, Ramesh A.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/); CML (http://cml.rice.edu/)Wavelet methods give a flexible alternative to Fourier methods in non-stationary signal analysis. The concept of band-limitedness plays a fundamental role in Fourier analysis. Since wavelet theory replaces frequency with scale, a natural question is whether there exists a useful concept of scale-limitedness. Obvious definitions of scale-limitedness are too restrictive, in that there would be few or no useful scale-limited signals. This paper introduces a viable definition for scale-limited signals, and shows that the class is rich enough to include bandlimited signals, and impulse trains, among others. Moreover, for a wide choice of criteria, we show how to design the optimal wavelet for representing a given signal, and how to design robust wavelets that optimally represent certain classes of signals.Item Simultaneous Speckle Reduction and Data Compression using Best Wavelet Packet Bases with Applications to SAR based ATD/R(1995-04-20) Wei, Dong; Guo, Haitao; Odegard, Jan E.; Lang, Markus; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)We propose a novel method for simultaneous speckle reduction and data compression based on shrinking, quantizing and coding the wavelet packet coefficients of the logarithmically transformed image. A fast algorithm is used to find the best wavelet packet basis in the rate-distortion sense from the entire library of admissible wavelet packet bases. Soft-thresholding in wavelet domain can significantly suppress the speckles of the synthetic aperture radar (SAR) images while maintaining bright reflections for subsequent detection and recognition. Optimal bit allocation, quantization and entropy coding achieve the goal of compression while maintaining the fidelity of the SAR image.Item Smooth biorthogonal wavelets for applications in image compression(1996-09-20) Odegard, Jan E.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)In this paper we introduce a new family of smooth, symmetric biorthogonal wavelet basis. The new wavelets are a generalization of the Cohen, Daubechies and Feauveau (CDF) biorthogonal wavelet systems. Smoothness is controlled independently in the analysis and synthesis bank and is achieved by optimization of the discrete finite variation (DFV) measure recently introduced for orthogonal wavelet design. The DFV measure dispenses with a measure of differentiability (for smoothness) which requires a large number of vanishing wavelet moments (e.g., Holder and Sobolev exponents) in favor of a smoothness measure that uses the fact that only a finite depth of the filter bank tree is involved in most practical applications. Image compression examples applying the new filters using the embedded wavelet zerotree (EZW) compression algorithm due to Shapiro shows that the new basis functions performs better when compared to the classical CDF 7/9 wavelet basis.Item Time Frequency Analysis Applications in Geophysics(CRC Press, 2002-01-15) Steeghs, Philippe; Baraniuk, Richard G.; Odegard, Jan E.; Antonia Papandreou-Suppappola; Digital Signal Processing (http://dsp.rice.edu/)In this chapter, we overview a number of applications of time-frequency representations in seismic data processing, from the analysis of seismic sequences to efficient attribute extraction to 3-D attributes for volumetric data.