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Enhanced Directional Smoothing Algorithm for EdgePreserving Smoothing of SyntheticAperture Radar Images
 Journal of Measurement Science Review
, 2004
"... Abstract. Synthetic aperture radar (SAR) images are subject to prominent speckle noise, which is generally considered a purely multiplicative noise process. In theory, this multiplicative noise is that the ratio of the standard deviation to the signal value, the “coefficient of variation, ” is theor ..."
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Cited by 14 (11 self)
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Abstract. Synthetic aperture radar (SAR) images are subject to prominent speckle noise, which is generally considered a purely multiplicative noise process. In theory, this multiplicative noise is that the ratio of the standard deviation to the signal value, the “coefficient of variation, ” is theoretically constant at every point in a SAR image. Most of the filters for speckle reduction are based on this property. Such property is irrelevant for the new filter structure, which is based on directional smoothing (DS) theory, the enhanced directional smoothing (EDS) that removes speckle noise from SAR images without blurring edges. We demonstrate the effectiveness of this new filtering method by comparing it to established speckle noise removal techniques on SAR images.
Spectral Factorization of Laurent Polynomials
 Advances in Computational Mathematics
, 1997
"... . We analyse the performance of five numerical methods for factoring a Laurent polynomial, which is positive on the unit circle, as the modulus squared of a real algebraic polynomial. It is found that there is a wide disparity between the methods, and all but one of the methods are significantly inf ..."
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Cited by 14 (1 self)
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. We analyse the performance of five numerical methods for factoring a Laurent polynomial, which is positive on the unit circle, as the modulus squared of a real algebraic polynomial. It is found that there is a wide disparity between the methods, and all but one of the methods are significantly influenced by the variation in magnitude of the coefficients of the Laurent polynomial, by the closeness of the zeros of this polynomial to the unit circle, and by the spacing of these zeros. Keywords: spectral factorization, Toeplitz matrices, EulerFrobenius polynomials, Daubechies wavelets. AMS subject classification: 12D05, 15A23. 1. Introduction Our recent interest in the asymptotic behaviour of the GramSchmidt iteration for orthonormalization of a large number of integer translates of a fixed function [11, 12] and also in techniques used for wavelet construction, cf. [7] and [20], has led us to experiment numerically with several existing algorithms to factor a Laurent polynomial, ass...
The Systematized Collection of Daubechies Wavelets
 Tech. Rep. CT199806, Computational Toolsmiths
, 1998
"... A single unifying algorithm has been developed to systematize the collection of compact Daubechies wavelets. This collection comprises all classes of real and complex orthogonal and biorthogonal wavelets with the maximal number K of vanishing moments for their finite length. Named and indexed famili ..."
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Cited by 6 (4 self)
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A single unifying algorithm has been developed to systematize the collection of compact Daubechies wavelets. This collection comprises all classes of real and complex orthogonal and biorthogonal wavelets with the maximal number K of vanishing moments for their finite length. Named and indexed families of wavelet filters were generated by spectral factorization of a product filter in which the optimal subset of roots was selected by a defining criterion within a combinatorial search of subsets meeting required constraints. Several new families have been defined some of which were demonstrated to be equivalent to families with roots selected solely by geometric criteria that do not require an optimizing search. Extensive experimental results are tabulated for 1 # K # 24 for each of the families and most of the filter characteristics defined in both time and frequency domains. For those families requiring optimization, a conjecture for K>24 is provided for a search pattern t...
Computational Algorithms for Daubechies LeastAsymmetric, Symmetric, and MostSymmetric Wavelets
, 1997
"... Computational algorithms have been developed for generating minlength maxflat FIR filter coe#cients for orthogonal and biorthogonal wavelets with varying degrees of asymmetry or symmetry. These algorithms are based on spectral factorization of the Daubechies polynomial with a combinatorial search ..."
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Cited by 5 (5 self)
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Computational algorithms have been developed for generating minlength maxflat FIR filter coe#cients for orthogonal and biorthogonal wavelets with varying degrees of asymmetry or symmetry. These algorithms are based on spectral factorization of the Daubechies polynomial with a combinatorial search of root sets selected by a desired optimization criterion. Daubechies filter families were systematized to include Real Orthogonal Least Asymmetric (DROLA), Real Biorthogonal symmetric balanced Most Regular (DRBMR), Complex Orthogonal Least Asymmetric (DCOLA), and Complex Orthogonal Most Symmetric (DCOMS). Total phase nonlinearity was the criterion minimized to select the roots for the DROLA, DCOLA, and DCOMS filters. Timedomain regularity was used to select the roots for the DRBMR filters (which have linear phase only). New filters with distinguishing features are demonstrated with examples. 1 Introduction Compact maximally flat wavelets with varying degrees of asymmetry or symmetry can b...
Wavelet Image Compression Rate Distortion Optimizations and Complexity Reductions
 Proceedings of the ACM Workshop on Java for High Performance Network Computing
, 2000
"... Compression of digital images has been a topic of research for many years and a number of image compression standards has been created for different applications. The role of compression is to reduce bandwidth requirements for transmission and memory requirements for storage of all forms of data. ..."
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Cited by 4 (0 self)
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Compression of digital images has been a topic of research for many years and a number of image compression standards has been created for different applications. The role of compression is to reduce bandwidth requirements for transmission and memory requirements for storage of all forms of data. While todaymorethanever before new technologies provide high speed digital communications and large memories, image compression is still of major importance, because along with the advances in technologies there is increasing demand for image communications, as well as demand for higher quality image printing and display. In this work we focus on some key new technologies for image compression, namely wavelet based image coders. Wavelet coders apart from offering superior compression ratios have also very useful features such as resolution scalability,i.e. they allow decoding a given image at a number of different resolutions depending on the application. We start by presenting in a simple manner a collection of tools and techniques
Explicit Formulas for Orthogonal IIR Wavelets
, 1997
"... Explicit solutions are given for the rational function P (z) for two classes of IIR orthogonal 2band wavelet bases, for which the scaling filter is maximally flat. P (z) denotes the rational transfer function H(z)H(1=z) where H(z) is the (lowpass) scaling filter. The first is the class of solution ..."
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Cited by 3 (3 self)
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Explicit solutions are given for the rational function P (z) for two classes of IIR orthogonal 2band wavelet bases, for which the scaling filter is maximally flat. P (z) denotes the rational transfer function H(z)H(1=z) where H(z) is the (lowpass) scaling filter. The first is the class of solutions that are intermediate, between the Daubechies and the Butterworth wavelets. It is found that the Daubechies, the Butterworth, and the intermediate solutions are unified by a single formula. The second is the class of scaling filters realizable as a parallel sum of two allpass filters (a particular case of which yields the class of symmetric IIR orthogonal wavelet bases). For this class, an explicit solution is provided by the solution to an older problem in group delay approximation by digital allpole filters. This work has been supported by NSF and Nortel. 1 Introduction The results of this paper supplement the paper by Herley and Vetterli [6] in which orthogonal IIR wavelets are exa...
Systholic Boolean Orthonormalizer Network in Wavelet Domain for Microarray Denoising
 International Journal of Signal Processing, Volume 2, Number
, 2005
"... Abstract—We describe a novel method for removing noise (in wavelet domain) of unknown variance from microarrays. The method is based on the following procedure: We apply 1) Bidimentional Discrete Wavelet Transform (DWT2D) to the Noisy Microarray, 2) scaling and rounding to the coefficients of the h ..."
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Cited by 3 (3 self)
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Abstract—We describe a novel method for removing noise (in wavelet domain) of unknown variance from microarrays. The method is based on the following procedure: We apply 1) Bidimentional Discrete Wavelet Transform (DWT2D) to the Noisy Microarray, 2) scaling and rounding to the coefficients of the highest subbands (to obtain integer and positive coefficients), 3) bitslicing to the new highest subbands (to obtain bitplanes), 4) then we apply the Systholic Boolean Orthonormalizer Network (SBON) to the input bitplane set and we obtain two orthonormal otput bitplane sets (in a Boolean sense), we project a set on the other one, by means of an AND operation, and then, 5) we apply reassembling, and, 6) rescaling. Finally, 7) we apply Inverse DWT2D and reconstruct a microarray from the modified wavelet coefficients. Denoising results compare favorably to the most of methods in use at the moment.
Systolic Boolean Othonormalizer Network in Wavelet Domain for . . .
, 2005
"... We describe a novel method for removing noise (in wavelet domain) of unknown variance from microarrays. The method is based on the following procedure: We apply 1) Bidimentional Discrete Wavelet Transform (DWT2D) to the Noisy Microarray, 2) scaling and rounding to the coefficients of the highest s ..."
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We describe a novel method for removing noise (in wavelet domain) of unknown variance from microarrays. The method is based on the following procedure: We apply 1) Bidimentional Discrete Wavelet Transform (DWT2D) to the Noisy Microarray, 2) scaling and rounding to the coefficients of the highest subbands (to obtain integer and positive coefficients), 3) bitslicing to the new highest subbands (to obtain bitplanes), 4) then we apply the Systholic Boolean Orthonormalizer Network (SBON) to the input bitplane set and we obtain two orthonormal otput bitplane sets (in a Boolean sense), we project a set on the other one, by means of an AND operation, and then, 5) we apply reassembling, and, 6) rescaling. Finally, 7) we apply Inverse DWT2D and reconstruct a microarray from the modified wavelet coefficients. Denoising results compare favorably to the most of methods in use at the moment.
Union is Strength in Lossy Image Compression
 WORLD ACADEMY OF SCIENCE, ENGINEERING AND TECHNOLOGY 59
, 2009
"... In this work, we present a comparison between different techniques of image compression. First, the image is divided in blocks which are organized according to a certain scan. Later, several compression techniques are applied, combined or alone. Such techniques are: wavelets (Haar's basis), Karhunen ..."
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In this work, we present a comparison between different techniques of image compression. First, the image is divided in blocks which are organized according to a certain scan. Later, several compression techniques are applied, combined or alone. Such techniques are: wavelets (Haar's basis), KarhunenLoève Transform, etc. Simulations show that the combined versions are the best, with minor Mean Squared Error (MSE), and higher Peak Signal to Noise Ratio (PSNR) and better image quality, even in the presence of noise.