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Extending the scope of wavelet regression methods by coefficient-dependent thresholding

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2000年第449期95卷 172-183页

作者： Kovac, A Silverman, BW Univ Essen Gesamthsch Fachbereich 6 Essen Germany Univ Bristol Sch Math Bristol BS8 1TW Avon England

Various aspects of the wavelet approach to nonparametric regression are considered, with the overall aim of extending the scope of wavelet techniques to irregularly spaced data, to regularly spaced datasets of arbitrary size, to heteroscedastic and correlated data, and to data that contain outliers. The core of the methodology is an algorithm for finding all of the variances and within-level covariances in the wavelet table of a sequence with given covariance structure. If the original covariance matrix is band-limited, then the algorithm is linear in the length of the sequence. The variance calculation algorithm allows data on any set of independent variable values to be treated, by first interpolating to a fine regular grid of suitable length, and than constructing a wavelet expansion of the gridded data. Various thresholding methods are discussed and investigated. Exact risk formulas for the mean square error of the methodology for given design are derived. Good performance is obtained by noise-proportional thresholding, with thresholds somewhat smaller than the classical universal threshold. Outliers in the data can be removed or downweighted, and aspects of such robust techniques are developed and demonstrated in an example. Another natural application is to correlated data, where the covariance of the wavelet coefficients is not due to an initial grid transform but rather is an intrinsic feature. The use of the method in these circumstances is demonstrated by an application to data synthesized in the study of ion channel gating. Our basic approach has many other potential applications, some of which are discussed briefly.

关键词： adaptive estimation correlated data discrete wavelet transform exact risk calculation irregular data pyramid algorithm nonparametric repression robust regression

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Iterated function systems, representations, and Hilbert space

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INTERNATIONAL JOURNAL OF MATHEMATICS 2004年第8期15卷 813-832页

作者： Jorgensen, PET Univ Iowa Dept Math Iowa City IA 52242 USA

In this paper, we axe concerned with spectral-theoretic features of general iterated function systems (IFS). Such systems arise from the study of iteration limits of a finite family of maps tau(i) = 1,...,N, in some Hausdorff space Y. There is a standard construction which generally allows us to reduce to the case of a compact invariant subset X subset of Y. Typically, some kind of contractivity property for the maps tau(i) is assumed, but our present considerations relax this restriction. This means that there is then not a natural equilibrium measure p available which allows us to pass the point-maps tau(i) to operators on the Hilbert space L-2(mu). Instead, we show that it is possible to realize the maps tau(i) quite generally in Hilbert spaces H(X) of square-densities on X. The elements in H(X) axe equivalence classes of pairs (phi, mu), where phi is a Borel function on X, mu is a positive Borel measure on X, and integral(X) \phi\(2) dmu < infinity. We say that (phi, mu) similar to (phi, nu) if there is a positive Borel measure lambda such that mu much less than lambda, nu much less than lambda, and phirootdmu/dlambda = psirootdnu/dlambda, lambda a.e. on X. We prove that, under general conditions on the system (X, tau(i)), there are isometries S-i: (phi, mu) --> (phi (.) sigma, mu (.) tau(i)(-1)) in H(X) satisfying Sigma(i=1)(N) SiSi* = I = the identity operator in H(X). For the construction we assume that some mapping sigma: X --> X satisfies the conditions sigma (.) tau(i) = id(X), i = 1,...N. We further prove that this representation in the Hilbert space H(X) has several universal properties.

关键词： Hilbert space Cuntz algebra completely positive map creation operators wavelet packets pyramid algorithm product measures orthogonality relations equivalence of measures iterated function systems (IFS) scaling function multiresolution subdivision scheme singular measures absolutely continuous measures

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Optimal wavelet expansion via sampled-data control theory

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IEEE SIGNAL PROCESSING LETTERS 2004年第2期11卷 79-82页

作者： Kashima, K Yamamoto, Y Nagahara, M Kyoto Univ Grad Sch Informat Dept Appl Anal & Complex Dynam Syst Kyoto 6068501 Japan

Discrete wavelet transform is usually executed by the so-called pyramid algorithm. It, however, requires a proper initialization, i.e., expansion coefficients with respect to the basis of one of the desired approximation subspaces. An interesting question here is how we can obtain such coefficients when only sampled values of signals are available. This letter provides a design method for a digital filter that (sub-)optimally gives such coefficients assuming certain a Priori knowledge on the frequency characteristic of target functions. We then extend the result to the case of nonorthogonal wavelets. Examples show the effectiveness of the proposed method.

关键词： discrete wavelet transform (DWT) pyramid algorithm sampled-data control

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Segmentwise Computation of 2D Forward Discrete Wavelet Transform

Segmentwise Computation of 2D Forward Discrete Wavelet Trans...

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33rd International Conference on Telecommunication and Signal Processing

作者： Prusa, Zdenek Rajmic, Pavel Maly, Jan Brno Univ Technol Fac Elect Engn & Commun Dept Telecommun Brno 61200 Czech Republic

ISBN: (纸本)9789638898104

In this paper we present a new algorithm for segmentwise computation of 2D forward discrete-time wavelet transform. The idea of the algorithm is that the 2D discrete signal (image) is divided into rectangular segments and the computation of the wavelet transform coefficients can be performed on each of the segments independently. The algorithm introduces substantial advantage in that the transform can be performed on segments in parallel with the cost of a slight redundancy (several coefficients are computed more than once). The size of the segments is arbitrary in both the vertical and the horizontal directions, so there is place for performance tuning. Another usage of the algorithm is in the processing of large-scale images. Such images are not expected to fit into operating memory of the device, so the natural approach is to load one segment at a time and process it. We also present our implementation of the algorithm in parallel 2D forward DTWT using C++ and Intel Threading Building Blocks library.

关键词： digital image processing pyramid algorithm parallelization discrete-time wavelet transform segmentation Intel Threading Building Blocks

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Quasi-convolution pyramidal blurring

Quasi-convolution pyramidal blurring

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3rd International Conference on Computer Graphics Theory and Applications

作者： Kraus, Martin Tech Univ Munich Comp Graph & Visualizat Grp D-8046 Garching Germany

ISBN: (纸本)9789898111203

Efficient image blurring techniques based on the pyramid algorithm can be implemented on modem graphics hardware;thus, image blurring with arbitrary blur width is possible in real time even for large images. However, pyramidal blurring methods do not achieve the image quality provided by convolution filters;in particular, the shape of the corresponding filter kernel varies locally, which potentially results in objectionable rendering artifacts. In this work, a new analysis filter is designed that significantly reduces this variation for a particular pyramidal blurring technique. Moreover, an efficient implementation for programmable graphics hardware is presented. The proposed method is named "quasi-convolution pyramidal blurring" since the resulting effect is very close to image blurring based on a convolution filter for many applications.

关键词： rendering image processing blurring pyramid algorithm GPU real-time

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Support Vector Machine-based Image Segmentation Approach for Automatic Agriculture Vehicle

Support Vector Machine-based Image Segmentation Approach for...

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4th International Conference on Image Analysis and Signal Processing (IASP)

作者： Han, Yonghua Wang, Yaming Zhao, Yun Zhejiang Univ Sch Biosyst Engn & Food Sci Hangzhou 310003 Zhejiang Peoples R China Zhejiang Sci Tech Univ Coll Elect & Informat Hangzhou Peoples R China Zhejiang Sci Tech Univ Mech Coll Hangzhou Peoples R China

ISBN: (纸本)9781467325455;9781467325479

Support Vector Machine, a statistic procedure, is robust and has good performance when applied to farmland image segmentation. It can effectively identify the crop rows, even though they have some intersection at some points because of weeds of the leaves growth of the crops. However, the Support Vector Machine has relatively high time complexity and cannot meet the requirements of real-time processing. Based on the pyramid algorithm, we can obtain a low-resolution representation of the images being processed. Then training and testing are applied in the low-resolution images only. Through this method, the time consumption is significantly lower than the original Support Vector Machine Procedure. The objects in farmland images are large and there are only two major types of structures in them, so the examination accuracy of the proposed method is changed little. At the same time, based on spatial structure and color distribution of the farmland image, the kernel and main parameters of Support Vector Machine are selected.

关键词： guidance Support Vector Machine image segmentation pyramid algorithm

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Improvement Mean Shift-based Image Segmentation Approach for Automatic Agriculture Vehicle

Improvement Mean Shift-based Image Segmentation Approach for...

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Conference on International Conference on Image Processing and Pattern Recognition in Industrial Engineering

作者： Han, Yong-hua Wang, Ya-ming Zhao, Yun Zhejiang Univ Sch Biosyst Engn & Food Sci Hangzhou 310029 Zhejiang Peoples R China Zhejiang Sci Tech Univ Coll Elect & Informat Hangzhou 310018 Peoples R China

ISBN: (纸本)9780819483294

Mean Shift algorithm, a statistic iterative procedure, is robust when applied to farmland image segmentation. It can effectively overcome the influence of shadow, weeds or illumination changes, etc. However, the Mean Shift procedure has relatively high time complexity and can not meet the requirements of real-time processing. Based on pyramid algorithm, we can obtain a low resolution representation of the images being processed. Then, run Mean shift algorithm on a set of seed points that selected in the low resolution image. Through this method, the time consumption is significantly lower than the original Mean Shift Procedure. The objects in farmland images are large and there are only two major types of structure in it, so the examination accuracy of proposed method is changed little. At the same time based on spatial structure and color distribution of farmland image, Mean Shift Kernel radius in the spatial and range domain is selected. In addition, according to different seasons, crops show different colors. In this case, the equations which convert color image into a grayscale image are discussed.

关键词： Mean Shift image segmentation pyramid algorithm seed points auto-navigation

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Uniform approximation of wavelet coefficients

Uniform approximation of wavelet coefficients

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4th Conference on Wavelet Applications in Signal and Image Processing

作者： Svenson, TD Ward, JA Harrison, KJ UNIV SYDNEY SCH MATH & STATSYDNEYNSW 2006AUSTRALIA

ISBN: (纸本)0819422134

Mallat's pyramid algorithm relates the scaling coefficients of a function at one level to the scaling and wavelet coefficients at lower levels. In practice, the scaling coefficients are estimated at some level m, and the algorithm is used to produce estimates of the scaling and wavelet coefficients at lower levels. Initial errors propagate to lower level estimates. this paper descries conditions under which this process generates estimates which are uniformly reliable at a particular level, and under which the errors at that level tend uniformly to zero as m increases.

关键词： scaling function wavelet scaling coefficient wavelet coefficient pyramid algorithm approximation scheme error propagation

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Spatial and temporal satellite data fusion with morphological pyramids for terrestrial surfaces survey

Spatial and temporal satellite data fusion with morphologica...

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Conference on Image and Signal Processing for Remote Sensing VII

作者： Laporterie, F Flouzat, G Amram, O CESBIO F-31401 Toulouse 4 France

ISBN: (纸本)0819442666

Nowadays, terrestrial dynamics study is more and more often performed with the help of satellite sensors. Usually, vegetation cover surveys are performed with wide field of view sensors, because of their high temporal resolution. However, a high spatial resolution will be appreciable to distinguish each component in a landscape. We propose to create merged images combining both sensors: our fusion method is based on both theories of pyramid algorithms and mathematical morphology. Let call HR (resp. BR) the spatial resolution of the high resolution (resp. coarse) sensor image, for example SPOT 4 HRVIR and VEGETATION. The principle is: 1. To decompose the high resolution image into a low-frequency and several high-frequencies images (HFI). 2. To perform the inverse transform on the HFI images and the coarse resolution sensor data and produce the merged image. Consequently, from a temporal set of VEGETATION data and from a few HRVIR scenes, we are able to create 20m (or less) resolution synthesis data having the temporal repetitivity of the VEGETATION data set.

关键词： multiresolution data fusion temporal fusion pyramid algorithm mathematical morphology

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Image fusion with high-speed DSP

Image fusion with high-speed DSP

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Conference on Electronic Imaging and Multimedia Systems II

作者： Cui, YM Pu, T Ni, GQ Zhong, YL Li, XY Beijing Inst Technol Dept Electroopt Engn Beijing 100081 Peoples R China

ISBN: (纸本)0819430226

Image fusion technique has gradually been paid more and more attention to for its advantage of integration of information from multisensors, and its application has been developed in many fields such as medicine, remote sensing, computer vision, weather forecast, etc. In this paper, some fusion algorithms on pixel level have been programmed and their effects have been analyzed. A new efficient method named after Contrast Modulation-pyramid algorithm ( CMPA) has been developed. The realization of this new algorithm has been designed and researched with Digital Signal Processor ( DSP) and has been programmed with relevant software. The result showed that image fusion would been completed at real-time or quasi-realtime speed.

关键词： image fusion pyramid algorithm DSP

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