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Combination of different observation types through a multi-resolution representation of the regional gravity field using the pyramid algorithm and parameter estimation

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JOURNAL OF GEODESY 2022年第10期96卷 1-20页

作者： Liu, Qing Schmidt, Michael Sanchez, Laura Tech Univ Munchen DGFI TUM Deutsch Geodat Forschungsinst Arcisstr 21 D-80333 Munich Germany

The optimal combination of different types of gravity observations is the key to obtaining a high-resolution and high-precision regional gravity model. Current studies based on spherical radial basis functions (SRBFs) majorly consider a single-level approach for data combination. Despite the promising results reported in numerous publications, it has been suspected that the single-level model might be biased towards high-resolution measurements. Instead, a multi-resolution representation (MRR) can be applied to further take into consideration the varying spectral sensitivities of different observation techniques. In this study, we develop a new MRR scheme based on the pyramid algorithm and sequential parameter estimation. We propose strategies to solve the challenges in the practical application of the pyramid algorithm, and this study represents its first successful realization in regional gravity field modeling. The modeling results based on both simulated and real gravity data show that either the single-level approach or the MRR without pyramid algorithm is able to capture gravity information from lower resolution measurements as sufficient as our newly developed MRR algorithm. In the simulated case, the RMS error w.r.t. the validation data obtained by the MRR based on the pyramid algorithm decreases by 50% and 35%, in comparison to that of the single-level model and the MRR without pyramid algorithm, respectively. In the real case, the improvement achieved by the MRR based on the pyramid algorithm is 35% and 23% in the onshore area, and it reaches 63% and 57% in the offshore area, compared to the single-level approach and the MRR without pyramid algorithm, respectively.

关键词： Heterogeneous data combination Multi-resolution representation pyramid algorithm Regional gravity filed modeling Spherical radial basis functions

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How to Get the Original Discrete Approximation for the pyramid algorithm of Multiresolution Decomposition

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Communications in Mathematical Research 1999年第2期 33-46页

作者： Liang Xuezhang Liu Mingcai and Chen Shaotian (Department of Mathematics, Jilin University, Changchun, 130023)

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒ，ｗｅｕｓｅｔｈｅｎｏｔａｔｉｏｎｓＺ，Ｒ，Ｌ２（Ｒ）ａｎｄｌ２ｆｏｒｔｈｅｓｅｔｏｆｉｎｔｅｇｅｒｓ，ｒｅ－ａｌｓ，ｓｑｕａｒｅｉｎｔｅｇｒａｂｌｅｆｕｎｃｔ... 详细信息

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒ，ｗｅｕｓｅｔｈｅｎｏｔａｔｉｏｎｓＺ，Ｒ，Ｌ２（Ｒ）ａｎｄｌ２ｆｏｒｔｈｅｓｅｔｏｆｉｎｔｅｇｅｒｓ，ｒｅ－ａｌｓ，ｓｑｕａｒｅｉｎｔｅｇｒａｂｌｅｆｕｎｃｔｉｏｎｓａｎｄｓｑｕａｒｅｓｕｍｍａｂ...

关键词： pyramid algorithm Multiresolution Decomposition Orthogonal Spline Wavelet

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A Novel Technique for Non-overlapping Image Mosaicing based on pyramid Method

A Novel Technique for Non-overlapping Image Mosaicing based ...

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10th Annual Conference of the IEEE-India-Council (INDICON)

作者： Pandey, Achala Pati, Umesh C. Natl Inst Technol Dept Elect & Commun Engn Rourkela 769008 India

ISBN: (纸本)9781479922741;9781479922758

Image mosaicing has been used in various arenas of image engineering. The main purpose of this research work is to develop a novel blending algorithm for mosaicing of two non-overlapping images with minimum distortion and no visible seam. In the proposed method, images are mosaiced using the pyramid technique and Savitzky-Golay filter is used for smoothing the seam between the images in the generated mosaic. Savitzky-Golay filter, is based on the least square fitting of polynomial functions of image intensities. It effectively reduces the noise and preserves the image information content resulting in a visually pleasing mosaiced image. The results and comparative analysis show the effectiveness of the proposed method.

关键词： Image blending mosaicing pyramid algorithm Savitzky-Golay filter

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pyramid filters based on bilinear interpolation

Pyramid filters based on bilinear interpolation

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2nd International Conference on Computer Graphics Theory and Applications/2nd International Conference on Computer Vision Theory and Applications

作者： Kraus, Martin Strengert, Magnus Tech Univ Munich Comp Graph & Visualizat Grp D-8000 Munich Germany Univ Stuttgart Visualizat & Interact Syst Grp Stuttgart Germany

ISBN: (纸本)9789728865719

The implementation of several pyramid methods on programmable graphics processing units (GPUs) in recent years led to additional research interest in pyramid algorithms for real-time computer graphics. Of particular interest are efficient analysis and synthesis filters based on hardware-supported bilinear texture interpolation because they can be used as building blocks for many GPU-based pyramid methods. In this work, several new and extremely efficient GPU-implementations of pyramid filters are presented for the first time. The discussion employs a new notation, which was developed for the consistent and precise specification of these filters and also allowed us to systematically explore appropriate filter designs. The presented filters cover analysis and synthesis filters, (quasi-)interpolation and approximation, as well as discontinuous, continuous, and smooth filters. Thus, a toolbox of filters and their efficient implementations for a great variety of GPU-based pyramid methods is presented.

关键词： signal processing image processing multi resolution pyramid algorithm graphics hardware

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Multitemporal and multiresolution fusion of wide field of view and high spatial resolution images through morphological pyramid

Multitemporal and multiresolution fusion of wide field of vi...

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Conference on Image and Signal Processing for Remote Sensing X

作者： Laporterie-Dejean, F Flouzat, G Lopez-Ornelas, E CNES F-31401 Toulouse 9 France

ISBN: (纸本)0819455202

To study vegetation from space, both high spatial resolution and high temporal frequency images are needed. However, a satellite sensor, for technological reasons, cannot provides such images. But merge several kinds of images coming from several sensors enables to overgo this problem. In this article, we propose a fusion method based on pyramid algorithms and on morphological filtering to create synthesis images having both high spatial resolution and high temporal frequency. This process is validated by high resolution reference images. The study uses the ADAM (C) database provided with courtesy of Centre National d'Etude Spatiale (CNES - French Space Agency).

关键词： fusion multiresolution spatial resolution pyramid algorithm mathematical morphology SPOT4

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Wavelet-Galerkin method for the Kolmogorov equation

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MATHEMATICAL AND COMPUTER MODELLING 2004年第9-10期40卷 1093-1121页

作者： Liang, ZG Yau, SST Univ Illinois Dept MSCS Chicago IL 60607 USA

It is well known that the Kolmogorov equation plays an important role in applied science. For example, the nonlinear filtering problem, which plays a key role in modern technologies, was solved by Yau and Yau [1] by reducing it to the off-line computation of the Kolmogorov equation. In this paper, we develop a theorical foundation of using the wavelet-Galerkin method to solve linear parabolic P.D.E. We apply our theory to the Kolmogorov equation. We give a rigorous proof that the solution of the Kolmogorov equation can be approximated very well in any finite domain by our wavelet-Galerkin method. An example is provided by using Daubechies D-4 scaling functions. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： nonlinear filtering Kolmogorov equation Wavelet-Galerkin method Daubechies scaling function pyramid algorithm

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Chemical Identification in the Specular and Off-Specular Rough-Surface Scattered Terahertz Spectra Using Wavelet Shrinkage

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IEEE ACCESS 2021年 9卷 29746-29754页

作者： Khani, Mahmoud E. Arbab, M. Hassan SUNY Stony Brook Dept Biomed Engn Stony Brook NY 11794 USA

We present the development and implementation of a novel wavelet shrinkage technique for the retrieval of obscured characteristic resonant signatures in the scattered terahertz (THz) reflectivity of molecular crystals. In this implementation, the wavelet basis functions associated with the absorption features were identified using the second-order total variation of the wavelet coefficients. Additionally, wavelet coefficients at certain scales were modified using the phase function corrections and wavelet hard thresholding. Reconstruction of the original spectra using these modified wavelet coefficients yielded the exact resonant frequencies of the chemicals, which were otherwise unrecognizable in the spectral artifacts of the rough surface scattering. We examined the robustness of this method over controlled levels of rough surface scattering, validated using the Kirchhoff approximation, in spectroscopic targets made from alpha-lactose monohydrate and 4-aminobenzoic acid (PABA), which have close spectral lines. We successfully retrieved the spectral absorption fingerprints in both specular and off-specular reflection geometries. This technique can be utilized for stand-off material characterization using the THz reflection spectroscopy in uncontrolled environments and potentially can be adopted for other broadband spectroscopic modalities.

关键词： Chemical identification maximal overlap discrete wavelet transform (MODWT) phase function effects pyramid algorithm reflection-mode spectroscopy rough surface scattering terahertz time-domain spectroscopy (THz-TDS) wavelet shrinkage off-specular scattered spectra

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Efficient image reconstruction for point-based and line-based rendering

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COMPUTERS & GRAPHICS-UK 2008年第2期32卷 189-203页

作者： Marroquim, Ricardo Kraus, Martin Cavalcanti, Paulo Roma Tech Univ Munich Comp Graph & Visualizat Grp D-85748 Garching Germany Univ Fed Rio de Janeiro COPPE Sistemas BR-21945970 Rio De Janeiro RJ Brazil

We address the problem of an efficient image-space reconstruction of adaptively sampled scenes in the context of point-based and line-based graphics. The image-space reconstruction offers an advantageous time complexity compared to surface splatting techniques and, in fact, our improved GPU implementation performs significantly better than splatting implementations for large point-based models. We discuss the integration of elliptical Gaussian weights for enhanced image quality and generalize the image-space reconstruction to line segments. Furthermore, we present solutions for the efficient combination of points, lines, and polygons in a single image. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： point-based graphics point-based rendering line-based rendering pyramid algorithm

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Efficient wavelet prefilters with optimal time-shifts

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2005年第7期53卷 2451-2461页

作者： Ericsson, S Grip, N Lulea Univ Technol Dept Math SE-97187 Lulea Sweden

A wavelet prefilter maps sample values of an analyzed signal to the scaling function coefficient input of standard discrete wavelet transform (DWT) algorithms. The prefilter is the inverse of a certain posyfilter convolution matrix consisting of integer sample values of a noninteger-shifted wavelet scaling function. For the prefilter and the DWT algorithms to have similar computational complexity, it is often necessary to use a "short enough" approximation of the prefilter. In addition to well-known quadrature formula and identity matrix prefilter approximations, we propose a Neumann series approximation, which is a band matrix truncation of the optimal prefilter, and derive simple formulas for the operator norm approximation error. This error shows a dramatic dependence on how the postfilter noninteger shift is chosen. We explain the meaning of this shift in practical applications, describe how to choose it, and plot optimally shifted prefilter approximation errors for 95 different Daubechies, Symlet, and B-spline wavelets. Whereas the truncated inverse is overall superior, the Neumann filters are by far the easiest ones to compute, and for some short support wavelets, they also give the smallest approximation error. For example, for Daubechies 1-5 wavelets, the simplest Neumann prefilter provide an approximation error reduction corresponding to 100-10 000 times oversampling in a nonprefiltered system.

关键词： biorthogonal wavelet B-spline wavelet Daubechies wavelet FWT algorithm initialization Lagrange interpolant Neumann series prefilter pyramid algorithm quadrature formula quadrature mirror filter sampling Sard optimal Symlet

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Measures in wavelet decompositions

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ADVANCES IN APPLIED MATHEMATICS 2005年第3期34卷 561-590页

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

In applications, choices of orthonormal bases in Hilbert space H may come about from the simultaneous diagonalization of some specific abelian algebra of operators. This is the approach of quantum theory as suggested by John von Neumann;but as it turns out, much more recent constructions of bases in wavelet theory, and in dynamical systems, also fit into this scheme. However, in these modem applications, the basis typically comes first, and the abelian algebra might not even be made explicit. It was noticed recently that there is a certain finite set of non-commuting operators F-i, first introduced by engineers in signal processing, which helps to clarify this connection, and at the same time throws light on decomposition possibilities for wavelet packets used in pyramid algorithms. There are three interrelated components to this: an orthonormal basis, an abelian algebra, and a projection-valued measure. While the operators F-i were originally intended for quadrature mirror filters of signals, recent papers have shown that they are ubiquitous in a variety of modem wavelet constructions, and in particular in the selection of wavelet packets from libraries of bases. These are constructions which make a selection of a basis with the best frequency concentration in signal or data-compression problems. While the algebra A generated by the F-i-system is non-abelian, and goes under the name "Cuntz algebra" in C*-algebra theory, each of its representations contains a canonical maximal abelian subalgebra, i.e., the subalgebra is some C(X) for a Gelfand space X. A given representation of A, restricted to C(X), naturally induces a projection-valued measure on X, and each vector in H induces a scalar-valued measure on X. We develop this construction in the general context with a view to wavelet applications, and we show that the measures that had been studied earlier for a very restrictive class of F-i-systems (i.e., the Lemarie-Meyer quadrature mirror filters) in the theory of

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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