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Parallel- and Cyclic-Iterative Variational Bayes for fast Kalman Filtering in Large-Dimensions

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2022年 70卷 5871-5884页

作者： Ait-El-Fquih, Boujemaa Hoteit, Ibrahim King Abdullah Univ Sci & Technol KAUST Div Phys Sci & Engn Thuwal 23955 Saudi Arabia

This paper considers the linear-Gaussian filtering problem in large-dimensions, a framework in which the Kalman filter (KF) can be computationally prohibitive. As a remedy, a hybrid scheme combining KF with variational Bayes (VB), an approach that designs an approximation of the filtering probability density function (pdf) based on a separable form under the Kullback-Leibler divergence minimization criterion, has been proposed. Despite its approximate and cyclic-iterative characters, this VBKF algorithm can provide comparable performances to the KF, at reduced computational requirements. Here, we resort to the memory gradient subspace (MGS) optimization in the space of separable pdfs to derive a new variant of VBKF endowed with a parallel-iterative structure. At a given iteration of the proposed MGS-VBKF, all separate marginals of the approximate filtering pdf are updated in parallel, which could lead to significant computational time savings, especially when the state is split into small enough partitions. We establish the connection between VBKF and MGS-VBKF, showing that the latter can be derived from the former by iterating instead in parallel on its equations and inserting a correction term representing the contribution of the gradient and memory directions. We further extend these algorithms to the case of unsupervised systems with unknown observation noise uncertainties. The performances of the proposed filters are finally studied and compared to those of the KF and a deterministic ensemble Kalman filter through numerical experiments.

关键词： Unsupervised Bayesian filtering Kalman filtering variational Bayes high dimension fast algorithms subspace optimization

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fast Hartley transform implementation on DSP chips

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MICROPROCESSORS AND MICROSYSTEMS 1996年第4期20卷 233-240页

作者： Prabhu, KMM Sundaram, RS Department of Electrical Engineering Indian Institute of Technology Madras 600 036 India

Of late, the fast Hartley transform (FHT) has attracted considerable research interest as an alternative tool to the fast Fourier transform (FFT). In this paper, efficient implementation of the FHT on different DSP processors is considered. Instead of counting the required arithmetic operations, the necessary number of instruction cycles for an implementation of FHT is used as a measure. Also, different scaling schemes, which are available in the literature, have been considered to increase the signal-to-noise ratio (SNR) of the algorithm. Finally, the details of the programs on ADSP2101, TMS320C25 and TMS320C30 have been presented.

关键词： fast algorithms Hartley transform DSP processors

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Efficient fast recursive least-squares adaptive complex filtering using real valued arithmetic

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SIGNAL PROCESSING 2005年第9期85卷 1759-1779页

作者： Glentis, GO Technol Educ Inst Crete Branch Chania Dept Elect Khania 73133 Greece

In this paper, a novel implementation of the fast recursive least squares (FRLS) algorithm for complex adaptive filtering, is presented. Complex signals are treated as pairs of real signals, and operations are re-organized on a real arithmetic basis. A new set of signals and filtering parameters is introduced, which are expressed either as the sum, or as the difference between the real and the imaginary part of the original variables. The algorithmic strength reduction technique is subsequently applied, resulting in significant computational savings. In this way, an efficient, FRLS algorithm is derived, where only two real valued filters are propagated, based on novel three-terms recursions for the time updating of the pertinent parameters. The proposed algorithm is implemented using real valued arithmetic only, whilst reducing the number of the required real valued multiplication operations by 23.5%, at the expense of a marginal 2.9% increase in the number of the real valued additions. The performance of the proposed FRLS algorithm is investigated by computer simulations, in the context of adaptive system identification and adaptive channel equalization. (C) 2005 Elsevier B.V. All rights reserved.

关键词： adaptive filtering fast algorithms complex valued arithmetic

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fast Zernike moments

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JOURNAL OF REAL-TIME IMAGE PROCESSING 2008年第1-2期3卷 89-96页

作者： Al-Rawi, Mohammed Univ Jordan Dept Comp Sci King Abdullah II Sch Informat Technol Amman 11942 Jordan

Zernike moments are important digital image descriptors used in various applications starting from image watermarking to image recognition. Lots of fast algorithms have been proposed to speedup the computation of Zernike moments. This work provides computational complexity analysis of methods for the computation of Zernike moments, as well as a thorough study and simplification to the methods of finding Zernike moments from geometric moments. A new formula that relates Zernike moments to moments of digital filters is introduced that is very efficient and accurate. Comparisons are performed using Zernike moment via geometric moments method, the Q-recursive method, the coefficient method, and the symmetry method. Using a well defined performance metric, this work finds out that Zernike moments from geometric moments of digital filters is nearly 70 times faster than the best method known as the symmetry method.

关键词： Computational complexity Zernike moments Digital filters Symmetry Digital image fast algorithms

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A fast high-order solver for problems of scattering by heterogeneous bodies

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2003年第11期51卷 3142-3154页

作者： Bruno, OP Sei, A CALTECH Dept Appl & Computat Math Pasadena CA 91125 USA

A new high-order integral algorithm for the solution of scattering problems by heterogeneous bodies is presented. Here, a scatterer is described by a (continuously or discontinuously) varying refractive index n(x) within a two-dimensional (2-D) bounded region;solutions of the associated Helmholtz equation under given incident fields are then obtained by high-order inversion of the Lippmann-Schwinger integral equation. The algorithm runs in O(N log(N)) operations where N is the number of discretization points. A wide variety of numerical examples provided include applications to highly singular geometries, high-contrast configurations, as well as acoustically/electrically large problems for which supercomputing resources have been used recently. Our method provides highly accurate solutions for such problems on small desktop computers in CPU times of the order of seconds.

关键词： electromagnetic scattering fast algorithms high-order inhomogeneous scatterer penetrable scatterer

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Parallel implementation of the steepest descent fast multipole method (SDFMM) on a beowulf cluster for subsurface sensing applications

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IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS 2002年第1期12卷 24-26页

作者： Jiang, D Meleis, W El-Shenawee, M Mizan, E Ashouei, A Rappaport, C Northeastern Univ Dept Elect & Comp Engn Boston MA 02115 USA Univ Arkansas Dept Elect Engn Fayetteville AR 72701 USA

We present the parallel, MPI-based implementation of the SDFMM computer code using a thirty two-node Intel Pentium-based Beowulf cluster. The SDFMM is a fast algorithm that is a hybridization of the method of moments (MoMs), the fast multipole method (FMM), and the steepest descent integration path (SDP), which is used to solve large-scale linear systems of equations produced in electromagnetic scattering problems. An overall speedup of 7.2 has been achieved on the 32-processor Beowulf cluster and a significant reduced runtime is achieved on the 4-processor 667 MHz Alpha workstation.

关键词： fast algorithms parallelization SDFMM subsurface sensing

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fast and stable reduction of diagonal plus semi-separable matrices to tridiagonal and bidiagonal form

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BIT 2001年第1期41卷 149-157页

作者： Mastronardi, N Chandrasekaran, S Van Huffel, S Univ Basilicata Dipartimento Matemat I-85100 Potenza Italy Univ Calif Santa Barbara Dept Elect & Comp Engn Santa Barbara CA 93106 USA Katholieke Univ Leuven ESAT SISTA Dept Elect Engn B-3001 Heverlee Belgium

A two-way chasing algorithm to reduce a diagonal plus a symmetric semi-separable matrix to a symmetric tridiagonal one and an algorithm to reduce a diagonal plus an unsymmetric semi-separable matrix to a bidiagonal one are considered. Both algorithms are fast and stable, requiring a computational cost of N-2, where N is the order of the considered matrix.

关键词： semi-separable matrix fast algorithms stable algorithms

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Recursive fast computation of the two-dimensional discrete cosine transform

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IEE PROCEEDINGS-VISION IMAGE AND SIGNAL PROCESSING 1999年第1期146卷 25-33页

作者： Fang, WH Hu, NC Shih, SK Natl Taiwan Univ Sci & Technol Dept Elect Engn Taipei Taiwan

An efficient algorithm is presented for computing the two-dimensional discrete cosine transform (2-D DCT) whose size is a power of a prime. Based on a generalised 2-D to one-dimensional (1-D) index mapping scheme, the proposed algorithm decomposes the 2-D DCT outputs into three parts. The first part forms a 2-D DCT of a smaller size. The remaining outputs are further decomposed into two parts, depending on the summation of their indices. The latter two parts can be reformulated as a set of circular correlation (CC) or skew-circular correlation (SCC) matrix-vector products by utilising the recently addressed maximum coset decomposition. Such a decomposition procedure can be repetitively carried out for the 2-D DCT of the first part, resulting in a sequence of CC and SCC matrix-vector products of various sizes. Employing fast algorithms for the computation of these CC/SCC operations can substantially reduce the numbers of multiplications compared with those of the conventional row-column decomposition approach. In the special case where the data size is a power of two, the proposed algorithm can be further simplified, calling for computations comparable with those of previous works.

关键词： signal processing 2D DCT circular correlation recursive estimation fast algorithms 2D discrete cosine transform multiplications Signal processing and detection correlation methods Linear algebra (numerical analysis) skew-circular correlation recursive fast computation row-column decomposition 2D to 1D index mapping data size discrete cosine transforms Integral transforms in numerical analysis matrix-vector products 2D DCT output decomposition maximum coset decomposition efficient algorithm matrix multiplication Signal processing theory

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A fast digital radon transform - An efficient means for evaluating the Hough transform (vol 28, pg 1985, 1995)

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PATTERN RECOGNITION 1996年第4期29卷 709-+页

作者： Gotz, WA Druckmuller, HJ UNIV INNSBRUCK INST COMP SCI A-6020 INNSBRUCK AUSTRIA

A fast digital Radon transform based on recursively defined digital straight lines is described, which has the sequential complexity of O(N-2 log N) additions for an N x N image. This transform can be used to evaluate the Hough transform to detect straight lines in a digital image. Whilst a parallel implementation of the Hough transform algorithm is difficult because of global memory access requirements, the fast digital Radon transform is vectorizable and therefore well suited for parallel computation. The structure of the fast algorithm is shown to be quite similar to the FFT algorithm for decimation in frequency. It is demonstrated that even for sequential computation the fast Radon transform is an attractive alternative to the classical Hough transform algorithm.

关键词： image processing line detection Hough transform radon transform fast algorithms

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A fast algorithm for APES and capon spectral estimation

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2008年第9期56卷 4207-4220页

作者： Glentis, George-Othon Univ Peloponnese Dept Sci & Technol Telecommun Tripolis 22100 Greece

In this paper, we derive a novel implementation of some very computationally demanding matched filter-bank-based spectral estimators, namely file amplitude and phase estimator (APES), the amplitude spectrum Capon (ASC) estimator, and the power spectrum Capon (PSC) estimator. Filter-bank-based spectral estimation methods that adopt data-dependent filter banks can provide spectra characterized by a significantly improved resolution compared to classical approaches. However, the computational complexity of the currently available implementation algorithms, is extremely high. A novel technique is introduced that provides efficient algorithms for the computation of the APES, ASC, and PSC spectra. The proposed method is based on suitable displacement representations of all pertinent data matrices, that are subsequently utilized for the computation of the associated complex valued polynomials. The computational complexity of the proposed algorithms is lower than all relevant existing methods.

关键词： amplitude and phase estimator (APES) Capon fast algorithms matched filter-bank spectral estimators

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