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SIGGRAPH Asia (SA) Doctoral Consortium

作者： Ghosh, Sanjay Indian Inst Sci Dept Elect Engn Bangalore Karnataka India

ISBN: (纸本)9781450370219

Image filtering is a fundamental preprocessing task in computer vision and image processing. While the dominant applications of kernel filtering are enhancement and denoising, it can also be used as a powerful regularizer for image reconstruction. In general, the brute-force implementations of kernel filtering is prohibitively expensive. They are often too slow for real-time applications. In the first half of the thesis, we propose fast algorithms for bilateral filtering (BLF) and nonlocal means (NLM). In particular, we demonstrate that by using the Fourier approximation of the underlying kernel, we can obtain state-of-the-art fast algorithms for BLF of grayscale images. We next extend the idea for fast filtering of color images, which involves the approximation of a three-dimensional kernel. We next propose a fast separable formulation for NLM of grayscale images. In the second half of the dissertation, we turn to some applications of kernel filtering. We introduce a scale-adaptive variant of BLF that is used for suppressing fine textures in images. We develop a fast implementation of a symmetrized variant of NLM that is used for regularization (i.e., as a prior) within the plug-and-play framework for image restoration. The core idea can be extended to other forms of kernel filtering.

关键词： Image filtering smoothing denoising image restoration fast algorithms bilateral filtering nonlocal means

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Automatic generation of fast algorithms for matrix-vector multiplication

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2018年第3期95卷 626-644页

作者： Andreatto, B. Cariow, A. West Pomeranian Univ Technol Fac Comp Sci & Informat Technol Szczecin Poland

This paper describes the methods for finding fast algorithms for computing matrix-vector products including the procedures based on the block-structured matrices. The proposed methods involve an analysis of the structural properties of matrices. The presented approaches are based on the well-known optimization techniques: the simulated annealing and the hill-climbing algorithm along with its several extensions. The main idea of the proposed methods consists in finding a decomposition of the original matrix into a sparse matrix and a matrix corresponding to an appropriate block-structured pattern. The main criterion for optimizing is a reduction of the computational cost. The methods presented in this paper can be successfully implemented in many digital signal processing tasks.

关键词： fast algorithms matrix-vector multiplication computational complexity reduction block matrices simulated annealing hill-climbing

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fast algorithms and Architectures for 8-Point DST-II/DST-VII Approximations

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JOURNAL OF CIRCUITS SYSTEMS AND COMPUTERS 2017年第3期26卷 1750045-1750045页

作者： Cintra, Renato J. Bayer, Fabio M. Madanayake, Arjuna Potluri, Uma S. Edirisuriya, Amila Univ Fed Pernambuco Signal Proc Grp Dept Stat Recife PE Brazil Inst Natl Sci Appl LIRIS Lyon France Univ Rennes 1 INRIA IRISA Equipe Cairn Rennes France Univ Fed Santa Maria Dept Stat Santa Maria RS Brazil Univ Fed Santa Maria LACESM Santa Maria RS Brazil Univ Akron ECE Akron OH 44325 USA

Multiplier-free fast algorithms are derived and analyzed for realizing the 8-point discrete sine transform of type II and type VII (DST-II and DST-VII) transforms with applications in image and video compression. A new fast algorithm is identified using numerical search methods for approximating DST-VII without employing multipliers. In addition, recently proposed fast algorithms for approximating the 8-point DCT-II are now extended to approximate DST-II. All proposed approximations for DST-II and DST-VII are compared with ideal transforms, and circuit complexity is measured using FPGA-based rapid prototypes on a 90nm Xilinx Virtex-4 device. The proposed architectures find applications in emerging video processing standards such as H.265/HEVC.

关键词： Approximate discrete transforms DCT DST fast algorithms FPGA low-complexity transform

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fast algorithms and Efficient GPU Implementations for the Radon Transform and the Back-Projection Operator Represented as Convolution Operators

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SIAM JOURNAL ON IMAGING SCIENCES 2016年第2期9卷 637-664页

作者： Andersson, Fredrik Carlsson, Marcus Nikitin, Viktor V. Lund Univ Ctr Math Sci S-22100 Lund Sweden

The Radon transform and its adjoint, the back-projection operator, can both be expressed as convolutions in log-polar coordinates. Hence, fast algorithms for the application of these operators can be constructed by using the FFT, if data is resampled at log-polar coordinates. Radon data is typically measured on an equally spaced grid in polar coordinates, and reconstructions are represented (as images) in Cartesian coordinates. Therefore, in addition to FFT, several steps of interpolation have to be conducted in order to apply the Radon transform and the back-projection operator by means of convolutions. However, in comparison to the interpolation conducted in Fourier-based gridding methods, the interpolation performed in the Radon and image domains will typically deal with functions that are substantially less oscillatory. Reasonable reconstruction results can thus be expected using interpolation schemes of moderate order. The approach also provides better control over the artifacts that can appear due to measurement errors. Both the interpolation and the FFT operations can be efficiently implemented on graphical processor units (GPUs). For the interpolation, it is possible to make use of the fact that linear interpolation is hard-wired on GPUs, meaning that it has the same computational cost as direct memory access. Cubic order interpolation schemes can be constructed by combining linear interpolation steps, and this provides important computation speedup. We provide details about how the Radon transform and the back-projection can be implemented efficiently as convolution operators on GPUs. For large data sizes, these algorithms are several times faster than those of other software packages based on GPU implementations of the Radon transform and the back-projection operator. Moreover, the gain in computational speed is substantially higher when comparing against other CPU-based algorithms.

关键词： Radon transform fast algorithms FFT GPU

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Two fast algorithms for projecting a point onto the canonical simplex

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2016年第5期56卷 730-743页

作者： Malozemov, V. N. Tamasyan, G. Sh. St Petersburg State Univ Univ Skaya Nab 7-9 St Petersburg 199034 Russia

Two fast orthogonal projection algorithms of a point onto the canonical simplex are analyzed. These algorithms are called the vector and scalar algorithms, respectively. The ideas underlying these algorithms are well known. Improved descriptions of both algorithms are given, their finite convergence is proved, and exact estimates of the number of arithmetic operations needed for their implementation are derived, and numerical results of the comparison of their computational complexity are presented. It is shown that on some examples the complexity of the scalar algorithm is maximal but the complexity of the vector algorithm is minimal and conversely. The orthogonal projection of a point onto the solid simplex is also considered.

关键词： quadratic programming projecting onto a simplex optimality condition fast algorithms

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The FFTRR-based fast direct algorithms for complex inhomogeneous biharmonic problems with applications to incompressible flows

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NUMERICAL algorithms 2017年第4期75卷 937-971页

作者： Daripa, Prabir Ghosh, Aditi Texas A&M Univ Dept Math College Stn TX 77843 USA

We develop analysis-based fast and accurate direct algorithms for several biharmonic problems in a unit disk derived directly from the Green's functions of these problems and compare the numerical results with the "decomposition" algorithms (see Ghosh and Daripa, IMA J. Numer. Anal. 36(2), 824-850 [17]) in which the biharmonic problems are first decomposed into lower order problems, most often either into two Poisson problems or into two Poisson problems and a homogeneous biharmonic problem. One of the steps in the "decomposition algorithm" as discussed in Ghosh and Daripa (IMA J. Numer. Anal. 36(2), 824-850 [17]) for solving certain biharmonic problems uses the "direct algorithm" without which the problem can not be solved. Using classical Green's function approach for these biharmonic problems, solutions of these problems are represented in terms of singular integrals in the complex z-plane (the physical plane) involving explicitly the boundary conditions. Analysis of these singular integrals using FFT and recursive relations (RR) in Fourier space leads to the development of these fast algorithms which are called FFTRR based algorithms. These algorithms do not need to do anything special to overcome coordinate singularity at the origin as often the case when solving these problems using finite difference methods in polar coordinates. These algorithms have some other desirable properties such as the ease of implementation and parallel in nature by construction. Moreover, these algorithms have O(logN) complexity per grid point where N (2) is the total number of grid points and have very low constant behind this order estimate of the complexity. Performance of these algorithms is shown on several test problems. These algorithms are applied to solving viscous flow problems at low and moderate Reynolds numbers and numerical results are presented.

关键词： Complex Biharmonic equation Green's function fast algorithms Stokes equations Steady incompressible flows FFT Recursive relations Numerical implementation in Matlab

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fast data-independent KLT approximations based on integer functions

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MULTIMEDIA TOOLS AND APPLICATIONS 2024年第26期83卷 67303-67325页

作者： Radunz, A. P. Coelho, D. F. G. Bayer, F. M. Cintra, R. J. Madanayake, A. Univ Fed Pernambuco Dept Estat BR-50670901 Recife Brazil Univ Fed Pernambuco Dept Tecnol Signal Proc Grp BR-55014900 Caruaru Brazil Univ Fed Santa Maria Dept Estat LACESM BR-97105900 Santa Maria Brazil Florida Int Univ Dept Elect & Comp Engn Miami FL 33174 USA

The Karhunen-Loeve transform (KLT) stands as a well-established discrete transform, demonstrating optimal characteristics in data decorrelation and dimensionality reduction. Its ability to condense energy compression into a select few main components has rendered it instrumental in various applications within image compression frameworks. However, computing the KLT depends on the covariance matrix of the input data, which makes it difficult to develop fast algorithms for its implementation. Approximations for the KLT, utilizing specific rounding functions, have been introduced to reduce its computational complexity. Therefore, our paper introduces a category of low-complexity, data-independent KLT approximations, employing a range of round-off functions. The design methodology of the approximate transform is defined for any block-length N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{N}$$\end{document}, but emphasis is given to transforms of N=8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{N} = 8$$\end{document} due to its wide use in image and video compression. The proposed transforms perform well when compared to the exact KLT and approximations considering classical performance measures. For particular scenarios, our proposed transforms demonstrated superior performance when compared to KLT approximations documented in the literature. We also developed fast algorithms for the proposed transforms, further reducing the arithmetic cost associated with their implementation. Evaluation of field programmable gate array (FPGA) hardware implementation metrics was conducted. Practical applicatio

关键词： Approximate transforms fast algorithms Image compression Karhunen-Loeve transform Low-complexity transforms

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Variational Bayes for fast and Accurate Empirical Likelihood Inference

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2024年第546期119卷 1089-1101页

作者： Yu, Weichang Bondell, Howard D. Univ Melbourne Sch Math & Stat Melbourne Australia

We develop a fast and accurate approach to approximate posterior distributions in the Bayesian empirical likelihood framework. Bayesian empirical likelihood allows for the use of Bayesian shrinkage without specification of a full likelihood but is notorious for leading to several computational difficulties. By coupling the stochastic variational Bayes procedure with an adjusted empirical likelihood framework, the proposed method overcomes the intractability of both the exact posterior and the arising evidence lower bound objective, and the mismatch between the exact posterior support and the variational posterior support. The optimization algorithm achieves fast algorithmic convergence by using the variational expected gradient of the log adjusted empirical likelihood function. We prove the consistency of the proposed approximate posterior distribution and an empirical likelihood analogue of the variational Bernstein-von-Mises theorem. Through several numerical examples, we confirm the accuracy and quick algorithmic convergence of our proposed method.

关键词： Adjusted empirical likelihood Bernstein-von-Mises theorem Empirical likelihood fast algorithms Posterior computation Stochastic variational Bayes

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fast algorithms for Low-Delay TDAC Filterbanks in MPEG-4 AAC-ELD

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IEEE-ACM TRANSACTIONS ON AUDIO SPEECH AND LANGUAGE PROCESSING 2014年第12期22卷 1701-1712页

作者： Chivukula, Ravi K. Reznik, Yuriy A. Hu, Yanyan Devarajan, Venkat Jayendra-Lakshman, Mythreya Indian Sch Business Mohali 140306 Punjab India InterDigital Inc San Diego CA 92121 USA Univ Texas Arlington Dept Elect Engn Arlington TX 76019 USA Qualcomm Inc San Diego CA 92121 USA

The MPEG committee has completed development of a new audio coding standard called "MPEG-4 advanced audio coding-enhanced low delay" (AAC-ELD). AAC-ELD uses low delay spectral band replication (LD-SBR) technology together with a low delay time domain alias cancellation (LD TDAC) filterbank in the encoder to achieve both high coding efficiency and low algorithmic delay. In this paper, we present fast algorithms for implementing LD-TDAC filterbanks in AAC-ELD. Two types of fast algorithms are presented. In the first, we map LD-TDAC analysis and synthesis filterbanks to modified discrete cosine transform (MDCT) and inverse modified discrete cosine transform (IMDCT), respectively. Since MDCT/IMDCT are already extensively used in AAC and they have many fast algorithms, this mapping not only provides a fast implementation but also allows a common implementation of the filterbanks in AAC Low Complexity (AAC-LC), AAC Low Delay (AAC-LD) and AAC-ELD codecs. In the second algorithm, we provide a mapping to discrete Cosine transform of type II. The mapping to DCT-II allows the merger of the matrix operations with the windowing stage that precedes or follows them. This further reduces the number of multiplications and leads to an algorithm with the lowest known arithmetic complexity. For filterbanks of lengths 1024 and 960, we also present a new fast factorization of 15-point DCT-II that requires only 14 irrational multiplications, 3 dyadic rational multiplications and 67 additions.

关键词： AAC audio coding DCT factorization fast algorithms filterbanks low delay MDCT MPEG speech coding time domain alias cancellation

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A fast, high-order scheme for evaluating volume potentials on complex 2D geometries via area-to-line integral conversion and domain mappings

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JOURNAL OF COMPUTATIONAL PHYSICS 2023年 472卷

作者： Anderson, Thomas G. Zhu, Hai Veerapaneni, Shravan Univ Michigan Dept Math Ann Arbor MI 48103 USA

While potential theoretic techniques have received significant interest and found broad success in the solution of linear partial differential equations (PDEs) in mathematical physics, limited adoption is reported in the case of nonlinear and/or inhomogeneous problems (i.e. with distributed volumetric sources) owing to outstanding challenges in producing a particular solution on complex domains while simultaneously respecting the competing ideals of allowing complete geometric flexibility, enabling source adaptivity, and achieving optimal computational complexity. This article presents a new high-order accurate algorithm for finding a particular solution to the PDE by means of a convolution of the volumetric source function with the Green's function in complex geometries. Utilizing volumetric domain decomposition, the integral is computed over a union of regular boxes (lending the scheme compatibility with adaptive box codes) and triangular regions (which may be potentially curved near boundaries). Singular and near-singular quadrature is handled by converting integrals on volumetric regions to line integrals bounding a reference volume cell using cell mappings and elements of the Poincare lemma, followed by leveraging existing one-dimensional near-singular and singular quadratures appropriate to the singular nature of the kernel. The scheme achieves compatibility with fast multipole methods (FMMs) and thereby optimal asymptotic complexity by coupling global rules for target-independent quadrature of smooth functions to local target -dependent singular quadrature corrections, and it relies on orthogonal polynomial systems on each cell for well-conditioned, high-order and efficient (with respect to number of required volume function evaluations) approximation of arbitrary volumetric sources. Our domain discretization scheme is naturally compatible with standard meshing software such as Gmsh, which are employed to discretize a narrow region surrounding the domain boun

关键词： Newton potential Inhomogeneous PDEs fast algorithms Potential theory Singular and near -singular multi -dimensional quadrature

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