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An algorithm for fast Multiplication of Pauli Numbers

ADVANCES IN APPLIED CLIFFORD ALGEBRAS 2015年第1期25卷 53-63页

作者： Cariow, A. Cariowa, G. West Pomeranian Univ Technol Fac Comp Sci & Informat Technol PL-71210 Szczecin Poland

In this paper we introduce an efficient algorithm for the multiplication of Pauli numbers. The direct multiplication of two Pauli numbers requires 64 real multiplications and 56 real additions. More effective solutions still do not exist. We show how to compute a product of the Pauli numbers with 24 conventional multiplications, 8 multiplications by 1/2 and 56 real additions.

关键词： Pauli numbers multiplication of Pauli numbers fast algorithm matrix notation

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A fast MATRIX-FREE algorithm FOR SPECTRAL APPROXIMATIONS TO THE SCHRODINGER EQUATION

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2015年第4期37卷 A2003-A2025页

作者： Brumm, B. Univ Tubingen Math Inst D-72076 Tubingen Germany

We consider the linear time-dependent Schrodinger equation with a time-dependent smooth potential on an unbounded domain. A Galerkin spectral method with a tensor-product Hermite basis is used as a discretization in space. Discretizing the resulting ODE for the Hermite expansion coefficients involves the computation of the action of the Galerkin matrix on a vector in each time step. We propose a fast algorithm for the direct computation of this matrix-vector product without actually assembling the matrix itself. The costs scale linearly in the size of the basis. Together with the application of a hyperbolically reduced basis, this reduces the computational effort considerably and helps cope with the infamous curse of dimensionality. The application of the fast algorithm is limited to the case of the potential being significantly smoother than the solution. The error analysis is based on a binary tree representation of the three-term recurrence relation for the one-dimensional Hermite functions. The fast algorithm constitutes an efficient tool for schemes involving the action of a matrix due to spectral discretization on a vector, and it is also applicable in the context of spectral approximations for linear problems other than the Schrodinger equation.

关键词： linear Schrodinger equation spectral Galerkin methods reduced index sets fast algorithm direct computation curse of dimensionality binary trees

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Artifact reduction for separable nonlocal means

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JOURNAL OF ELECTRONIC IMAGING 2017年第6期26卷 063012-063012页

作者： Ghosh, Sanjay Chaudhury, Kunal N. Indian Inst Sci Dept Elect Engn Bangalore Karnataka India

It was recently demonstrated that one can perform fast nonlocal means (NLM) denoising of one-dimensional (1-D) signals using a method called lifting. The cost of lifting is independent of the patch length, which dramatically reduces the run-time for large patches. Unfortunately, it is difficult to directly extend lifting for NLM denoising of images. To bypass this, the authors proposed a separable approximation in which the image rows and columns are filtered using lifting. The overall algorithm is significantly faster than NLM, and the results are comparable in terms of PSNR. However, the separable processing often produces vertical and horizontal stripes in the image. This problem was previously addressed using a bilateral filter-based postsmoothing, which was effective in removing some of the stripes. We demonstrate that stripes can be mitigated in the first place simply by involving the neighboring rows (or columns) in the filtering. In other words, we use a two-dimensional (2-D) search (similar to NLM), while still using 1-D patches (as in the previous proposal). The innovation is in the observation that one can use lifting for performing 2-D searches. The proposed approach produces artifact-free images, whose quality and PSNR are comparable to NLM, while being significantly faster. (C) 2017 SPIE and IS&T

关键词： denoising nonlocal means fast algorithm lifting artifact

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Local regularization of linear inverse problems via variational filtering

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INVERSE PROBLEMS 2017年第8期33卷 085002-085002页

作者： Lamm, Patricia K. Michigan State Univ Dept Math 619 Red Cedar Rd E Lansing MI 48824 USA

We develop local regularization methods for ill-posed linear inverse problems governed by general Fredholm integral operators. The methods are executed as filtering algorithms which are simple to implement and computationally efficient for a large class of problems. We establish a convergence theory and give convergence rates for such methods, and illustrate their computational speed in numerical tests for inverse problems in geomagnetic exploration and imaging.

关键词： inverse problem regularization method filtering fast algorithm localization image deblurring

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fast BILATERAL FILTERING OF VECTOR-VALUED IMAGES 23

FAST BILATERAL FILTERING OF VECTOR-VALUED IMAGES

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23rd IEEE International Conference on Image Processing (ICIP)

作者： Ghosh, Sanjay Chaudhury, Kunal N. Indian Inst Sci Dept Elect Engn Bangalore Karnataka India

ISBN: (纸本)9781467399616

In this paper, we consider a natural extension of the edge-preserving bilateral filter for vector-valued images. The direct computation of this non-linear filter is slow in practice. We demonstrate how a fast algorithm can be obtained by first approximating the Gaussian kernel of the bilateral filter using raised-cosines, and then using Monte Carlo sampling. We present simulation results on color images to demonstrate the accuracy of the algorithm and the speedup over the direct implementation.

关键词： Bilateral filter vector-valued image color image Monte Carlo method approximation fast algorithm

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Feature-based fast coding unit partition algorithm for high efficiency video coding

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Journal of Applied Research and Technology 2015年第2期13卷 205-219页

作者： Lin, Yih-Chuan Lai, Jian-Cheng Department of Computer Science and Information Engineering National Formosa University Yunlin 63201 Taiwan

High Efficiency Video Coding (HEVC), which is the newest video coding standard, has been developed for the efficient compression of ultra high definition videos. One of the important features in HEVC is the adoption of a quad-tree based video coding structure, in which each incoming frame is represented as a set of non overlapped coding tree blocks (CTB) by variable-block sized prediction and coding process. To do this, each CTB needs to be recursively partitioned into coding unit (CU), predict unit (PU) and transform unit (TU) during the coding process, leading to a huge computational load in the coding of each video frame. This paper proposes to extract visual features in a CTB and uses them to simplify the coding procedure by reducing the depth of quad-tree partition for each CTB in HEVC intra coding mode. A measure for the edge strength in a CTB, which is defined with simple Sobel edge detection, is used to constrain the possible maximum depth of quad-tree partition of the CTB. With the constrained partition depth, the proposed method can reduce a lot of encoding time. Experimental results by HM10.1 show that the average time-savings is about 13.4% under the increase of encoded BD-Rate by only 0.02%, which is a less performance degradation in comparison to other similar methods. © 2015 Universidad Nacional Autónoma de México, Centro de Ciencias Aplicadas y Desarrollo Tecnológico. All Rights Reserved.

关键词： Coding unit CTB fast algorithm Feature-based approach HEVC Quad-tree partition Sobel edge

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Pattern Matching Using Partial Fourier Spectrum

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY 2016年第7期26卷 1229-1240页

作者： Shahhosseini, Saeid Rezaie, Bahman Alucid Technol Inc San Francisco CA 94607 USA St Marys Univ San Antonio Dept Elect Engn San Antonio TX 78228 USA

Pattern matching is a fundamental technique in image processing. The majority of improvements that have been proposed in the literature are geared toward small-to mid-size templates and images. The rapidly increasing resolution and size of images demand a more efficient template-matching algorithm. The main focus of this paper is to address this problem by proposing a novel template-matching algorithm using partial Fourier spectrum (PFS) components as its feature set. It is shown that regardless of the content of the template in terms of correlation in spatial domain, the use of PFS components results in a smooth error surface, which facilitates the evaluation of the region of interest by predicting the error change within the foreseeable distance. It is also shown that this approach generates a broad global minimum area around the best match, which is on the order of the size of the template. Based on these characteristics, three algorithms are developed and the performance of the algorithms is analyzed through extensive mathematical analysis and experimental simulations. The experimental results, generated using over 13 000 image/template pairs, indicate that the proposed algorithms outperform the most efficient algorithms currently available in the literature by over an order of magnitude.

关键词： fast algorithm pattern matching regional distortion evaluation template matching

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fast algorithm of (k, k-1) Type Discrete Walsh-Haar Transformation and Application in Image Edge Detection

Fast Algorithm of (k, k-1) Type Discrete Walsh-Haar Transfor...

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7th Symposium on Multispectral Image Processing and Pattern Recognition (MIPPR) - Remote Sensing Image Processing, Geographic Information Systems, and Other Applications

作者： Lu, Li Shi, Bao-Chang Huazhong Univ Sci & Technol Sch Software Engn Wuhan 430074 Hubei Peoples R China Huazhong Univ Sci & Technol Sch Math & Stat Wuhan 430074 Peoples R China

ISBN: (纸本)9780819485809

Walsh-Haar function system that was first introduced by us is a new kind of function systems, and has a good global / local property. This function system is called Walsh ordering function system since its generation kernel functions belong to Walsh ordering Walsh function system. We worked out a recursive property of the matrix WHKRm+1 corresponding to the first (KRm+1) Walsh-Haar functions in Walsh-Haar function system, and proved that Walsh-Haar function system is perfect and orthogonal similar to Walsh function system and Haar function system. Thus, discrete Walsh-Haar transformation (DW-HT) is an orthogonal transformation that can be widely used in signal processing. In this paper, using the recursive property of the matrix WHKRm+1 and the fast algorithm of discrete Walsh transformation in Walsh ordering, we have designed a fast algorithm of Walsh ordering (k, k-1) type DW-HT based on the bisection technique. As one of its applications, we use it to detect image edges. Compare with some edge-detecting methods, the method in this paper detects more details of image edge. The idea and method used to design the fast algorithm in this paper can be used to design fast algorithms of other ordering (k, k-1) type DW-HTs and other discrete orthogonal transformations.

关键词： Walsh-Haar matrix discrete Walsh-Haar transformation the bisection technique fast algorithm edge detection

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fast Realistic Block-Based Refocusing for Sparse Light Fields

Fast Realistic Block-Based Refocusing for Sparse Light Field...

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IEEE International Symposium on Circuits and Systems (ISCAS)

作者： Huang, Li-Ren Wang, Yu-Wen Huang, Chao-Tsung Natl Tsing Hua Univ Dept Elect Engn Hsinchu 30013 Taiwan

ISBN: (纸本)9781479953417

View-interpolation-based refocusing achieves realistic quality for sparse light fields but requires lots of computation. In this paper, we aim to reduce the computation load while maintaining the superior refocusing quality. The idea is to interpolate only few views for infocused regions and to perform refocusing on downsampled pixels for defocused area. This is achieved by a proposed block-based refocusing algorithm which consists of multi-level refocusing mode decision and timing-based block merging. For each variable-size block, the former chooses the fastest downsampling mode given that the distortion is negligible based on a localized filter response analysis. Then, the latter determines the fastest quadtree block partition by minimizing the timing cost which is accurately estimated for each block. Experimental results show that a 10x speedup on average is achieved for realistic refocusing. Also, the computation time becomes comparable to the conventional fast depth-dependent blurring which has serious boundary artifacts.

关键词： refocus light field fast algorithm quad-tree block partition

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Improving the Accuracy of Single-Source Equivalence Principle algorithm by Using Tangential Field Projection Scheme

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ELECTROMAGNETICS 2016年第8期36卷 534-545页

作者： Shao, Hanru Dong, Jianfeng Hu, Jun Ningbo Univ Fac Elect Engn & Comp Sci Ningbo 315211 Zhejiang Peoples R China Univ Elect Sci & Technol China Sch Elect Engn Chengdu Peoples R China

The single-source equivalence principle algorithm has been proposed as an efficient solution for analyzing large array structures. However, due to the discretization error of the identity operator, the accuracy of single-source equivalence principle algorithm is not good. In this paper, a single-source tangential equivalence principle algorithm is proposed to improve the accuracy by using the tangential field projection scheme. Based on this scheme and extinction theorem, a new relation between equivalence electric current and magnetic current can be established which has more accurate discretization. Moreover, it is demonstrated that the single-source equivalence principle algorithm can be derived from one type of single-source tangential equivalence principle algorithm. Numerical examples are designed to demonstrate the accuracy improvement of the proposed method.

关键词： Electromagnetic scattering equivalence principle fast algorithm integral equation

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