Recurrent matrix methods and methods based on the Walsh transform and rotation matrices generating orthogonal slant transforms of high and low correlation are proposed. These methods are used to develop efficient fast...
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Recurrent matrix methods and methods based on the Walsh transform and rotation matrices generating orthogonal slant transforms of high and low correlation are proposed. These methods are used to develop efficient fast slant-transform algorithms without multiplication and additional permutations of output data.
Some application driven fast algorithms developed by the author and his collaborators for elliptic partial differential equations are briefly reviewed here. Subsequent use of the ideas behind development of these algo...
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Some application driven fast algorithms developed by the author and his collaborators for elliptic partial differential equations are briefly reviewed here. Subsequent use of the ideas behind development of these algorithms for further development of other algorithms some of which are currently in progress is briefly mentioned. Serial and parallel implementation of these algorithms and their applications to some pure and applied problems are also briefly reviewed.
A new technique of trilinear operations of aggregating, uniting and canceling is introduced and applied to constructing fast linear noncommutative algorithms for matrix multiplication. The result is an asymptotic impr...
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A new technique of trilinear operations of aggregating, uniting and canceling is introduced and applied to constructing fast linear noncommutative algorithms for matrix multiplication. The result is an asymptotic improvement of Strassen’s famous algorithms for matrix operations.
In this paper we present an evaluation of the fast algorithms used for motion estimation and compensation. The presented algorithms are classified in two categories. The first category contains the algorithms with fix...
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ISBN:
(纸本)9781612081236
In this paper we present an evaluation of the fast algorithms used for motion estimation and compensation. The presented algorithms are classified in two categories. The first category contains the algorithms with fixed number of iterations, i.e., Three Step Search (TSS), New Three Step Search (NTSS), and Four Step Search (FSS). The second category includes motion estimation algorithms with variable number of iterations, i.e., Orthogonal Search (OS), Two Dimensional Logarithmic Search (TDLS), and Adaptive Rood Pattern Search (ARPS). It is proved that for the second category of algorithms the number of iterations depends on the dimension of the search window. The evaluation is done by comparing the peak signal-to-noise ratio (PSNR) of the compensated motion frame and the number of blocks that are used.
The paper is devoted to design, fast implementation and applications of a family of 8-points integer orthogonal transforms based on a parametric matrix. A unified algorithm for their efficient computations is develope...
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ISBN:
(纸本)0819452017
The paper is devoted to design, fast implementation and applications of a family of 8-points integer orthogonal transforms based on a parametric matrix. A unified algorithm for their efficient computations is developed. Derived fast transforms have close coding gain performance to the optimal Karhunen-Loeve transform for the first order Markov process. Among them are also such that closely approximate the DCT-II and. at the same time, have a larger coding gain. For a particular set of parameters, integer transforms with reduced computational complexity are obtained. The comparative analysis of these transforms with the DCT-II in the framework of image denoising and video coding is performed.
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 regular...
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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.
Any paraxial optical system which can be implemented using only thin lenses and propagation through free space or through sections of graded index (GRIN) media, belongs to the class of systems known as Quadratic Phase...
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ISBN:
(纸本)0819462438
Any paraxial optical system which can be implemented using only thin lenses and propagation through free space or through sections of graded index (GRIN) media, belongs to the class of systems known as Quadratic Phase Systems (QPS). Given some input optical wave field, the output of any QPS can be described using the linear canonical,2 transform (LCT), a unitary, additive, three-parameter class of linear integral transform first discovered in the 1970s'. The terminology used in relation to the LCT is not at all consistent across the literature, and it is frequently called by other names, such as Quadratic-phase Integral and Generalized Fresnel Transform. In this paper, we examine a new, more flexible numerical implementation of the FLCT. This algorithm is similar to the Sande-Tukey FFT algorithm, and is of general radix. We demonstrate the savings possible in terms of required samples with the flexibility inherent in a general radix algorithm.
fast algorithms are presented for implementing the public key cryptosystem proposed by Rivest, Shamir and Adleman. The fast algorithms are based on the fast integer multiplications scheme due to Schonhage and Strassen...
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fast algorithms are presented for implementing the public key cryptosystem proposed by Rivest, Shamir and Adleman. The fast algorithms are based on the fast integer multiplications scheme due to Schonhage and Strassen and the proposed iterative division algorithm.
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 ne...
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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.
We present fast algorithms for the summation of Dyson series and the inchworm Monte Carlo method for quantum systems that are coupled with harmonic baths. The algorithms are based on evolving the integro-differential ...
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We present fast algorithms for the summation of Dyson series and the inchworm Monte Carlo method for quantum systems that are coupled with harmonic baths. The algorithms are based on evolving the integro-differential equations where the most expensive part comes from the computation of bath influence functionals. To accelerate the computation, we design fast algorithms based on reusing the bath influence functionals computed in the previous time steps to reduce the number of calculations. It is proven that the proposed fast algorithms reduce the number of such calculations by a factor of O (N), where N is the total number of time steps. Numerical experiments are carried out to show the efficiency of the method and to verify the theoretical results. (C) 2022 Elsevier B.V. All rights reserved.
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