Comparison of fast discrete wavelet transform algorithms

This paper presents an analysis on and experimental comparison of several typical fast algorithms for discrete wavelet transform (DWT) and their implementation in image compression, particularly the Mallat algorithm, FFT-based algorithm, Short- length based algorithm and Lifting algorithm. The principles, structures and computational complexity of these algorithms are explored in details respectively. The results of the experiments for comparison are consistent to those simulated by MATLAB. It is found that there are limitations in the implementation of DWT. Some algorithms are workable only for special wavelet transform, lacking in generality. Above all, the speed of wavelet transform, as the governing element to the speed of image processing, is in fact the retarding factor for real-time image processing.

Improving path planning efficiency for underwater gravity-aided navigation based on a new depth sorting fast search algorithm

This study focuses on the improvement of path planning efficiency for underwater gravity-aided navigation.Firstly,a Depth Sorting Fast Search(DSFS)algorithm was proposed to improve the planning speed of the Quick Rapidly-exploring Random Trees*(Q-RRT*)algorithm.A cost inequality relationship between an ancestor and its descendants was derived,and the ancestors were filtered accordingly.Secondly,the underwater gravity-aided navigation path planning system was designed based on the DSFS algorithm,taking into account the fitness,safety,and asymptotic optimality of the routes,according to the gravity suitability distribution of the navigation space.Finally,experimental comparisons of the computing performance of the ChooseParent procedure,the Rewire procedure,and the combination of the two procedures for Q-RRT*and DSFS were conducted under the same planning environment and parameter conditions,respectively.The results showed that the computational efficiency of the DSFS algorithm was improved by about 1.2 times compared with the Q-RRT*algorithm while ensuring correct computational results.

Fast algorithm for constructing neighbor-joining phylogenetic trees

To improve the performance of Saitou and Nei＇s algorithm （SN） and Studier and Keppler＇s improved algorithm （SK） for constructing neighbor-joining phylogenetic trees and reduce the time complexity of the computation, a fast algorithm is proposed. The proposed algorithm includes three techniques. First, a linear array A[N] is introduced to store the sum of every row of the distance matrix （the same as SK）, which can eliminate many repeated computations. Secondly, the value of A [i] is computed only once at the beginning of the algorithm, and is updated by three elements in the iteration. Thirdly, a very compact formula for the sum of all the branch lengths of operational taxonomic units （OTUs） i and j is designed, and the correctness of the formula is proved. The experimental results show that the proposed algorithm is from tens to hundreds times faster than SN and roughly two times faster than SK when N increases, constructing a tree with 2 000 OTUs in 3 min on a current desktop computer. To earn the time with the cost of the space and reduce the computations in the innermost loop are the basic solutions for algorithms with many loops.

Improvement and performance of parallel multilevel fast multipole algorithm

The method of establishing data structures plays an important role in the efficiency of parallel multilevel fast multipole algorithm（PMLFMA）.Considering the main complements of multilevel fast multipole algorithm（MLFMA） memory,a new parallelization strategy and a modified data octree construction scheme are proposed to further reduce communication in order to improve parallel efficiency.For far interaction,a new scheme called dynamic memory allocation is developed.To analyze the workload balancing performance of a parallel implementation,the original concept of workload balancing factor is introduced and verified by numerical examples.Numerical results show that the above measures improve the parallel efficiency and are suitable for the analysis of electrical large-scale scattering objects.

Fast precise integration method for hyperbolic heat conduction problems

A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to the fact that the matrix exponential is sparse. The presented method employs the sparsity of the matrix exponential to improve the original precise integration method. The merits are that the proposed method is suitable for large hyperbolic heat equations and inherits the accuracy of the original version and the good computational efficiency, which are verified by two numerical examples.

Fast algorithm for simulation of normal and oblique penetration into limestone targets

A fast algorithm is proposed to predict penetration trajectory in simulation of normal and oblique penetration of a rigid steel projectile into a limestone target. The algorithm is designed based on the idea of isolation between the projectile and the target. Corresponding factors of influence are considered, including analytical load model, cratering effect, free surface effect, and separation-reattachment phenomenon. Besides, a method of cavity ring is used to study the process of cavity expansion. Further, description of the projectile＇s three-dimensional gesture is coded for fast calculation, named PENE3D. A presented. As a result, the algorithm is series of cases with selected normal and oblique penetrations are simulated by the algorithm. The predictions agree with the results of tests, showing that the proposed algorithm is fast and effective in simulation of the penetration process and prediction of the penetration trajectory.

A novel fast classification filtering algorithm for LiDAR point clouds based on small grid density clustering

Clustering filtering is usually a practical method for light detection and ranging(LiDAR)point clouds filtering according to their characteristic attributes.However,the amount of point cloud data is extremely large in practice,making it impossible to cluster point clouds data directly,and the filtering error is also too large.Moreover,many existing filtering algorithms have poor classification results in discontinuous terrain.This article proposes a new fast classification filtering algorithm based on density clustering,which can solve the problem of point clouds classification in discontinuous terrain.Based on the spatial density of LiDAR point clouds,also the features of the ground object point clouds and the terrain point clouds,the point clouds are clustered firstly by their elevations,and then the plane point clouds are selected.Thus the number of samples and feature dimensions of data are reduced.Using the DBSCAN clustering filtering method,the original point clouds are finally divided into noise point clouds,ground object point clouds,and terrain point clouds.The experiment uses 15 sets of data samples provided by the International Society for Photogrammetry and Remote Sensing(ISPRS),and the results of the proposed algorithm are compared with the other eight classical filtering algorithms.Quantitative and qualitative analysis shows that the proposed algorithm has good applicability in urban areas and rural areas,and is significantly better than other classic filtering algorithms in discontinuous terrain,with a total error of about 10%.The results show that the proposed method is feasible and can be used in different terrains.

A Fast Super-Resolution Reconstruction from Image Sequence

Based on the mechanism of imagery, a novel method called the delaminating combining template method, used for the problem of super-resolution reconstruction from image sequence, is described in this paper. The combining template method contains two steps： a delaminating strategy and a combining template algorithm. The delaminating strategy divides the original problem into several sub-problems; each of them is only eonnected to one degrading factor. The combining template algorithm is suggested to resolve each sub-problem. In addition, to verify the valid of the method, a new index called oriental entropy is presented. The results from the theoretical analysis and experiments illustrate that this method to be promising and efficient.

Fast recursive algorithm for two-dimensional Tsallis entropy thresholding method

Recently, a two-dimensional （2-D） Tsallis entropy thresholding method has been proposed as a new method for image segmentation. But the computation complexity of 2-D Tsallis entropy is very large and becomes an obstacle to real time image processing systems. A fast recursive algorithm for 2-D Tsallis entropy thresholding is proposed. The key variables involved in calculating 2-D Tsallis entropy are written in recursive form. Thus, many repeating calculations are avoided and the computation complexity reduces to O（L2） from O（L4）. The effectiveness of the proposed algorithm is illustrated by experimental results.

A novel adjustable multiple cross-hexagonal search algorithm for fast block motion estimation

In this paper,we propose a novel adjustable multiple cross-hexagonal search(AMCHS) algorithm for fast block motion estimation. It employs adjustable multiple cross search patterns(AMCSP) in the first step and then uses half-way-skip and half-way-stop technique to determine whether to employ two hexagonal search patterns(HSPs) subsequently. The AMCSP can be used to find small motion vectors efficiently while the HSPs can be used to find large ones accurately to ensure prediction quality. Simulation results showed that our proposed AMCHS achieves faster search speed,and provides better distortion performance than other popular fast search algorithms,such as CDS and CDHS.

General and efficient parallel approach of finite element-boundary integral-multilevel fast multipole algorithm

A general and efficient parallel approach is proposed for the first time to parallelize the hybrid finiteelement-boundary-integral-multi-level fast multipole algorithm （FE-BI-MLFMA）. Among many algorithms of FE-BI-MLFMA, the decomposition algorithm （DA） is chosen as a basis for the parallelization of FE-BI-MLFMA because of its distinct numerical characteristics suitable for parallelization. On the basis of the DA, the parallelization of FE-BI-MLFMA is carried out by employing the parallelized multi-frontal method for the matrix from the finiteelement method and the parallelized MLFMA for the matrix from the boundary integral method respectively. The programming and numerical experiments of the proposed parallel approach are carried out in the high perfor- mance computing platform CEMS-Liuhui. Numerical experiments demonstrate that FE-BI-MLFMA is efficiently parallelized and its computational capacity is greatly improved without losing accuracy, efficiency, and generality.

Fast 3D EM scattering and radiation solvers based on MLFMA

As the fastest integral equation solver to date, the multilevel fast multipole algorithm （MLFMA） has been applied successfully to solve electromagnetic scattering and radiation from 3D electrically large objects. But for very large-scale problems, the storage and CPU time required in MLFMA are still expensive. Fast 3D electromagnetic scattering and radiation solvers are introduced based on MLFMA. A brief review of MLFMA is first given. Then, four fast methods including higher-order MLFMA （HO-MLFMA）, fast far field approximation combined with adaptive ray propagation MLFMA （FAFFA-ARP-MLFMA）, local MLFMA and parallel MLFMA are introduced. Some typical numerical results demonstrate the efficiency of these fast methods.

Efficient analysis of dielectric radomes using multilevel fast multipole algorithm with CRWG basis

A full-wave analysis of the electromagnetic problem of a three-dimensional （3-D） antenna radiating through a 3-D dielectric radome is preserued. The problem is formulated using the Poggio-Miller-Chang-Harrington- Wu（PMCHW） approach for homogeneous dielectric objects and the electric field integral equation for conducting objects. The integral equations are discretized by the method of moment （MoM）, in which the conducting and dielectric surface/interfaces are represented by curvilinear triangular patches and the unknown equivalent electric and magnetic currents are expanded using curvilinear RWG basis functions. The resultant matrix equation is then solved by the multilevel fast multipole algorithm （MLFMA） and fast far-field approximation （FAFFA） is used to further accelerate the computation. The radiation patterns of dipole arrays in the presence of radomes are presented. The numerical results demonstrate the accuracy and versatility of this method.

Fast and accurate analysis of electromagnetic scattering from targets situated in dielectric half space

Electromagnetic scattering from targets situated in half space is solved by applying fast inhomogeneous plane wave algorithm combined with a tabulation and interpolation method. The integral equation is set up based on derivation of dyadic Green＇s functions in this environment. The coupling is divided into nearby region and well-separated region by grouping. The Green＇s function can be divided into two parts： primary term and reflected term. In the well-separated region, the two terms are both expressed as Sommerfeld integral, which can be accelerated by deforming integral path and taking interpolation and extrapolation. For the nearby region, the direct Sommerfeld integral makes the filling of impedance matrix time-expensive. A tabulation and interpolation method is applied to speed up this process. This infinite integral is pre-computed in sampling region, and a two-dimensional table is then set up. The impedance elements can then be obtained by interpolation. Numerical results demonstrate the accuracy and efficiency of this algorithm.

Fast interactive segmentation algorithm of image sequences based on relative fuzzy connectedness

A fast interactive segmentation algorithm of image-sequences based on relative fuzzy connectedness is presented. In comparison with the original algorithm, the proposed one, with the same accuracy, accelerates the segmentation speed by three times for single image. Meanwhile, this fast segmentation algorithm is extended from single object to multiple objects and from single-image to image-sequences. Thus the segmentation of multiple objects from complex hackground and batch segmentation of image-sequences can be achieved. In addition, a post-processing scheme is incorporated in this algorithm, which extracts smooth edge with one-pixel-width for each segmented object. The experimental results illustrate that the proposed algorithm can obtain the object regions of interest from medical image or image-sequences as well as man-made images quickly and reliably with only a little interaction.

An adaptive reanalysis method for genetic algorithm with application to fast truss optimization

Although the genetic algorithm （GA） for structural optimization is very robust, it is very computationally intensive and hence slower than optimality criteria and mathematical programming methods. To speed up the design process, the authors present an adaptive reanalysis method for GA and its applications in the optimal design of trusses. This reanalysis technique is primarily derived from the Kirsch＇s combined approximations method. An iteration scheme is adopted to adaptively determine the number of basis vectors at every generation. In order to illustrate this method, three classical examples of optimal truss design are used to validate the proposed reanalysis-based design procedure. The presented numerical results demonstrate that the adaptive reanalysis technique affects very slightly the accuracy of the optimal solutions and does accelerate the design process, especially for large-scale structures.

Fast direction of arrival algorithm based on vector-sensor arrays using wideband sources

An acoustic vector sensor(AVS)can capture more information than a conventional acoustic pressure sensor(APS).As a result,more output channels are required when multiple AVS are formed into arrays,making processing the data stream computationally intense.This paper proposes a new algorithm based on the propagator method for wideband coherent sources that eliminates eigen-decomposition in order to reduce the computational burden.Data from simulations and lake trials showed that the new algorithm is valid:it resolves coherent sources,breaks left/right ambiguity,and allows inter element spacing to exceed a half-wavelength.

AUTOMATIC FAST CLASSIFICATION OF PRODUCT-IMAGES WITH CLASS-SPECIFIC DESCRIPTOR

To achieve online automatic classification of product is a great need of e-commerce de-velopment. By analyzing the characteristics of product images, we proposed a fast supervised image classifier which is based on class-specific Pyramid Histogram Of Words (PHOW) descriptor and Im-age-to-Class distance (PHOW/I2C). In the training phase, the local features are densely sampled and represented as soft-voting PHOW descriptors, and then the class-specific descriptors are built with the means and variances of distribution of each visual word in each labelled class. For online testing, the normalized chi-square distance is calculated between the descriptor of query image and each class-specific descriptor. The class label corresponding to the least I2C distance is taken as the final winner. Experiments demonstrate the effectiveness and quickness of our method in the tasks of product clas-sification.

FAST DFT ALGORITHM WITH (N-1) / 2 MULTIPLICATIONS

A fast algorithm is proposed for recursively computing the DFTs of prime length. Only (N-1) / 2 real multiplications are required to compute all N frequency components in terms of permuting the input data. The multiplication in recursive computation is replaced by shifting. Complexity of the algorithm is studied. A factor η is introduced and presented. When the ratio of multiplier's period Tm to adder's period Ta is greater than the factor η (i.e.Tm / Ta >η), the new algorithm is faster than FFT. The necessary condition and error of the algorithm are studied. The signal-to-noise ratio for different length N is presented. A high accuracy scheme is proposed for improving the SNR about 20 -30dB.

A Fast Algorithm for Matching Remote Scene Images

An iterative algorithm to calculate mutual correlation using hierarchical key points and the search space mark principle is proposed. An effective algorithm is designed to improve the matching speed. By hi-erarchical key point algorithm and mutual correlation coefficients of the matching images, the important points can be iteratively calculated in the images hierarchically, and the correlation coefficient can be ob-tained with satisfactory precision. Massive spots in the parameter space which are impossible to match can be removed by the search space mark principle. Two approximate continuities in the correlation image matching process, the image gray level distribution continuity and the correlation coefficient value in the parameter space continuity, are considered in the method. The experiments show that the new algorithm can greatly enhance matching speed and achieve accurate matching results.