scholarly journals An Efficient Algorithm for Overcomplete Sparsifying Transform Learning with Signal Denoising

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Beiping Hou ◽  
Zhihui Zhu ◽  
Gang Li ◽  
Aihua Yu
Keyword(s):  
Closed Form ◽  
Efficient Algorithm ◽  
Synthetic Data ◽  
Closed Form Solution ◽  
Form Solution ◽  
Signal Denoising ◽  
Alternating Minimization ◽  
Computation Complexity ◽  
Learning Problem ◽  
Computation Efficiency

This paper deals with the problem of overcomplete transform learning. An alternating minimization based procedure is proposed for solving the formulated sparsifying transform learning problem. A closed-form solution is derived for the minimization involved in transform update stage. Compared with existing ones, our proposed algorithm significantly reduces the computation complexity. Experiments and simulations are carried out with synthetic data and real images to demonstrate the superiority of the proposed approach in terms of the averaged representation and denoising errors, the percentage of successful and meaningful recovery of the analysis dictionary, and, more significantly, the computation efficiency.

scholarly journals Rotation Estimation: A Closed-Form Solution Using Spherical Moments

Sensors ◽  
2019 ◽  
Vol 19 (22) ◽  
pp. 4958
Author(s):  
Hicham Hadj-Abdelkader ◽  
Omar Tahri ◽  
Houssem-Eddine Benseddik
Keyword(s):  
Image Processing ◽  
Closed Form ◽  
Synthetic Data ◽  
Closed Form Solution ◽  
Form Solution ◽  
Unified Model ◽  
Experimental Results ◽  
Motion Information ◽  
Vision Sensors ◽  
Spherical Projection

Photometric moments are global descriptors of an image that can be used to recover motion information. This paper uses spherical photometric moments for a closed form estimation of 3D rotations from images. Since the used descriptors are global and not of the geometrical kind, they allow to avoid image processing as features extraction, matching, and tracking. The proposed scheme based on spherical projection can be used for the different vision sensors obeying the central unified model: conventional, fisheye, and catadioptric. Experimental results using both synthetic data and real images in different scenarios are provided to show the efficiency of the proposed method.

scholarly journals A Nonlinear Circuit Analysis Technique for Time-Variant Inductor Systems

Sensors ◽  
2019 ◽  
Vol 19 (10) ◽  
pp. 2321 ◽  
Author(s):  
Xinning Wang ◽  
Chong Li ◽  
Dalei Song ◽  
Robert Dean
Keyword(s):  
Closed Form ◽  
Eddy Currents ◽  
High Efficiency ◽  
Nonlinear Differential Equations ◽  
Closed Form Solution ◽  
Form Solution ◽  
Circuit Analysis ◽  
Nonlinear Method ◽  
Sensors And Actuators ◽  
Computation Efficiency

Time-variant inductors exist in many industrial applications, including sensors and actuators. In some applications, this characteristic can be deleterious, for example, resulting in inductive loss through eddy currents in motors designed for high efficiency operation. Therefore, it is important to investigate the electrical dynamics of systems with time-variant inductors. However, circuit analysis with time-variant inductors is nonlinear, resulting in difficulties in obtaining a closed form solution. Typical numerical algorithms used to solve the nonlinear differential equations are time consuming and require powerful processors. This investigation proposes a nonlinear method to analyze a system model consisting of the time-variant inductor with a constraint that the circuit is powered by DC sources and the derivative of the inductor is known. In this method, the Norton equivalent circuit with the time-variant inductor is realized first. Then, an iterative solution using a small signal theorem is employed to obtain an approximate closed form solution. As a case study, a variable inductor, with a time-variant part stimulated by a sinusoidal mechanical excitation, is analyzed using this approach. Compared to conventional nonlinear differential equation solvers, this proposed solution shows both improved computation efficiency and numerical robustness. The results demonstrate that the proposed analysis method can achieve high accuracy.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

scholarly journals A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 10 (7) ◽  
pp. 435
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Point Clouds ◽  
Form Solution ◽  
Spatial Transformation ◽  
Dual Quaternions ◽  
Feature Based ◽  
Planar Feature

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.

A CLOSED-FORM PRICING FORMULA FOR EUROPEAN EXCHANGE OPTIONS WITH STOCHASTIC VOLATILITY

2021 ◽  
pp. 1-10
Author(s):  
Puneet Pasricha ◽  
Anubha Goel
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Closed Form Solution ◽  
Form Solution ◽  
Stochastic Volatility Model ◽  
Strike Price ◽  
Volatility Model ◽  
Exchange Options ◽  
Pricing Formula ◽  
Exchange Option

This article derives a closed-form pricing formula for the European exchange option in a stochastic volatility framework. Firstly, with the Feynman–Kac theorem's application, we obtain a relation between the price of the European exchange option and a European vanilla call option with unit strike price under a doubly stochastic volatility model. Then, we obtain the closed-form solution for the vanilla option using the characteristic function. A key distinguishing feature of the proposed simplified approach is that it does not require a change of numeraire in contrast with the usual methods to price exchange options. Finally, through numerical experiments, the accuracy of the newly derived formula is verified by comparing with the results obtained using Monte Carlo simulations.

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