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Asilomar Conference on Signals, Systems & Computers

作者： R.A. Soni W.K. Jenkins Coordinated Science Laboratory Department of Electrical and Computer Engineering University of Illinois Urbana-Champaign Urbana-Champaign IL USA University of Illinois at Urbana-Champaign Urbana IL US

In this paper we present a family of "new" two-dimensional adaptive filtering algorithms for image processing applications. These algorithms are multidimensional versions of the families of data-reusing and projection algorithms. These two classes of algorithms allow the adaptive filtering system designer to choose performance and computational complexity by changing parameters without actually changing algorithm structure. By changing parameters, the desired convergence rate can be achieved at the expense of additional computational complexity. Experiments show that significant improvement may be obtained by marginal increases in computational complexity over the traditional normalized LMS algorithm.

关键词： projection algorithms Adaptive filters Filtering algorithms Convergence Least squares approximation Application software Computational complexity Tin Algorithm design and analysis Autocorrelation

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A Unified View of Adaptive Variable-Metric projection algorithms

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EURASIP JOURNAL ON ADVANCES IN SIGNAL PROCESSING 2009年第1期2009卷 589260-589260页

作者： Yukawa, Masahiro Yamada, Isao RIKEN BSI Math Neurosci Lab Wako Saitama 3510198 Japan Tokyo Inst Technol Dept Commun & Integrated Syst Meguro Ku Tokyo 1528552 Japan

We present a unified analytic tool named variable-metric adaptive projected subgradient method (V-APSM) that encompasses the important family of adaptive variable-metric projection algorithms. The family includes the transform-domain adaptive filter, the Newton-method-based adaptive filters such as quasi-Newton, the proportionate adaptive filter, and the Krylov-proportionate adaptive filter. We provide a rigorous analysis of V-APSM regarding several invaluable properties including monotone approximation, which indicates stable tracking capability, and convergence to an asymptotically optimal point. Small metric-fluctuations are the key assumption for the analysis. Numerical examples show (i) the robustness of V-APSM against violation of the assumption and (ii) the remarkable advantages over its constant-metric counterpart for colored and nonstationary inputs under noisy situations. Copyright (C) 2009 M. Yukawa and I. Yamada. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

关键词： TDAF LNAF QNAF projection algorithms adaptive filters Self tuning Robustness

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Fast alternated inertial projection algorithms for pseudo-monotone variational inequalities

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2022年 415卷

作者： Shehu, Yekini Dong, Qiao-Li Liu, Lu-Lu Zhejiang Normal Univ Coll Math & Comp Sci Jinhua 321004 Zhejiang Peoples R China Civil Aviat Univ China Coll Sci Tianjin 300300 Peoples R China

In this paper, we propose an alternated inertial subgradient extragradient algorithm for variational inequalities with self-adaptive step-sizes and obtain weak and linear convergence results. We also obtain linear convergence results using an alternated inertial projected gradient algorithm for which knowledge of the modulus of strong pseudomonotonicity and Lipschitz constant of the cost function are not needed. We compare numerically our algorithms with other projection-type algorithms in the literature. (C) 2022 Elsevier B.V. All rights reserved.

关键词： projection algorithms Variational inequality Pseudo-monotone operator Weak convergence Linear rate Hilbert spaces

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Tight l ∞ and l 1 error bounds for projection algorithms in conditional set membership estimation

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IFAC Proceedings Volumes 1999年第2期32卷 4106-4111页

作者： A. Garulli Dipartimento di Ingegneria dell'Informazione Università di Siena Via Roma 56 53100 Siena Italy

In set membership estimation, conditional problems arise when the estimate must belong to a given set of specified structure. Central and interpolatory projection algorithms provide conditional estimates that are suboptimal in terms of the worst-case estimation error. In order to precisely evaluate the suboptimality level of these estimators, tight upper bounds on the estimation error must be computed as a function of the conditional radius of information, which represents the minimum achievable error. In this paper, tight bounds are derived in the V ∞ and V 1 cases, for a general setting which allows to consider any compact set of feasible problem elements and linearly parametrized estimates.

关键词： Set membership estimation identification projection algorithms

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Random projection algorithms for convex set intersection problems

Random projection algorithms for convex set intersection pro...

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IEEE Conference on Decision and Control

作者： A. Nedić Department of Industrial and Enterprise Systems Engineering University of Illinois Urbana IL USA

The focus of this paper is on the set intersection problem for closed convex sets admitting projection operation in a closed form. The objective is to investigate algorithms that would converge (in some sense) if and only if the problem has a solution. To do so, we view the set intersection problem as a stochastic optimization problem of minimizing the “average” residual error of the set collection. We consider a stochastic gradient method as a main tool for investigating the properties of the stochastic optimization problem. We show that the stochastic optimization problem has a solution if and only if the stochastic gradient method is convergent almost surely. We then consider a special case of the method, namely the random projection method, and we analyze its convergence. We show that a solution of the intersection problem exists if and only if the random projection method exhibits certain convergence behavior almost surely. In addition, we provide convergence rate results for the expected residual error.

关键词： Convergence Gradient methods Random variables Markov processes projection algorithms Approximation methods

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Transient and steady-state analysis of filtered-x affine projection algorithms with imperfect secondary path estimate

Transient and steady-state analysis of filtered-x affine pro...

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International Symposium on Image and Signal Processing and Analysis

作者： A. Carini G.L. Sicuranza STI-University of Urbino Italy DEEI-Università di Trieste Italy

This paper provides an analysis based on energy conservation arguments of the transient and steady-state behaviors of two filtered-x affine projection algorithms in presence of an imperfect estimation of the secondary paths of an active noise control system. Very mild assumptions are posed on the system model, which is only required to have a linear dependence of the output from the filter coefficients.

关键词： Transient analysis Steady-state Algorithm design and analysis projection algorithms Finite impulse response filter Active noise reduction Nonlinear filters Convergence Adaptive filters Control systems

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Optimal Constraint Vectors for Set-Membership Proportionate Affine projection algorithms

Optimal Constraint Vectors for Set-Membership Proportionate ...

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IEEE/SP Workshop on Statistical Signal Processing (SSP)

作者： Marcelo J. M. Spelta Wallace A. Martins Federal University of Rio de Janeiro (UFRJ) PEE/COPPE Rio de Janeiro Brazil

Sparsity is an inherent feature of certain practical systems and appears in problems such as channel equalization and echo cancellation. Designed for exploiting the intrinsic structure of sparse environments, while also taking advantage of the data reuse and selection strategies, the set-membership proportionate affine projection algorithm (SM-PAPA) relies on the choice of a constraint vector (CV) that affects the behavior of the adaptive system. Although the selection of this CV has been based on some heuristics, a recent work proposes an optimal CV for the set-membership affine projection algorithm, a particular instance of the SM-PAPA. This paper adopts a convex optimization framework and generalizes the optimal CV concept for the SM-PAPA, allowing its use in sparse systems. Moreover, by using the gradient projection method for solving the related constrained convex problem, this paper demonstrates that the optimal CV can indeed be applied in real-time applications.

关键词： Signal processing algorithms Optimization IP networks Signal processing projection algorithms Convergence Conferences

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New variable step size affine projection algorithms

New variable step size affine projection algorithms

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International Conference on Communications (COMM)

作者： Felix Albu Constantin Paleologu Silviu Ciochina Faculty of Electrical Engineering Valahia University of Targoviste Targoviste Romania Telecommunication Department Politehnica University of Bucharest Bucuresti Romania

In this paper, we propose new variable step size affine projection algorithms whose step sizes are adjusted according to the square of a time-averaging estimate of the autocorrelation of a priori and a posteriori errors. The proposed algorithms have fast convergence, robustness against near-end signal variations (including double-talk) and do not require any a priori information about the acoustic environment. The simulation results indicate the good performance of the proposed algorithms when compared to similar algorithms.

关键词： Speech projection algorithms Adaptive filters Vectors Echo cancellers Convergence

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A Study on Multi-Constraint Robotic Arm Path Planning and Energy Optimization Based on RRT* and Gradient projection algorithms

A Study on Multi-Constraint Robotic Arm Path Planning and En...

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IEEE International Conference on Artificial Intelligence and Computer Applications (ICAICA)

作者： Yunye Li Jing Luo School of Economics and Management Changsha University of Science & Technology Changsha China

ISBN: (数字)9798350377255

ISBN: (纸本)9798350377262

To optimize the path planning of a six-degree-of-freedom robotic arm in complex environments, this paper proposes a multi-objective optimization method that integrates the gradient projection method and the RRT* algorithm. Based on the D-H parameter method, the kinematic model of the robotic arm is constructed. The gradient projection method is employed to optimize joint trajectories for energy efficiency, while the RRT* algorithm is used to solve the obstacle avoidance problem. On this basis, a multi-objective path planning model is established, aiming to minimize end-effector error and energy consumption. MATLAB simulations verify the effectiveness of the proposed method. Experimental results demonstrate that the method excels in path smoothness, energy optimization, and obstacle avoidance, providing theoretical and technical support for the application of robotic arms in industrial and service fields.

关键词： Energy consumption Service robots Heuristic algorithms Optimization methods End effectors Real-time systems Mathematical models Trajectory Collision avoidance projection algorithms

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Detecting Instability Potentials in Regularization for Fast Affine projection algorithms

Detecting Instability Potentials in Regularization for Fast ...

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Asilomar Conference on Signals, Systems & Computers

作者： Heping Ding Institute for Microstructural Sciences National Research Council Canada

In fast affine projection (FAP) adaptation algorithms, it is needed to explicitly or implicitly perform a matrix inversion, during which a small positive regularization factor plays an important role in keeping the algorithm stable and optimized. While existing schemes choose the regularization factor based on certain system criteria not related to the inversion, this paper proposes a simple scheme that dynamically diagnoses the inversion process itself for potentials of instability. This work paves the way for further studies on "minimal regularization and step-size control" technique. A FAP adopting this technique can be compared with FAPs with existing regularization schemes for convergence and steady state performance.

关键词： projection algorithms Financial advantage program Adaptive filters Convergence Stability Noise cancellation Size control Councils Steady-state Adaptive equalizers

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