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The advances in convex optimization techniques have offered new formulations of design with improved control over the performance of FIR filters. By using lifting techniques, the design of a length-L FIR filter can be formulated as a convex semidefinite program (SDP) in terms of an L\times L matrix that must be rank-1. Although this formulation provides means for introducing highly flexible design constraints on the magnitude and phase responses of the filter, convex solvers implementing interior point methods almost never provide a rank-1 solution matrix. To obtain a rank-1 solution, we propose a novel Directed Iterative Rank Refinement (DIRR) algorithm, where at each iteration a matrix is obtained by solving a convex optimization problem. The semidefinite cost function of that convex optimization problem favors a solution matrix whose dominant singular vector is on a direction determined in the previous iterations. Analytically it is shown that the DIRR iterations provide monotonic improvement, and the global optimum is a fixed point of the iterations. Over a set of design examples it is illustrated that the DIRR requires only a few iterations to converge to an approximately rank-1 solution matrix. The effectiveness of the proposed method and its flexibility are also demonstrated for the cases where in addition to the magnitude constraints, the constraints on the phase and group delay of filter are placed on the designed filter. [ABSTRACT FROM PUBLISHER]

A novel design approach is proposed for point-to-point iterative learning control (ILC), enabling system constraints to be satisfied while simultaneously addressing the requirement for high-performance tracking. It is shown that point-to-point ILC design can be formulated and solved using a successive projection first proposed by J. von Neumann, allowing a number of new point-to-point ILC algorithms to be developed and analyzed. To illustrate this framework, two new algorithms are derived with different convergence and computational properties for the constrained point-to-point ILC design problem. The proposed algorithms are validated on a robotic arm with experimental results demonstrating their effectiveness. [ABSTRACT FROM PUBLISHER]

In this work, we propose a strategy for optimizing a superpixel algorithm for video signals, in order to get closer to real time performances which are on the one hand needed for egocentric vision applications and on the other must be bearable by wearable technologies. Instead of applying the algorithm frame by frame, we propose a technique inspired to Bayesian filtering and to video coding which allows to re-initialize superpixels using the information from the previous frame. This results in faster convergence and demonstrates how performances improve with respect to the standard application of the algorithm from scratch at each frame. [ABSTRACT FROM AUTHOR]

Efficient optimization techniques are important to manage interference in emerging dense wireless networks. Here, we address interference management through power control as a general utility maximization problem. For the class of utility functions that are concave in the logarithm of the optimization variables, we propose a power control algorithm based on fixed-point iterations. The iterations converge to the globally optimal power vector. One key benefit is that, for a network with N transmitters and a centralized implementation of the power control algorithm, the computational complexity per iteration of the algorithm is \cal O(N^2). When implemented in a distributed fashion and allowing for a signaling complexity of N messages per iteration, the computation complexity is reduced to \cal O(N). We show that the proposed centralized and distributed versions of the algorithm converge to the optimal power vector at a linear rate. Our numerical results suggest that in most instances, the algorithm takes fewer than ten iterations to converge, even fewer if the initialization is close to the optimal power vector. The proposed algorithm is, therefore, very efficient for power control in slowly fading channels. Furthermore, unlike previous works in the literature, the proposed algorithm does not require the objective function to be separable into a sum of individual utilities. As an example, we present results for power control in a two-hop decode-and-forward cooperative relay network and illustrate the performance gains due to interference management. [ABSTRACT FROM AUTHOR]

This letter proposes a novel sparsity-aware adaptive filtering scheme and algorithms based on an alternating optimization strategy with shrinkage. The proposed scheme employs a two-stage structure that consists of an alternating optimization of a diagonally-structured matrix that speeds up the convergence and an adaptive filter with a shrinkage function that forces the coefficients with small magnitudes to zero. We devise alternating optimization least-mean square (LMS) algorithms for the proposed scheme and analyze its mean-square error. Simulations for a system identification application show that the proposed scheme and algorithms outperform in convergence and tracking existing sparsity-aware algorithms. [ABSTRACT FROM AUTHOR]

Statistical image reconstruction using penalized weighted least-squares (PWLS) criteria can improve image-quality in X-ray computed tomography (CT). However, the huge dynamic range of the statistical weights leads to a highly shift-variant inverse problem making it difficult to precondition and accelerate existing iterative algorithms that attack the statistical model directly. We propose to alleviate the problem by using a variable-splitting scheme that separates the shift-variant and (“nearly”) invariant components of the statistical data model and also decouples the regularization term. This leads to an equivalent constrained problem that we tackle using the classical method-of-multipliers framework with alternating minimization. The specific form of our splitting yields an alternating direction method of multipliers (ADMM) algorithm with an inner-step involving a “nearly” shift-invariant linear system that is suitable for FFT-based preconditioning using cone-type filters. The proposed method can efficiently handle a variety of convex regularization criteria including smooth edge-preserving regularizers and nonsmooth sparsity-promoting ones based on the \ell1-norm and total variation. Numerical experiments with synthetic and real in vivo human data illustrate that cone-filter preconditioners accelerate the proposed ADMM resulting in fast convergence of ADMM compared to conventional (nonlinear conjugate gradient, ordered subsets) and state-of-the-art (MFISTA, split-Bregman) algorithms that are applicable for CT. [ABSTRACT FROM PUBLISHER]

A small population-based particle swarm optimization (SPPSO) approach is presented to solve the problem of short-term hydrothermal scheduling (STHS). In the proposed approach, a novel mutation operation that selects the flying guides for each individual is employed to enhance the diversity of the small population. A DE algorithm is employed as an acceleration operation to accelerate the convergence of the approach in case that the optimal result has no significant improvements after several iterations. A migration operation is adopted to keep the swarm's crowding diversity above a desired level. In addition, a special repair procedure, instead of the penalty function approach, is applied to handle the complex equality constraints of STHS. The effectiveness of the approach is demonstrated through three hydrothermal test systems published in literature. The results are also compared with those obtained by other evolutionary methods. The fuel cost as well as other performance of the proposed approach has been found to be quite impressive. It is shown that the SPPSO approach can provide a better solution at lesser computational time and effort. [ABSTRACT FROM PUBLISHER]

Consensus algorithms have generated a lot of interest due to their ability to compute globally relevant statistics by only exploiting local communications among sensors. However, when implemented over wireless sensor networks, the inherent iterative nature of consensus algorithms may cause a large energy consumption. Hence, to make consensus algorithms really appealing in sensor networks, it is necessary to minimize the energy necessary to reach a consensus, within a given accuracy. We propose a method to optimize the network topology and the power allocation over each active link in order to minimize the energy consumption. We consider two network models: a deterministic model, where the nodes are located arbitrarily but their positions are known, and a random model, where the network topology is modeled as a random geometric graph (RGG). In the first case, we show how to convert the topology optimization problem, which is inherently combinatorial, into a parametric convex problem, solvable with efficient algorithms. In the second case, we optimize the power transmitted by each node, exploiting the asymptotic distributions of the eigenvalues of the adjacency matrix of an RGG. We further show that the optimal power can be found as the solution of a convex problem. The theoretical findings are corroborated with extensive simulation results. [ABSTRACT FROM PUBLISHER]

We present two efficient discrete parameter simulation optimization (DPSO) algorithms for the long-run average cost objective. One of these algorithms uses the smoothed functional approximation (SFA) procedure, while the other is based on simultaneous perturbation stochastic approximation (SPSA). The use of SFA for DPSO had not been proposed previously in the literature. Further, both algorithms adopt an interesting technique of random projections that we present here for the first time. We give a proof of convergence of our algorithms. Next, we present detailed numerical experiments on a problem of admission control with dependent service times. We consider two different settings involving parameter sets that have moderate and large sizes, respectively. On the first setting, we also show performance comparisons with the well-studied optimal computing budget allocation (OCBA) algorithm and also the equal allocation algorithm. [ABSTRACT FROM AUTHOR]

In cooperative spectrum sensing (CSS), an optimal decision fusion rule can effectively improve the performance of the secondary system. Considering that a priori knowledge about the characteristics of primary users and secondary users (SUs) is usually unknown in practice, we propose a learning automata-based algorithm to derive the optimal voting rule for decision fusion in CSS. The proposed algorithm can work with any detection method used at SUs. Its convergence and robustness are shown here. Its stability is also analyzed by using noncooperative game theory. The condition that the obtained optimal voting rule remains unchanged is derived based on the concept of subgame perfect Nash equilibrium. It is shown that the proposed algorithm generally does not need to run many times and can work at a low cost in practice. Computer simulations validate the effectiveness of the proposed scheme. [ABSTRACT FROM PUBLISHER]

This article proposes a new algorithm to compute the projection on the set of images whose total variation is bounded by a constant. The projection is computed through a dual formulation that is solved by first order non-smooth optimization methods. This yields an iterative algorithm that applies iterative soft thresholding to the dual vector field, and for which we establish convergence rate on the primal iterates. This projection algorithm can then be used as a building block in a variety of applications such as solving inverse problems under a total variation constraint, or for texture synthesis. Numerical results are reported to illustrate the usefulness and potential applicability of our TV projection algorithm on various examples including denoising, texture synthesis, inpainting, deconvolution and tomography problems. We also show that our projection algorithm competes favorably with state-of-the-art TV projection methods in terms of convergence speed. [ABSTRACT FROM AUTHOR]

We propose a new fast algorithm for solving one of the standard formulations of image restoration and reconstruction which consists of an unconstrained optimization problem where the objective includes an l2 data-fidelity term and a nonsmooth regularizer. This formulation allows both wavelet-based (with orthogonal or frame-based representations) regularization or total-variation regularization. Our approach is based on a variable splitting to obtain an equivalent constrained optimization formulation, which is then addressed with an augmented Lagrangian method. The proposed algorithm is an instance of the so-called alternating direction method of multipliers, for which convergence has been proved. Experiments on a set of image restoration and reconstruction benchmark problems show that the proposed algorithm is faster than the current state of the art methods. [ABSTRACT FROM AUTHOR]

We give the first complete theoretical convergence analysis for the iterative extensions of the Sturm/Triggs algorithm. We show that the simplest extension, SIESTA, converges to nonsense results. Another proposed extension has similar problems, and experiments with ‘balanced’ iterations show that they can fail to converge or become unstable. We present CIESTA, an algorithm that avoids these problems. It is identical to SIESTA except for one simple extra computation. Under weak assumptions, we prove that CIESTA iteratively decreases an error and approaches fixed points. With one more assumption, we prove it converges uniquely. Our results imply that CIESTA gives a reliable way of initializing other algorithms such as bundle adjustment. A descent method such as Gauss-Newton can be used to minimize the CIESTA error, combining quadratic convergence with the advantage of minimizing in the projective depths. Experiments show that CIESTA performs better than other iterations. [ABSTRACT FROM AUTHOR]

Mean-Shift (MS) is a powerful nonparametric clustering method. Although good accuracy can be achieved, its computational cost is particularly expensive even on moderate data sets. In this paper, for the purpose of algorithmic speedup, we develop an agglomerative MS clustering method along with its performance analysis. Our method, namely Agglo-MS, is built upon an iterative query set compression mechanism which is motivated by the quadratic bounding optimization nature of MS algorithm. The whole framework can be efficiently implemented in linear running time complexity. We then extend Agglo-MS into an incremental version which performs comparably to its batch counterpart. The efficiency and accuracy of Agglo-MS are demonstrated by extensive comparing experiments on synthetic and real data sets. [ABSTRACT FROM PUBLISHER]

This work proposes an in-network distributed algorithm for the energy optimal routing in a wireless sensor network. The routing problem is described as a minimum-cost multi-commodity network flow problem by Linear programming. Based on the convex programming theory we use the dual decomposition theorem to derive the distributed algorithm on a mathematical basic. The algorithm computes the exact energy optimal routing in the network without any central node or the knowledge about the whole network structure, using only peer-to-peer communication between neighboring nodes. In contrast to other works in this area, the presented approach is not limited to strictly convex objective functions and it handles linear objective functions. [ABSTRACT FROM PUBLISHER]

For parallel distributed sensor systems with statistically independent sensor decision rules, Chair and Varshney in [2] has obtained the optimal fusion rule. On the other hand, under a given fusion rule, the optimal sensor compression rules have been proposed by Zhu et al. in [21], [23] for generally distributed and dependent sensor observations. An open problem is how to simultaneously obtain an optimal fusion rule and optimal sensor compression rules for general parallel distributed sensor decision systems. Obviously, the exhaustive method for searching for the optimal fusion rule is computationally intractable. For general parallel distributed sensor decision systems, we provide necessary conditions of an optimal fusion rule and optimal sensor compression rules and propose a computationally efficient iterative algorithm to simultaneously/alternately search for a fusion rule and sensor compression rules by combining both Zhu's and Chair and Varshney's methods. Moreover, the algorithm is extended to multiple bit compression and Network decision systems. Numerical examples show that the fusion rule obtained by the algorithm is in most cases the same as the optimal fusion rule obtained by the exhaustive method, therefore, it is effective and near optimal. [ABSTRACT FROM AUTHOR]