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We present a simple and computationally efficient algorithm, based on the accelerated Newton's method, to solve the root finding problem associated with the projection onto the ℓ1-ball problem. Considering an interpretation of the Michelot's algorithm as Newton method, our algorithm can be understood as an accelerated version of the Michelot's algorithm, that needs significantly less major iterations...
This paper presents a new model order selection technique for signal processing applications related to source localization or subspace orthogonal projection techniques in large dimensional regime (Random Matrix Theory) when the noise environment is Complex Elliptically Symmetric (CES) distributed, with unknown scatter matrix. The proposed method consists first in estimating the Toeplitz structure...
This paper proposes a new Newton-based adaptive filtering algorithm, namely the Quasi-Newton Least-Mean Fourth (QNLMF) algorithm. The main goal is to have a higher order adaptive filter that usually fits the non-Gaussian signals with an improved performance behavior, which is achieved using the Newton numerical method. Both the convergence analysis and the steady-state performance analysis are derived...
This paper describes new algorithms that incorporates the non-uniform norm constraint into the zero-attracting and reweighted modified filtered-x affine projection or pseudo affine projection algorithms for active noise control. The simulations indicate that the proposed algorithms can obtain better performance for primary and secondary paths with various sparseness levels with insignificant numerical...
In this paper, we develop a greedy algorithm for sparse learning over a doubly stochastic network. In the proposed algorithm, nodes of the network perform sparse learning by exchanging their individual intermediate variables. The algorithm is iterative in nature. We provide a restricted isometry property (RIP)-based theoretical guarantee both on the performance of the algorithm and the number of iterations...
We present the theory of sequences of random graphs and their convergence to limit objects. Sequences of random dense graphs are shown to converge to their limit objects in both their structural properties and their spectra. The limit objects are bounded symmetric functions on [0,1]2. The kernel functions define an equivalence class and thus identify collections of large random graphs who are spectrally...
We extend our previous work on learning smooth graph signals from a small number of noisy signal samples. Minimizing the signal's total variation amounts to a non-smooth convex optimization problem. We propose to solve this problem using a combination of Nesterov's smoothing technique and accelerated coordinate descent. The resulting algorithm converges substantially faster, specifically for graphs...
This work examines the mean-square error performance of diffusion stochastic algorithms under a generalized coordinate-descent scheme. In this setting, the adaptation step by each agent is limited to a random subset of the coordinates of its stochastic gradient vector. The selection of which coordinates to use varies randomly from iteration to iteration and from agent to agent across the network....
This work develops a distributed optimization algorithm with guaranteed exact convergence for a broad class of left-stochastic combination policies. The resulting exact diffusion strategy is shown to have a wider stability range and superior convergence performance than the EXTRA consensus strategy. The exact diffusion solution is also applicable to non-symmetric left-stochastic combination matrices,...
In hearing aids (HAs), the acoustic coupling between the microphone and the receiver results in the system becoming unstable under certain conditions and causes artifacts commonly referred to as whistling or howling. The least mean square (LMS) class of algorithms is commonly used to mitigate this by providing adaptive feedback cancellation (AFC). The speech quality after AFC and the amount of added...
We present a method for segmenting a one-dimensional piecewise polynomial signal corrupted by an additive noise. The method's principal part is based on sparse modeling, and its formulation as a reweighted convex optimization problem is solved numerically by proximal splitting. The method solves a sequence of weighted l21-minimization problems, where the weights used for the next iteration are computed...
To realize a consensus problem based on wireless communications, it is necessary to consider several constraints caused by the natures of wireless communications such as communication error, coverage, capacity, multi-user interference, half-duplex and so on. This work focuses on half-duplex constraint and multi-user interference for a consensus problem and proposes a new Slotted-ALOHA that changes...
We propose a novel parallel essentially cyclic asynchronous algorithm for the minimization of the sum of a smooth (nonconvex) function and a convex (nonsmooth) regularizer. The framework hinges on Successive Convex Approximation (SCA) techniques and on a new global model that describes many asynchronous environments in a more faithful and exhaustive way with respect to state-of-the-art models. A key...
The approximation of stable linear time-invariant systems is a central task in many applications. Therefore, it is important to know if a given approximation process is stable and converges for all signals from the signal space or if it is unstable and diverges for certain signals. Further, in the case of divergence, it is interesting to know whether the set of signals with divergent approximation...
The iterative methods are well-known approaches to solve the one-dimensional phase retrieval problem. Amongst them, the error-reduction algorithm is often used since it can easily implement support constraints. Unfortunately this method often stagnates. Recently we have formulated the extended form of the one-dimensional discrete phase retrieval problem and we have assumed that the stagnation can...
Although the Hilbert transform plays an important role in many different applications, it is usually impossible to calculate it exactly in closed form. Therefore approximation methods are applied to determine numerically the Hilbert transform. The present paper studies a general class of approximation methods on signal spaces of finite Dirichlet energy. This class is characterized by two natural axioms,...
In this paper, a fractional order calculus based least mean square algorithm is proposed for complex system identification. The proposed algorithm, named as, fractional complex least mean square (FCLMS), successfully deals with the problem of complex error due to negative weights or complex input/output in the FLMS. For the evaluation purpose a complex linear system is considered. The FCLMS algorithm...
In this paper, we propose an adaptive framework for the variable step size of the fractional least mean square (FLMS) algorithm. The proposed algorithm named the robust variable step size-FLMS (RVSS-FLMS), dynamically updates the step size of the FLMS to achieve high convergence rate with low steady state error. For the evaluation purpose, the problem of system identification is considered. The experiments...
Finding a common point of multiple closed sets in a real Hilbert space has been an important task in a wide range of signal processing. In this paper, we study asymptotic properties of the parallel projection method (PPM) for closed sets satisfying a special feasibility condition, which holds in the context of certain sparse signal processing. Our analysis guarantees that the cluster point set of...
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