RLS Algorithm With Convex Regularization

Ekşioğlu, Ender M.; Tanc, A. Korhan

doi:10.1109/lsp.2011.2159373

Cited by 137 publications

(175 citation statements)

References 8 publications

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“…Many algorithms have been developed to solve the problem in (3) in the literature [12][13][14][15][16][17][18][19][20], where the mean square error (MSE) [21] criterion based on second-order statistics has been employed for these algorithms, which show their optimality when e is Gaussian noise. In practical applications, however the transmitted signals are distorted by not only Gaussian noise, but also other kinds of noise, such as burst noise and high noise.…”

Section: Introductionmentioning

confidence: 99%

Sparse Coding Algorithm with Negentropy and Weighted ℓ1-Norm for Signal Reconstruction

Zhao

Liu

Wang

et al. 2017

Entropy

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Abstract:Compressive sensing theory has attracted widespread attention in recent years and sparse signal reconstruction has been widely used in signal processing and communication. This paper addresses the problem of sparse signal recovery especially with non-Gaussian noise. The main contribution of this paper is the proposal of an algorithm where the negentropy and reweighted schemes represent the core of an approach to the solution of the problem. The signal reconstruction problem is formalized as a constrained minimization problem, where the objective function is the sum of a measurement of error statistical characteristic term, the negentropy, and a sparse regularization term, p -norm, for 0 < p < 1. The p -norm, however, leads to a non-convex optimization problem which is difficult to solve efficiently. Herein we treat the p -norm as a serious of weighted 1 -norms so that the sub-problems become convex. We propose an optimized algorithm that combines forward-backward splitting. The algorithm is fast and succeeds in exactly recovering sparse signals with Gaussian and non-Gaussian noise. Several numerical experiments and comparisons demonstrate the superiority of the proposed algorithm.

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Section: Introductionmentioning

confidence: 99%

Sparse Coding Algorithm with Negentropy and Weighted ℓ1-Norm for Signal Reconstruction

Zhao

Liu

Wang

et al. 2017

Entropy

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“…The work of [15] proposes an adaptive version of the greedy least squares method using partial orthogonalization to systems. The work of [16] modifies the RLS algorithm by using a general convex function of the system parameters, resulting in the l 0 -RLS and l 1 -RLS algorithms. In comparison to the LMS based algorithms, the RLS based algorithms have a faster convergence speed as well as yield more accurate parameter estimates.…”

Section: Introductionmentioning

confidence: 99%

“…Similar to [10], [16], the l 1 -norm of the parameter vector penalty is added to the RLS cost function. For tractability, we further approximate the l 1 -norm of the parameter vector penalty term as an adaptively weighted l 2 -norm of the parameter vector term, in which the weights are readily given by the inversion of the associated l 1 -norm of the parameter estimates that are currently available in the adaptive learning environment.…”

Section: Introductionmentioning

confidence: 99%

“…Additionally, an analysis on the convergence of the proposed algorithms is given. Sparse channel identification results are included to demonstrate that our ZA-RLS approach achieves better performance, in comparison to the existing l 1 -RLS algorithm of [16] and SPARLS algorithm of [14].…”

Section: Introductionmentioning

confidence: 99%

“…The l 1 -RLS algorithm: The l 1 -RLS algorithm [16] is based on minimizing the following cost function…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Zero Attracting Recursive Least Squares Algorithms

Hong

Gao

Chen

2016

IEEE Trans. Veh. Technol.

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Abstract-The l1-norm sparsity constraint is a widely used technique for constructing sparse models. In this contribution, two zero-attracting recursive least squares algorithms, referred to as ZA-RLS-I and ZA-RLS-II, are derived by employing the l1-norm of parameter vector constraint to facilitate the model sparsity. In order to achieve a closed-form solution, the l1-norm of the parameter vector is approximated by an adaptively weighted l2-norm, in which the weighting factors are set as the inversion of the associated l1-norm of parameter estimates that are readily available in the adaptive learning environment. ZA-RLS-II is computationally more efficient than ZA-RLS-I by exploiting the known results from linear algebra as well as the sparsity of the system. The proposed algorithms are proven to converge, and adaptive sparse channel estimation is used to demonstrate the effectiveness of the proposed approach.Index Terms-Zero attracting recursive least squares algorithm, adaptive channel estimation, sparse model, l1-norm

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Group sparse RLS algorithms

Ekşioğlu

2013

Adaptive Control & Signal

Self Cite

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Group sparsity is one of the important signal priors for regularization of inverse problems. Sparsity with group structure is encountered in numerous applications. However, despite the abundance of sparsity-based adaptive algorithms, attempts at group sparse adaptive methods are very scarce. In this paper, we introduce novel recursive least squares (RLS) adaptive algorithms regularized via penalty functions, which promote group sparsity. We present a new analytic approximation for`p ,0 norm to utilize it as a group sparse regularizer. Simulation results confirm the improved performance of the new group sparse algorithms over regular and sparse RLS algorithms when group sparse structure is present.

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RLS Algorithm With Convex Regularization

Cited by 137 publications

References 8 publications

Sparse Coding Algorithm with Negentropy and Weighted ℓ1-Norm for Signal Reconstruction

Sparse Coding Algorithm with Negentropy and Weighted ℓ1-Norm for Signal Reconstruction

Zero Attracting Recursive Least Squares Algorithms

Group sparse RLS algorithms

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