Performance Analysis of $l_0$ Norm Constraint Least Mean Square Algorithm

Su, Guolong; Jin, Jian; Gu, Yuantao; Wang, Jian

doi:10.1109/tsp.2012.2184537

Cited by 169 publications

(136 citation statements)

References 41 publications

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“…The measurement of e in Equation (13) is a Frobenius norm which is the common model of error [26]. As described in Section 2, we apply the negentropy and weighted 1 -norm to form the objective function, where the measurement of e is negentropy and the sparsity constraint can result in sparser results.…”

Section: The Reconstructed Signal Comparison Between Mse Criterion Anmentioning

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: The Reconstructed Signal Comparison Between Mse Criterion Anmentioning

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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show abstract

“…Several sparsity-aware modifications of the standard LMS have been introduced in the literature [7,8,9,10,11,12,13,24].…”

Section: Standard Lmsmentioning

confidence: 99%

“…In order to ensure a constant value for the term ησ 2 n /(2 − η) in the excess MSE equation of (49) for different values of sparsity S, σ 2 n is a constant set to 0.01. The step size µ is set to 0.05, while ρ r = 5 × 10 −4 and ǫ r = 0.05 in (10).…”

Section: Excess Msementioning

confidence: 99%

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Reweighted l1-norm penalized LMS for sparse channel estimation and its analysis

Taheri

Vorobyov

2014

Signal Processing

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A new reweighted l 1 -norm penalized least mean square (LMS) algorithm for sparse channel estimation is proposed and studied in this paper. Since standard LMS algorithm does not take into account the sparsity information about the channel impulse response (CIR), sparsity-aware modifications of the LMS algorithm aim at outperforming the standard LMS by introducing a penalty term to the standard LMS cost function which forces the solution to be sparse. Our reweighted l 1 -norm penalized LMS algorithm introduces in addition a reweighting of the CIR coefficient estimates to promote a sparse solution even more and approximate l 0 -pseudo-norm closer. We provide in depth quantitative analysis of the reweighted l 1 -norm penalized LMS algorithm. An expression for the excess mean square error (MSE) of the algorithm is also derived which suggests that under the right conditions, the reweighted l 1 -norm penalized LMS algorithm outperforms the standard LMS, which is expected. However, our quantitative analysis also answers the question of what is the maximum sparsity level in the channel for which the reweighted l 1 -norm penalized LMS algorithm is better than the standard LMS. Simulation results showing the better performance of the reweighted l 1 -norm penalized LMS algorithm compared to other existing LMS-type algorithms are given.

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“…where sgn(w i ) is a component-wise function, which is defined as: sgn(w i ) = w i /|w i | when w i ≠ 0 and sgn (w i ) = 0 when w i = 0; and ε is a threshold, which controls sparseness of w. In this letter, we set ε = 10 in computer simulation which was suggested by [21]. Then, update equation of sparse NLMS algorithm is given by…”

Section: System Model and Problem Formulationmentioning

confidence: 99%

Adaptive sparse system identification using normalized least mean fourth algorithm

Gui

Adachi

2013

Int J Communication

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SUMMARYNormalized least mean square (NLMS) was considered as one of the classical adaptive system identification algorithms. Because most of systems are often modeled as sparse, sparse NLMS algorithm was also applied to improve identification performance by taking the advantage of system sparsity. However, identification performances of NLMS type algorithms cannot achieve high-identification performance, especially in low signal-to-noise ratio regime. It was well known that least mean fourth (LMF) can achieve highidentification performance by utilizing fourth-order identification error updating rather than second-order. However, the main drawback of LMF is its instability and it cannot be applied to adaptive sparse system identifications. In this paper, we propose a stable sparse normalized LMF algorithm to exploit the sparse structure information to improve identification performance. Its stability is shown to be equivalent to sparse NLMS type algorithm. Simulation results show that the proposed normalized LMF algorithm can achieve better identification performance than sparse NLMS one.

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Performance Analysis of $l_0$ Norm Constraint Least Mean Square Algorithm

Cited by 169 publications

References 41 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

Reweighted l1-norm penalized LMS for sparse channel estimation and its analysis

Adaptive sparse system identification using normalized least mean fourth algorithm

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