Robust MIMO radar target localization based on lagrange programming neural network

Shi, Zhang-Lei; Wang, Hao; Leung, C. M.; So, Hing Cheung; Eurasip, Member

doi:10.1016/j.sigpro.2020.107574

Cited by 43 publications

(13 citation statements)

References 41 publications

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“…Since the

l_{1}

‐norm in the LASSO is not differentiable at

x = 0

, the conventional LPNN is not immediately applicable in this form. Although a regularization strategy is utilized in References 8,35, our proposed regularization ensures a rigorous theoretical convergence proof of the solution of the new smooth problem towards that of the LASSO. Given any

x \in ℝ

, we start with the following approximate for the absolute value (see Reference 38 for the whole procedure)

| x | \approx {| x |}_{k} = \frac{1}{k} \ln (2 (1 + \cosh (k x))), k \in ℕ .

…”

Section: Background and Motivationmentioning

confidence: 99%

“…Compressive sampling (CS) considers models for recovering signals from incomplete or even highly incomplete observation measurements 1–3 . CS arises in various engineering fields including, but not limited to, computer vision, acoustic networking, geotechnical engineering, magnetic resonance imaging 4–9 . CS‐based approaches have provided remarkable and efficient improvements, for example, a myriad of challenging applications have been developed in computer vision field such as autonomous driving systems, video surveillance, object detection, and tracking 7,10–12 .…”

Section: Introductionmentioning

confidence: 99%

“…In the last decades, numerous optimization issues that arise in various engineering applications require real‐time processing 8,20,21 . Classical digital techniques, as gradient projection‐based algorithms or subgradient strategies and so forth, are mostly not convenient from the standpoint of computational time or resource allocation in computer networks 16,17,22–23 .…”

Section: Introductionmentioning

confidence: 99%

“…The spirit of the approach is traced back to Reference 35, where a smooth approximation to the

l_{1} -

norm is utilized within the LPNN context. Later, the same strategy has been employed in Reference 8. In both latter papers, the approximation method implicitly introduces a new optimization problem, whose solution depends on a certain tuning parameter.…”

Section: Introductionmentioning

confidence: 99%

“…Also, the stability of the equilibrium point of the intermediate problems has not been examined as well. Actually, the reliability of the

l_{1} -

approximator approach used in References 8,35 has been empirically validated only.…”

Section: Introductionmentioning

confidence: 99%

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LPNN‐based approach for LASSO problem via a sequence of regularized minimizations

ZeglaouiAnis

HoumiaAnouar

Mejai

et al. 2021

Adaptive Control & Signal

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Summary In compressive sampling theory, the least absolute shrinkage and selection operator (LASSO) is a representative problem. Nevertheless, the non‐differentiable constraint impedes the use of Lagrange programming neural networks (LPNNs). We present in this article the 𝒫k‐LPNN model, a novel algorithm that tackles the LASSO minimization together with the underlying theory support. First, we design a sequence of smooth constrained optimization problems, by introducing a convenient differentiable approximation to the non‐differentiable l1‐norm constraint. Next, we prove that the optimal solutions of the regularized intermediate problems converge to the optimal sparse signal for the LASSO. Then, for every regularized problem from the sequence, the 𝒫k‐LPNN dynamic model is derived, and the asymptotic stability of its equilibrium state is established as well. Finally, numerical simulations are carried out to compare the performance of the proposed 𝒫k‐LPNN algorithm with both the LASSO‐LPNN model and a standard digital method.

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“…Since the