arXiv subjects

Youval Klioui

Publications and source records attributed to Youval Klioui.

4 recordsLinked to original sources

arXiv2026

SR-TL1: A Square-Root TL1-Norm Framework for Robust SMV DoA Estimation under Highly-Coherent Dictionaries

This paper proposes a Square-Root Transformed $L_1$-norm ($SR\text{-}TL_{1}$) sparse recovery framework for single-measurement-vector (SMV) direction of arrival (DoA) estimation under highly-coherent overcomplete dictionaries with angular-dependent array imperfections. The proposed framework combines the square-root Least Absolute Shrinkage and Selection Operator (square-root LASSO) framework which is known to be robust against noise variance with the Transformed $L_1$-norm ($TL_1$-norm), a non-convex penalty that shows a stronger recovery performance than the classical convex $L_1$-norm under highly-coherent dictionaries. We use the Difference of Convex Algorithm (DCA) along with the Alternating Direction Method of Multipliers (ADMM) algorithm to obtain simple, closed-form update rules and provide an efficient implementation that leverages the low-rank nature of the Gram matrix of the dictionary so as to obtain a computational complexity of at most $\mathcal{O}(MN)$ per iteration where $M$ is the array size and $N$ is the length of the dictionary. We additionally provide a convergence guarantee for the DCA iterates of $SR\text{-}TL_{1}$. Experimental verification of the proposed framework shows a lower sensitivity of the regularization hyperparameter to the noise variance level and a competitive recovery performance compared to state-of-the-art baselines.

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arXiv2025

Fast Single-Snapshot Harmonic Recovery with 2D Sparse Arrays using BCCB Matrices

We introduce an efficient implementation of sparse recovery methods for the problem of harmonic estimation with 2D sparse arrays using a single snapshot. By imposing a uniformity constraint on the harmonic grids of the subdictionaries used in the sparse recovery problem, in addition to a mild constraint on the array topology that consists in having the elements lie on a grid specified in half-wavelength units, we show that the Gram matrices that appear in these sparse recovery methods exhibit a block-circulant with circulant blocks (BCCB) structure. The BCCB structure is then exploited to reduce the computational complexity of the matrix-vector products that appear in these methods through the use of 2D fast Fourier transforms (FFT) from O((L1L2)^2) down to O(L1L2 log(L1L2)) operations per iterations, where L1, L2 are the lengths of the subdictionaries used for estimating the harmonics in the first and second dimension, respectively. We experimentally verify the proposed implementation using the iterative shrinkage thresholding algorithm (ISTA), the fast iterative shrinkage-thresholding algorithm (FISTA), and the alternating direction method of multipliers (ADMM) where we observe improvements

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arXiv2025

Circulant ADMM-Net for Fast High-resolution DoA Estimation

This paper introduces CADMM-Net and CHADMM-Net, two deep neural networks for direction of arrival estimation within the least-absolute shrinkage and selection operator (LASSO) framework. These two networks are based on a structured deep unfolding of the alternating direction method of multipliers (ADMM) algorithm through the use of circulant as well as Hermitian-circulant matrices. Along with a computational complexity of $\mathcal{O}(N\log(N))$ per layer for the inference, where $N$ is the length of the dictionary $\mathbf{A}$, they additionally exhibit a memory footprint of $N$ and approximately half of $N$ for CADMMNet and CHADMM-Net, respectively, compared with $N^{2}$ for ADMM-Net. Furthermore, these structured networks exhibit a competitive performance against ADMM-Net, LISTA, TLISTA, and THLISTA with respect to the detection rate, the angular root-mean square error, and the normalized mean squared error.

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arXiv2025

Toeplitz-Hermitian ADMM-Net for DoA Estimation

This paper presents Toeplitz-Hermitian ADMM-Net (THADMM-Net), a deep neural network obtained by deep unfolding the alternating direction method of multipliers (ADMM) algorithm for solving the least absolute shrinkage thresholding operator problem in the context of direction of arrival estimation. By imposing both a Toeplitz-Hermitian as well as positve semi-definite constraint on the learnable matrices, the total parameter count required per layer is reduced from $N^2$ to approximately $N$ where $N$ is the length of the dictionary used in the sparse recovery problem. Numerical simulations show that with a lower parameter count and depth, THADMM-Net outperforms Toeplitz-Lista with respect to the normalized mean-squared error, the detection rate, as well as the root mean-squared error over a signal-to-noise ratio between 0 dB and 35 dB.

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