# Sparsity-Aware Adaptive Algorithms Based on Alternating Optimization with Shrinkage

arXiv: https://arxiv.org/abs/1401.0463 · HTML: https://mlsanity.com/paper/1401.0463/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jan 2014.

## Built on by (most cited first, 15 of 15)

- [Robust Adaptive Filtering Based on Exponential Functional Link Network](https://mlsanity.com/paper/2102.02952/) (2021)
- [A survey on active noise control techniques -- Part I: Linear systems](https://mlsanity.com/paper/2110.00531/) (2021)
- [Online Graph Topology Learning via Time-Vertex Adaptive Filters: From Theory to Cardiac Fibrillation](https://mlsanity.com/paper/2411.01567/) (2024)
- [Study of Proximal Normalized Subband Adaptive Algorithm for Acoustic Echo Cancellation](https://mlsanity.com/paper/2108.10219/) (2021)
- [Active noise control techniques for nonlinear systems](https://mlsanity.com/paper/2110.09672/) (2021)
- [Study of Frequency domain exponential functional link network filters](https://mlsanity.com/paper/2201.05501/) (2022)
- [Study of filtered-x logarithmic recursive least p-power algorithm](https://mlsanity.com/paper/2202.00560/) (2022)
- [Conjugate Gradient Adaptive Learning with Tukey's Biweight M-Estimate](https://mlsanity.com/paper/2203.10205/) (2022)
- [Study of Robust Sparsity-Aware RLS algorithms with Jointly-Optimized Parameters for Impulsive Noise Environments](https://mlsanity.com/paper/2204.08990/) (2022)
- [Sparsity-Aware Robust Normalized Subband Adaptive Filtering algorithms based on Alternating Optimization](https://mlsanity.com/paper/2205.07172/) (2022)
- [Design and Analysis of Robust Resilient Diffusion over Multi-Task Networks Against Byzantine Attacks](https://mlsanity.com/paper/2206.12749/) (2022)
- [Study of General Robust Subband Adaptive Filtering](https://mlsanity.com/paper/2208.08856/) (2022)
- [Analysis of Partially-Calibrated Sparse Subarrays for Direction Finding with Extended Degrees of Freedom](https://mlsanity.com/paper/2408.03236/) (2024)
- [Direction of Arrival Estimation with Sparse Subarrays](https://mlsanity.com/paper/2409.00033/) (2024)
- [Design and Analysis of Robust Adaptive Filtering with the Hyperbolic Tangent Exponential Kernel M-Estimator Function for Active Noise Control](https://mlsanity.com/paper/2508.13018/) (2025)

## Abstract (arXiv)

This letter proposes a novel sparsity-aware adaptive filtering scheme and algorithms based on an alternating optimization strategy with shrinkage. The proposed scheme employs a two-stage structure that consists of an alternating optimization of a diagonally-structured matrix that speeds up the convergence and an adaptive filter with a shrinkage function that forces the coefficients with small magnitudes to zero. We devise alternating optimization least-mean square (LMS) algorithms for the proposed scheme and analyze its mean-square error. Simulations for a system identification application show that the proposed scheme and algorithms outperform in convergence and tracking existing sparsity-aware algorithms.