Least absolute deviations (LAD) is a statistical optimality criterion widely utilized in scenarios where a minority of measurements are contaminated by outliers of arbitrary magnitudes. In this paper, we delve into the robustness of the variant of adaptive iterative hard thresholding to outliers, known as graded fast hard thresholding pursuit (GFHTP$_1$) algorithm. Unlike the majority of the state-of-the-art algorithms in this field, GFHTP$_1$ does not require prior information about the signal's sparsity. Moreover, its design is parameterless, which not only simplifies the implementation process but also removes the intricacies of parameter optimization. Numerical experiments reveal that the GFHTP$_1$ algorithm consistently outperforms competing algorithms in terms of both robustness and computational efficiency.

翻译：最小绝对偏差（LAD）是一种统计最优性准则，在少数测量值被任意幅度的离群值污染的场景中被广泛使用。本文深入研究了自适应迭代硬阈值方法对离群值的鲁棒性变体，即分级快速硬阈值追踪（GFHTP$_1$）算法。与该领域大多数先进算法不同，GFHTP$_1$不需要关于信号稀疏性的先验信息。此外，其设计是无参数的，这不仅简化了实现过程，还消除了参数优化的复杂性。数值实验表明，GFHTP$_1$算法在鲁棒性和计算效率方面始终优于竞争算法。