Convergence of the Reweighted `1 Minimization Algorithm
نویسندگان
چکیده
The iteratively reweighted `1 minimization algorithm (IRL1) has been widely used for variable selection, signal reconstruction and image processing. However the convergence of the IRL1 has not been proved. In this paper, we prove that any sequence generated by the IRL1 is bounded and any accumulation point is a stationary point of the `2-`p minimization problem with 0 < p < 1. Moreover, the stationary point is a global minimizer and the convergence rate is approximately linear under certain conditions. We derive posteriori error bounds which can be used to construct practical stopping rules for the algorithm.
منابع مشابه
Improved Iteratively Reweighted Least Squares for Unconstrained
In this paper, we first study q minimization and its associated iterative reweighted algorithm for recovering sparse vectors. Unlike most existing work, we focus on unconstrained q minimization, for which we show a few advantages on noisy measurements and/or approximately sparse vectors. Inspired by the results in [Daubechies et al., Comm. Pure Appl. Math., 63 (2010), pp. 1–38] for constrained ...
متن کاملConvergence of the reweighted ℓ 1 minimization algorithm for ℓ 2-ℓ p minimization
The iteratively reweighted l1 minimization algorithm (IRL1) has been widely used for variable selection, signal reconstruction and image processing. In this paper, we show that any sequence generated by the IRL1 is bounded and any accumulation point is a stationary point of the l2-lp minimization problem with 0 < p < 1. Moreover, the stationary point is a global minimizer and the convergence ra...
متن کاملAn Iteratively Reweighted Least Square Implementation for Face Recognition
We propose, as an alternative to current face recognition paradigms, an algorithm using reweighted l2 minimization, whose recognition rates are not only comparable to the random projection using l1 minimization compressive sensing method of Yang et al [5], but also robust to occlusion. Through numerical experiments, reweighted l2 mirrors the l1 solution [1] even with occlusion. Moreover, we pre...
متن کاملConvergence of Reweighted `1 Minimization Algorithms and Unique Solution of Truncated `p Minimization
Extensive numerical experiments have shown that the iteratively reweighted `1 minimization algorithm (IRL1) is a very efficient method for variable selection, signal reconstruction and image processing. However no convergence results have been given for the IRL1. In this paper, we first give a global convergence theorem of the IRL1 for the `2-`p (0 < p < 1) minimization problem. We prove that a...
متن کاملImproved Iteratively Reweighted Least Squares for Unconstrained Smoothed 퓁q Minimization
In this paper, we first study q minimization and its associated iterative reweighted algorithm for recovering sparse vectors. Unlike most existing work, we focus on unconstrained q minimization, for which we show a few advantages on noisy measurements and/or approximately sparse vectors. Inspired by the results in [Daubechies et al., Comm. Pure Appl. Math., 63 (2010), pp. 1–38] for constrained ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011