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On the linear convergence rates of exchange and continuous methods for total variation minimization
Mathematical Programming ( IF 2.7 ) Pub Date : 2020-06-16 , DOI: 10.1007/s10107-020-01530-0
Axel Flinth , Frédéric de Gournay , Pierre Weiss

We analyze an exchange algorithm for the numerical solution total-variation regularized inverse problems over the space M($\Omega$) of Radon measures on a subset $\Omega$ of R d. Our main result states that under some regularity conditions, the method eventually converges linearly. Additionally, we prove that continuously optimizing the amplitudes of positions of the target measure will succeed at a linear rate with a good initialization. Finally, we propose to combine the two approaches into an alternating method and discuss the comparative advantages of this approach.

中文翻译:

交换的线性收敛率和总变差最小化的连续方法

我们分析了在 R d 的子集 $\Omega$ 上氡测度的空间 M($\Omega$) 上的数值解全变正正则化逆问题的交换算法。我们的主要结果表明,在某些规律性条件下,该方法最终线性收敛。此外,我们证明了持续优化目标度量位置的幅度将以线性速率成功并具有良好的初始化。最后,我们建议将这两种方法组合成一种交替方法,并讨论这种方法的比较优势。
更新日期:2020-06-16
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