Parallel residual projection: a new paradigm for solving linear inverse problems
Parallel residual projection: a new paradigm for solving linear inverse problems
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DOI：
10.1038/s41598-020-69640-5
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发表时间：
2020-07
影响因子：
4.6
通讯作者：
Wei Miao;Vignesh Narayanan;Jr-Shin Li
中科院分区：
文献类型：
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作者：
Wei Miao;Vignesh Narayanan;Jr-Shin Li
求解大规模线性逆问题（LIP）的一个重大挑战是在问题规模不增加的情况下保持计算效率和精度。尽管有大量的方法可用于解决lip，但由于数据量庞大，处理超大问题的计算资源不足，安全性和隐私问题以及对相关增量或递减问题的兴趣，最近出现了各种挑战。消除这些障碍需要对现有方法进行全面升级，以提高计算效率、易于处理，并配备可扩展功能。因此，我们开发了并行残差投影（PRP），这是一种并行计算框架，涉及将大规模LIP分解为低复杂度的子问题，并融合子问题的解以形成原始LIP的解。我们分析了PRP的收敛性，并通过将其应用于网络推理和重力测量等复杂问题来强调其优点。我们表明，任何现有的求解LIP的算法都可以集成到PRP框架中，并用于解决子问题，同时处理当前的挑战。
A grand challenge to solve a large-scale linear inverse problem (LIP) is to retain computational efficiency and accuracy regardless of the growth of the problem size. Despite the plenitude of methods available for solving LIPs, various challenges have emerged in recent times due to the sheer volume of data, inadequate computational resources to handle an oversized problem, security and privacy concerns, and the interest in the associated incremental or decremental problems. Removing these barriers requires a holistic upgrade of the existing methods to be computationally efficient, tractable, and equipped with scalable features. We, therefore, develop the parallel residual projection (PRP), a parallel computational framework involving the decomposition of a large-scale LIP into sub-problems of low complexity and the fusion of the sub-problem solutions to form the solution to the original LIP. We analyze the convergence properties of the PRP and accentuate its benefits through its application to complex problems of network inference and gravimetric survey. We show that any existing algorithm for solving an LIP can be integrated into the PRP framework and used to solve the sub-problems while handling the prevailing challenges.