Tradeoffs Between Convergence Speed and Reconstruction Accuracy in Inverse Problems
Tradeoffs Between Convergence Speed and Reconstruction Accuracy in Inverse Problems
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DOI：
10.1109/tsp.2018.2791945
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发表时间：
2018-04-01
影响因子：
5.4
通讯作者：
Sapiro, Guillermo
中科院分区：
文献类型：
--
作者：
Giryes, Raja;Eldar, Yonina C.;Sapiro, Guillermo
用迭代算法求解反问题是一种普遍的方法，特别是对于大数据量的反问题。由于时间限制，可能的迭代次数通常是有限的，可能会影响可达到的精度。给定一个愿意容忍的误差，一个重要的问题是，是否有可能修改原始迭代，以获得更快的收敛到最小值，实现允许的误差，而不增加每次迭代的计算成本显着。依赖于最近的恢复技术开发的设置中，所需的信号属于一些低维集，我们showthat使用粗略估计这一套可能会导致更快的收敛，在成本的额外的重建误差有关的准确性的集合近似。我们的理论与稀疏恢复、压缩感知和深度学习的最新进展有关。特别是，它可以提供一个可能的解释，成功的近似的l（1）-最小化的解决方案，由神经网络层表示迭代，实践中学习的迭代收缩阈值算法。
Solving inverse problems with iterative algorithms is popular, especially for large data. Due to time constraints, the number of possible iterations is usually limited, potentially affecting the achievable accuracy. Given an error one is willing to tolerate, an important question is whether it is possible to modify the original iterations to obtain faster convergence to a minimizer achieving the allowed error without increasing the computational cost of each iteration considerably. Relying on recent recovery techniques developed for settings in which the desired signal belongs to some low-dimensional set, we showthat using a coarse estimate of this set may lead to faster convergence at the cost of an additional reconstruction error related to the accuracy of the set approximation. Our theory ties to recent advances in sparse recovery, compressed sensing, and deep learning. Particularly, it may provide a possible explanation to the successful approximation of the l(1)-minimization solution by neural networks with layers representing iterations, as practiced in the learned iterative shrinkage-thresholding algorithm.