A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
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DOI：
10.1137/080716542
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发表时间：
2009-01-01
影响因子：
2.1
通讯作者：
Teboulle, Marc
中科院分区：
文献类型：
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作者：
Beck, Amir;Teboulle, Marc
我们考虑了一类迭代收缩阈值算法(ISTA)来解决信号/图像处理中出现的线性逆问题。这类方法可以看作是经典梯度算法的推广，由于其简单，因此即使在矩阵数据密集的情况下也足以解决大规模问题。然而，众所周知，这些方法的收敛速度也很慢。本文提出了一种新的快速迭代收缩阈值算法(FISTA)，它既保持了ISTA算法的计算简单性，又具有较好的全局收敛速度，在理论和实际应用上都有明显的改善。基于小波的图像去模糊的初步数值结果证明了FISTA的性能，其速度比ISTA快几个数量级。
We consider the class of iterative shrinkage-thresholding algorithms (ISTA) for solving linear inverse problems arising in signal/image processing. This class of methods, which can be viewed as an extension of the classical gradient algorithm, is attractive due to its simplicity and thus is adequate for solving large-scale problems even with dense matrix data. However, such methods are also known to converge quite slowly. In this paper we present a new fast iterative shrinkage-thresholding algorithm (FISTA) which preserves the computational simplicity of ISTA but with a global rate of convergence which is proven to be significantly better, both theoretically and practically. Initial promising numerical results for wavelet-based image deblurring demonstrate the capabilities of FISTA which is shown to be faster than ISTA by several orders of magnitude.