论文标题
线性和非线性未知数的反问题的平行采样算法
A parallel sampling algorithm for inverse problems with linear and nonlinear unknowns
论文作者
论文摘要
我们为计算逆问题得出了平行采样算法，该算法列出了未知的线性强迫项和要恢复的非线性参数的向量。假定数据是嘈杂的，并且问题的线性部分是错误的。非线性参数M的向量M被建模为随机变量。扩张参数alpha用于扩展线性未知的规律性，并且也被建模为随机变量。 （M; alpha）的后验概率分布是按照与最大似然正规化参数选择相关的方法得出的[5]。我们方法的一个主要区别在于，与[5]中不同，我们不会将自己限制在α的最大可能性价值上。然后，我们得出了一种并行采样算法，在该算法中，我们可以在[4]中像[4]中的[4]相结合以接受或拒绝它们的建议。该算法非常适合提案昂贵的问题。然后，我们将其应用于地震学的反问题。我们展示了我们的结果与从最大似然（ML），广义交叉验证（GCV）和受约束最小二乘（CLS）算法获得的结果相比。
We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is ill-posed. The vector of nonlinear parameters m is modeled as a random variable. A dilation parameter alpha is used to scale the regularity of the linear unknown and is also modeled as a random variable. A posterior probability distribution for (m; alpha) is derived following an approach related to the maximum likelihood regularization parameter selection [5]. A major difference in our approach is that, unlike in [5], we do not limit ourselves to the maximum likelihood value of alpha. We then derive a parallel sampling algorithm where we alternate computing proposals in parallel and combining proposals to accept or reject them as in [4]. This algorithm is well-suited to problems where proposals are expensive to compute. We then apply it to an inverse problem in seismology. We show how our results compare favorably to those obtained from the Maximum Likelihood (ML), the Generalized Cross Validation (GCV), and the Constrained Least Squares (CLS) algorithms.
