论文标题
在大规模贝叶斯逆问题中解决溶液分解的混合投影方法
Hybrid Projection Methods for Solution Decomposition in Large-scale Bayesian Inverse Problems
论文作者
论文摘要
我们开发了用于计算大规模反问题解决方案的混合投影方法，其中解决方案代表不同随机组件的总和。这种情况在许多成像应用（例如，大气排放断层扫描中的异常检测）中出现，其中重建溶液可以表示为两个或多个组件的组合，并且每个组件都包含不同的平滑度或随机性能。在确定性反转或反向建模框架中，这些假设对应于总和中每个解决方案的不同正则化项。尽管可以在我们的框架中包含各种先前的假设，但我们将重点放在解决方案是稀疏解决方案和平滑解决方案的情况下。对于计算解决方案估计，我们开发了基于柔性和广义的Golub-Kahan过程的溶液分解方法的混合投影方法。这种方法整合了从广义的Golub-kahan bidiagonalization和柔性Krylov方法中的技术。提出的方法的好处是，可以在迭代中进行溶液的分解，并且在每次迭代时都可以自适应地选择正则化项和正则化参数。光声断层扫描和大气反向建模的数值结果证明了这些方法用于异常检测的潜力。
We develop hybrid projection methods for computing solutions to large-scale inverse problems, where the solution represents a sum of different stochastic components. Such scenarios arise in many imaging applications (e.g., anomaly detection in atmospheric emissions tomography) where the reconstructed solution can be represented as a combination of two or more components and each component contains different smoothness or stochastic properties. In a deterministic inversion or inverse modeling framework, these assumptions correspond to different regularization terms for each solution in the sum. Although various prior assumptions can be included in our framework, we focus on the scenario where the solution is a sum of a sparse solution and a smooth solution. For computing solution estimates, we develop hybrid projection methods for solution decomposition that are based on a combined flexible and generalized Golub-Kahan processes. This approach integrates techniques from the generalized Golub-Kahan bidiagonalization and the flexible Krylov methods. The benefits of the proposed methods are that the decomposition of the solution can be done iteratively, and the regularization terms and regularization parameters are adaptively chosen at each iteration. Numerical results from photoacoustic tomography and atmospheric inverse modeling demonstrate the potential for these methods to be used for anomaly detection.
