论文标题
解决，跟踪和停止流线性反问题
Solving, Tracking and Stopping Streaming Linear Inverse Problems
论文作者
论文摘要
在大规模应用，包括医学成像，搭配差分方程求解器以及具有差异隐私的估计中，可以将基本的线性反问题重新构成流媒体问题。从理论上讲，可以使用记忆有效的，指数置的流求解器有效地解决流问题。在实践中，如果流式求解器在达到所需的准确性之前就被停止或良好，则会破坏其有效性。在特殊情况下，当潜在的线性逆问题是有限维度时，流求解器可以以实质性的计算成本定期评估剩余规范。当基础系统是无限的尺寸时，流求解器只能访问残差的嘈杂估计。尽管这种嘈杂的估计值在计算上是有效的，但仅当已知其精度时才有用。在这项工作中，我们严格地开发了一般的计算剩余估计量及其用于流求解器的不确定性集，并且我们在许多大规模的线性问题上证明了我们方法的准确性。因此，我们进一步使流求解器用于重要类别的线性反问题类别。
In large-scale applications including medical imaging, collocation differential equation solvers, and estimation with differential privacy, the underlying linear inverse problem can be reformulated as a streaming problem. In theory, the streaming problem can be effectively solved using memory-efficient, exponentially-converging streaming solvers. In practice, a streaming solver's effectiveness is undermined if it is stopped before, or well-after, the desired accuracy is achieved. In special cases when the underlying linear inverse problem is finite-dimensional, streaming solvers can periodically evaluate the residual norm at a substantial computational cost. When the underlying system is infinite dimensional, streaming solver can only access noisy estimates of the residual. While such noisy estimates are computationally efficient, they are useful only when their accuracy is known. In this work, we rigorously develop a general family of computationally-practical residual estimators and their uncertainty sets for streaming solvers, and we demonstrate the accuracy of our methods on a number of large-scale linear problems. Thus, we further enable the practical use of streaming solvers for important classes of linear inverse problems.
