论文标题
Tikhonov-TV正则化的自动平衡参数选择
Automatic balancing parameter selection for Tikhonov-TV regularization
论文作者
论文摘要
本文考虑了大规模线性不良反问题，其解决方案可以表示为平滑和分段恒定组件的总和。为了解决此类问题，我们考虑由两个必须平衡的术语组成的正规化器。也就是说，Tikhonov术语保证了平滑溶液组件的平滑度，而总变化（TV）正常器可促进非平滑溶液组件的块状。标量参数允许在这两个术语之间进行平衡，从而适当地分开并正规化解决方案的平滑和非平滑分量。本文提出了一种有效的算法，以通过乘数的交替方向方法（ADMM）解决此正则化问题。此外，使用可靠的统计数据，引入了一种用于自动选择平衡参数的新型算法。某些理论分析支持了所提出的方法，并提出了与不同的逆问题有关的数值实验，以验证平衡参数的选择。
This paper considers large-scale linear ill-posed inverse problems whose solutions can be represented as sums of smooth and piecewise constant components. To solve such problems we consider regularizers consisting of two terms that must be balanced. Namely, a Tikhonov term guarantees the smoothness of the smooth solution component, while a total-variation (TV) regularizer promotes blockiness of the non-smooth solution component. A scalar parameter allows to balance between these two terms and, hence, to appropriately separate and regularize the smooth and non-smooth components of the solution. This paper proposes an efficient algorithm to solve this regularization problem by the alternating direction method of multipliers (ADMM). Furthermore, a novel algorithm for automatic choice of the balancing parameter is introduced, using robust statistics. The proposed approach is supported by some theoretical analysis, and numerical experiments concerned with different inverse problems are presented to validate the choice of the balancing parameter.
