An Iterative Direct Sampling Method for Reconstructing Moving Inhomogeneities in Parabolic Problems
Bangti Jin, Fengru Wang, Jun Zou
我们在这项工作中提出了一种新的迭代直接采样方法,用于使用边界测量成像抛物线问题中的移动不均匀性。 它可以有效地识别移动不均匀性的位置和形状,当数据非常有限时,即使只有一对横向柯西数据,并且具有显着的数值稳定性,用于嘈杂数据和延长的时间范围。 该方法在抽象框架中制定,适用于线性和非线性抛物线问题,包括线性、非线性和混合型的不均匀性。 跨不同场景的数字实验显示了其对数据噪声的有效性和稳健性。
We propose in this work a novel iterative direct sampling method for imaging moving inhomogeneities in parabolic problems using boundary measurements. It can efficiently identify the locations and shapes of moving inhomogeneities when very limited data are available, even with only one pair of lateral Cauchy data, and enjoys remarkable numerical stability for noisy data and over an extended time horizon. The method is formulated in an abstract framework, and is applicable to linear and nonlinear...