标题： 固定频率下从散射振幅中对多尺度目标的新型采样方法 显示英文标题

标题： A novel sampling method for multiple multiscale targets from scattering amplitudes at a fixed frequency

摘要： 一种利用散射振幅的采样方法被提出用于逆声散射问题中的形状和位置重建。 计算中仅涉及矩阵乘法，因此这种新的采样方法非常容易和简单地实现。 借助远场算子的分解，我们建立了用于表征潜在散射体的inf-criterion。 此结果随后用于给出所提出的指示函数在散射体内部采样点的下界。 而对于散射体外部的采样点，我们证明了当采样点远离散射体边界时，指示函数像贝塞尔函数一样衰减。 我们还证明了所提出的指示函数对散射振幅连续依赖，这进一步表明该新的采样方法在数据误差方面具有极高的稳定性。 不同于经典的采样方法，如线性采样方法或分解方法，从数值角度来看，新的指示函数在其潜在目标边界附近取得最大值，并且当采样点远离边界时像贝塞尔函数一样衰减。 数值模拟也表明，所提出的采样方法可以处理多个多尺度情况，即使不同部件彼此靠近。 显示英文摘要

摘要： A sampling method by using scattering amplitude is proposed for shape and location reconstruction in inverse acoustic scattering problems. Only matrix multiplication is involved in the computation, thus the novel sampling method is very easy and simple to implement. With the help of the factorization of the far field operator, we establish an inf-criterion for characterization of underlying scatterers. This result is then used to give a lower bound of the proposed indicator functional for sampling points inside the scatterers. While for the sampling points outside the scatterers, we show that the indicator functional decays like the bessel functions as the sampling point goes away from the boundary of the scatterers. We also show that the proposed indicator functional continuously dependents on the scattering amplitude, this further implies that the novel sampling method is extremely stable with respect to errors in the data. Different to the classical sampling method such as the linear sampling method or the factorization method, from the numerical point of view, the novel indicator takes its maximum near the boundary of the underlying target and decays like the bessel functions as the sampling points go away from the boundary. The numerical simulations also show that the proposed sampling method can deal with multiple multiscale case, even the different components are close to each other.