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Semiclassical Sampling and Discretization of Certain Linear Inverse Problems
SIAM Journal on Mathematical Analysis ( IF 2.2 ) Pub Date : 2020-11-12 , DOI: 10.1137/19m123868x
Plamen Stefanov

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 5554-5597, January 2020.
We study sampling of functions $f$ and their images $Af$ under Fourier integral operators $A$ at rates $sh$ with $s$ fixed and $h$ a small parameter. We show that the Nyquist sampling limit of $Af$ and $f$ are related by the canonical relation of $A$ using semiclassical analysis. We apply this analysis to the Radon transform in the parallel and the fan-beam coordinates. We explain and illustrate the optimal sampling rates for $Af$, the aliasing artifacts, and the effect of averaging (blurring) the data $Af$. We prove a Weyl type of estimate on the minimal number of sampling points to recover $f$ stably in terms of the volume of its semiclassical wave front set.


中文翻译:

某些线性反问题的半经典采样和离散化

SIAM数学分析杂志,第52卷,第6期,第5554-5597页,2020年1月。
我们研究了函数$ f $及其图像$ Af $在傅立叶积分算子$ A $下以$ sh $和$ s $的比率进行采样的情况。固定和$ h $一个小参数。我们显示,使用半经典分析,$ Af $和$ f $的奈奎斯特采样极限与$ A $的规范关系相关。我们将此分析应用于平行和扇形束坐标中的Radon变换。我们解释并说明了$ Af $的最佳采样率,混叠失真以及对数据$ Af $进行平均(模糊)的效果。我们证明了Weyl类型的估计是根据其半经典波前集合的数量稳定地恢复$ f $的最小采样点数。
更新日期:2020-11-13
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