Resolution Analysis of Imaging with ℓ1 Optimization
Resolution Analysis of Imaging with ℓ1 Optimization
复制标题
通过 ℓ1 优化进行成像分辨率分析
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Ilker Kocyigit
中科院分区：
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作者：
L. Borcea;Ilker Kocyigit
我们研究均匀介质中稀疏场景中点状光源或散射体的阵列成像。对于震源成像，阵列中的传感器是收集波场测量的接收器。对于成像散射体，阵列用波探测介质并记录回波。在任何一种情况下，成像都被描述为一个稀疏的促进$EELL_1$优化的问题，并且本文的目标是量化分辨率。我们同时考虑窄带和宽带成像，以及具有小阵列的几何设置。我们首先以未知因素位于成像网格上的情况为例，推导出依赖于场景稀疏性的分辨率极限。然后，我们考虑未知数在任意位置的一般情况。这种分析是基于对累积相互相干的估计和一个相关的概念，我们称之为相互作用系数。后者是对压缩传感最新结果的补充，它推导出了能够解释最差分辨率极限的确定性分辨率极限.
We study array imaging of a sparse scene of point-like sources or scatterers in a homogeneous medium. For source imaging, the sensors in the array are receivers that collect measurements of the wave field. For imaging scatterers, the array probes the medium with waves and records the echoes. In either case the image formation is stated as a sparsity promoting $ell_1$ optimization problem, and the goal of the paper is to quantify the resolution. We consider both narrow-band and broad-band imaging, and a geometric setup with a small array. We take first the case of the unknowns lying on the imaging grid and derive resolution limits that depend on the sparsity of the scene. Then we consider the general case with the unknowns at arbitrary locations. The analysis is based on estimates of the cumulative mutual coherence and a related concept, which we call the interaction coefficient. The latter complements recent results in compressed sensing by deriving deterministic resolution limits that account for worst-...