Compressed sensing radar imaging of polar mesospheric summer echoes using tracking and MIMO approaches (CS-PMSE-MIMO)

极地中间层夏季回波（PMSE）存在背后的基本物理原理如今已被很好地理解，其中大气湍流、带电冰粒和电子起着重要作用。鉴于这一基本认识，PMSE正被用作示踪剂来研究极地中间层高度复杂的大气动力学。典型大气雷达的PMSE观测很难解释，因为时间和空间特征不能分离。为了解决这些时间和空间的模糊性，由于所使用的系统（波束宽度、接收机数量有限等）和回波的性质，大气雷达成像（ARI）已经获得了不同程度的成功。一般来说，回声在水平漂移时呈现相对较长的相关时间（几百毫秒到几秒钟）。这种漂移不允许我们减少使用传统方法获得的空间相关性的不确定性。通常，波束形成类型的算法，其中一些包括某些类型的正则化，用于图像形成。不幸的是，这会导致图像中的伪影。一个可能的解决方案是利用关于图像的先验知识。通常，图像是稀疏的，只是随着时间缓慢变化。压缩感知（CS）技术在ARI中的应用已经被其他研究小组提出，但需要进一步的研究和实施。我们最近在ARI中应用相干MIMO技术来研究电离层的不规则性。这是MIMO首次应用于大气雷达。由于传感矩阵的高度结构化，MIMO与CS的结合提出了许多具有挑战性的研究问题。此外，CS与跟踪的结合为ARI开辟了一个新的研究领域。首先，理论上的挑战和机遇来自这样一个事实，即测量的数量可能不够大，因此现有的结果和算法无法应用于大问题。特殊的挑战来自于这样一个事实，即我们必须在没有可靠参考的情况下描述稀疏性，即它所处的域和时间动力学。这个问题的一个可能的解决方案可能是使用恢复和跟踪算法，这些算法不仅专注于在图像重建中尽最大努力，而且还会产生一些关于结果可信度的信息。除了模拟之外，我们将利用现有的雷达实验来创建稀疏性和时间动力学的物理动机模型，并进行新的实验来测试和改进我们提出的方法。包含MIMO，除了有助于反演之外，还可以作为测试场景来评估所提出的方法在无法使用MIMO的系统中的性能。

The basic physics behind the existence of polar mesospheric summer echoes (PMSE) is nowadays well understood, where atmospheric turbulence, charged ice particles and electrons play significant roles. Given this basic understanding, PMSE are being used as tracers to study the complicated atmospheric dynamics at polar mesospheric altitudes. PMSE observations with typical atmospheric radars are difficult to interpret, since temporal and spatial features can not be separated. In order to resolve these temporal and spatial ambiguities, atmospheric radar imaging (ARI) has been applied with different degrees of success, due to the systems used (beam widths, limited number of receivers, etc.), and due to the nature of the echoes. In general the echoes present relatively long correlations times (few hundreds of milliseconds to seconds) while they are horizontally drifting. Such drifting does not allow us to reduce the uncertainties on the obtained spatial correlations used in traditional methods. Usually, beamforming type algorithms, some of them including some type of regularization, are used for image formation. Unfortunately, this leads to artifacts in the image. A possible solution to this challenge is the exploitation of a priori knowledge about the image. Typically, the image is sparse and only changes slowly over time. The application of compressed sensing (CS) techniques in ARI has been proposed by other research groups but needs further investigation and implementation. We have recently applied coherent MIMO techniques in ARI to study ionospheric irregularities. This was the first time MIMO was used in atmospheric radars. Combining MIMO with CS rises many challenging research questions as the sensing matrix is highly structured. Furthermore, the combination of CS and tracking opens a new field of research in ARI. First theoretical challenges and opportunities arise from the fact that the number of measurements may not be large enough so that existing results and algorithms for large problems can not be applied. Special challenges arise from the fact that we have to characterize the sparsity, i.e., the domain in which it holds, and the time dynamics without having a reliable reference. A possible solution to this problem might be the use of recovery and tracking algorithms which do not focus on making a best effort in image reconstruction alone but also yield some information on the trustworthiness of the result. Besides simulations, we will exploit existing radar experiments to create physically motivated models for the sparsity and the time dynamics, and conduct new experiments to test and improve our proposed methods. The inclusion of MIMO, besides helping in the inversion, might serve also as test scenario to evaluate the performance of the proposed methods in systems not able to use MIMO.