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

极地中层夏季回波(PMSE)存在的基本物理机制现已为人们所熟知，大气湍流、带电冰粒和电子在其中发挥着重要作用。鉴于这一基本认识，PMSE正被用作研究极地中层高度复杂大气动力学的示踪剂。典型大气雷达的PMSE观测是很难解释的，因为时间和空间特征是不能分离的。为了解决这些时间和空间模糊问题，由于所使用的系统(波束宽度、接收器数量有限等)以及回波的性质，大气雷达成像(ARI)的应用取得了不同程度的成功。一般来说，回声在水平漂移时呈现出相对较长的关联时间(几百毫秒到几秒)。这种漂移不允许我们减少在传统方法中使用的所获得的空间相关性的不确定性。通常，波束形成类型的算法用于图像形成，其中一些算法包括某种类型的正则化。不幸的是，这会导致图像中出现伪影。这一挑战的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，并且随着时间的推移只会缓慢变化。压缩感知(CS)技术在ARI中的应用已经被其他研究小组提出，但还需要进一步的研究和实现。我们最近在ARI中应用了相干MIMO技术来研究电离层不规则性。这是MIMO首次用于大气雷达。由于感知矩阵的高度结构化，将MIMO与CS相结合提出了许多具有挑战性的研究问题。此外，CS和跟踪的结合为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，以至于现有的针对大型问题的结果和算法无法应用。特殊的挑战来自这样一个事实，即我们必须在没有可靠参考的情况下表征稀疏性，即它所在的域，以及时间动力学。这一问题的可能解决办法可能是使用恢复和跟踪算法，这些算法不仅侧重于尽最大努力进行图像重建，而且还提供一些关于结果可信度的信息。除了仿真，我们还将利用现有的雷达实验为稀疏性和时间动力学建立物理激励模型，并进行新的实验来测试和改进我们提出的方法。除了有助于反转之外，MIMO的加入还可以用作测试场景，以评估所提出的方法在不能使用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.