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）存在背后的基本物理现在已经很好地理解，其中大气湍流，带电冰粒子和电子起着重要作用。基于这一基本认识，PMSE正被用来作为示踪剂研究极地中层高度复杂的大气动力学。典型大气雷达的PMSE观测结果难以解释，因为时间和空间特征不能分离。为了解决这些时间和空间模糊性，大气雷达成像（ARI）已被应用于不同程度的成功，由于所使用的系统（波束宽度，有限数量的接收器等），以及回声的性质一般来说，当回波水平漂移时，它们呈现相对长的相关时间（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，其中一些包括某种类型的正则化，用于图像形成。不幸的是，这导致图像中的伪影。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，并且仅随时间缓慢变化。压缩感知（CS）技术在ARI中的应用已被其他研究小组提出，但需要进一步的研究和实施。我们最近应用相干MIMO技术在ARI研究电离层的不规则性。这是MIMO首次用于大气雷达。MIMO与CS相结合提出了许多具有挑战性的研究问题，因为传感矩阵是高度结构化的。此外，CS和跟踪的结合开辟了ARI的一个新的研究领域。首先，理论上的挑战和机遇来自于这样一个事实，即测量的数量可能不够大，使得现有的结果和算法不能应用于大的问题。特殊的挑战来自于我们必须描述稀疏性的事实，即，它保持的域，以及没有可靠参考的时间动态。这个问题的一个可能的解决方案可能是使用的恢复和跟踪算法，不专注于在图像重建单独的最大努力，但也产生一些信息的结果的可信度。除了模拟，我们将利用现有的雷达实验来创建稀疏性和时间动态的物理激励模型，并进行新的实验来测试和改进我们提出的方法。除了有助于反演之外，包括MIMO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.