论文标题
使用多个测量向量将罪恶和尖峰解散
Demixing Sines and Spikes Using Multiple Measurement Vectors
论文作者
论文摘要
在本文中，我们通过多个测量损坏的向量解决了线频谱估计问题。这种情况出现在许多实际应用中，例如雷达，光学和地震成像，其中感兴趣的信号可以建模为频谱稀疏和被称为离群值的块状信号的总和。我们的目的是将两个组成部分解散，为此，我们设计了一个凸面问题，其目标功能促进了这两个结构。使用阳性三角多项式（PTP）理论，我们将双重问题重新制定为半准计划（SDP）。我们的理论结果指出，对于固定数量的测量n和恒定数量的离群值，只要满足最小频率分离条件，就可以使用我们的SDP问题恢复多达O（n）光谱线。我们的仿真结果还表明，增加每个测量向量的样品数量，降低了成功恢复的最低所需频率分离。
In this paper, we address the line spectral estimation problem with multiple measurement corrupted vectors. Such scenarios appear in many practical applications such as radar, optics, and seismic imaging in which the signal of interest can be modeled as the sum of a spectrally sparse and a blocksparse signal known as outlier. Our aim is to demix the two components and for that, we design a convex problem whose objective function promotes both of the structures. Using positive trigonometric polynomials (PTP) theory, we reformulate the dual problem as a semi-definite program (SDP). Our theoretical results states that for a fixed number of measurements N and constant number of outliers, up to O(N) spectral lines can be recovered using our SDP problem as long as a minimum frequency separation condition is satisfied. Our simulation results also show that increasing the number of samples per measurement vectors, reduces the minimum required frequency separation for successful recovery.
