基于压缩感知的VLBI图像反卷积
Deconvolution of VLBI Images Based on Compressive Sensing
摘要：
VLBI（甚大基线干涉测量）射电望远镜中不完全可见度样本的直接反演会产生卷积伪影。由于天文射电源的正确分析和解释需要一幅无畸变的图像，而在紫外平面上填充所有采样点是不可能的任务，因此图像反卷积一直是VLBI成像的核心问题之一。目前应用最广泛的反褶积算法是基于最小二乘优化和最大熵方法的反褶积算法。在本文中，我们提出了一种新的算法，是基于一个新兴的范例称为压缩感知（CS）。在稀疏性条件下，压缩感知能够精确地重建信号或图像，只需要少量的随机样本。我们表明，CS是非常适合与VLBI成像问题，并证明所提出的方法是能够从其不完整的可见度样本采取椭圆轨迹在UV平面上的射电星系重建模拟图像。利用甚大阵3C459非对称射电星系的VLBI实测数据验证了该方法的有效性。
英文摘要：
Direct inversion of incomplete visibility samples in VLBI (Very Large Baseline Interferometry) radio telescopes produces images with convolutive artifacts. Since proper analysis and interpretations of astronomical radio sources require a non-distorted image, and because filling all of sampling points in the uv-plane is an impossible task, image deconvolution has been one of central issues in the VLBI imaging. Up to now, the most widely used deconvolution algorithms are based on least-squares-optimization and maximum entropy method. In this paper, we propose a new algorithm that is based on an emerging paradigm called compressive sensing (CS). Under the sparsity condition, CS capable to exactly reconstructs a signal or an image, using only a few number of random samples. We show that CS is well-suited with the VLBI imaging problem and demonstrate that the proposed method is capable to reconstruct a simulated image of radio galaxy from its incomplete visibility samples taken from elliptical trajectories in the uv-plane. The effectiveness of the proposed method is also demonstrated with an actual VLBI measured data of 3C459 asymmetric radio-galaxy observed by the VLA (Very Large Array).
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