High Dynamic Range Solar Radio Imaging Based on Deconvolution Using Prolate Spheroidal Wave Functions
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摘要: 利用综合孔径射电望远镜对太阳进行观测时，通过对图像中存在的明亮扩展源进行准确建模并移除，可以更好地观测视场内的微弱源并提高图像的动态范围。在射电天文领域，主要利用CLEAN算法对图像中的明亮源进行移除，以显示微弱的背景。然而，使用图像像素作为基函数的CLEAN算法的固有限制导致其对扩展源的建模效果较差。为了克服这种限制，将基于长椭球面波函数（Prolate Spheroidal Wave Functions, PSWF）的去卷积方法应用于太阳射电成像。PSWF最优正交基由脏图中的感兴趣区域（Region of Interest, ROI）和UV覆盖共同决定。为了验证该方法的有效性，基于PSWF正交基对均匀圆环阵观测的太阳射电图像进行去卷积，并从动态范围和保真度两个方面定量化对比了CLEAN算法和基于PSWF正交基方法的性能。基于PSWF正交基去卷积方法剩余脏图中的微弱源更接近真实情况且动态范围更高。Abstract: When the synthetic aperture radio telescope is used to observe the Sun, faint sources can be revealed by accurately removing the bright extended sources. Moreover, high dynamic range imaging can be achieved. The inherent limitations of using image pixels as basis functions in the CLEAN algorithm commonly used in radio astronomy lead to poor results for modeling extended sources. In this paper, a deconvolution method based on Prolate Spheroidal Wave Functions (PSWF) is applied to solar radio imaging to overcome the limitations of the CLEAN algorithm. The optimal PSWF orthogonal basis is determined by the Region of Interest (ROI) in dirty images and UV coverage of the interferometric array. The PSWF orthogonal basis is applied to the deconvolution of the solar radio images observed by the uniform circular array to confirm its efficiency. Moreover, the performance of the CLEAN algorithm and the method using PSWF were quantitatively compared from two aspects including dynamic range and fidelity. The faint sources in the residual dirty images produced by deconvolution using PSWF orthogonal basis are closer to the true model. A higher dynamic range imaging can also be obtained by using PSWF.
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图 1 81单元均匀圆环阵阵列排布（红色点）和瞬时UV覆盖（蓝色点）（a）以及采样网格划分（b）
Figure 1. Configuration (red dots), snapshot UV coverage (blue dots)（a） and sampling grids of 81-element uniform circular array (b)
图 2 基于数值模拟源的干涉成像实验。（a）基于数值模拟的模型图像，（b）模型图像（a）的dB形式，（c）可见度函数添加不相关噪声之后的反演脏图，（d）感兴趣区域
Figure 2. Synthesis imaging simulation using a simulated source. (a) Model image using a simulated source, (b) model image shown in dB, (c) dirty image retrieved by visibilities adding uncorrelated noise, (d) Region of Interest (ROI)
图 4 不同去卷积方法的剩余脏图。（a）基于PSWF正交基对脏图中明亮源进行去卷积之后的剩余脏图，（b）基于洁化分量对脏图中明亮源进行去卷积之后的剩余脏图
Figure 4. Residual dirty images of different deconvolution methods. (a) Residual dirty image produced by removing the bright extended sources using PSWF orthonormal basis; (b) residual dirty image produced by removing the bright extended sources using CLEAN components
图 5 原始脏图以及两种去卷积方法的剩余脏图中微弱源的亮温分布剖面
Figure 5. Profiles of faint source’s brightness temperature distribution in the residual dirty images produced by two deconvolution methods and the initial dirty image
图 6 微弱矩形源和微弱高斯源保真度的评估范围
Figure 6. Evaluation range of fidelity for the faint rectangular source and the faint Gaussian source
图 7 不同形状微弱源保真度的累积曲线图。（a）原始脏图以及两种去卷积方法剩余脏图中微弱矩形源保真度的累积曲线图，（b）原始脏图以及两种去卷积方法剩余脏图中微弱高斯源保真度的累积曲线图
Figure 7. Cumulative histogram of the fidelity values of faint sources. (a) Cumulative histogram of the fidelity values of faint rectangular sources in the residual dirty image produced by two deconvolution methods and the initial dirty image, (b) cumulative histogram of the fidelity values of faint Gaussian sources in the residual dirty image produced by two deconvolution method and the initial dirty image
图 8 基于NoRH观测数据的干涉成像实验。（a）基于NoRH观测数据的模型图像，（b）可见度数据添加不相关噪声之后所反演的脏图，（c）ROI，（d）特征值分布情况
Figure 8. Synthesis imaging simulation using observations from the NoRH. (a) Model image using observations from the NoRH, (b) dirty image retrieved by visibilities adding uncorrelated noise, (c) ROI, (d) distribution of eigenvalues
图 9 不同去卷积方法的剩余脏图。 （a）基于PSWF正交基对脏图中明亮源进行去卷积之后的剩余脏图，（b）基于洁化分量对脏图中明亮源进行去卷积之后的剩余脏图
Figure 9. Residual dirty images of different deconvolution methods. (a) Residual dirty image produced by removing the bright extended sources using PSWF orthonormal basis, (b) residual dirty image produced by removing the bright extended sources using CLEAN components
表 1 两种去卷积方法所得微弱源的实际亮温与真实亮温差值的均值和方差
Table 1. Mean and variance of the difference between the brightness temperature of faint sources revealed by two deconvolution methods and the true brightness temperature
方法 均值/K 方差/K PSWF 1.60×104 9.86×104 CLEAN 2.84×104 1.89×105 
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表 2 脏图和两种去卷积方法的动态范围
Table 2. Dynamic range of dirty images and two deconvolution methods
方法 动态范围/dB 脏图 25.71 CLEAN 27.04 PSWF 36.75
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表 3 脏图和两种去卷积方法的动态范围
Table 3. Dynamic range of dirty images and twodeconvolution methods
方法 动态范围/dB 脏图 11.76 CLEAN 11.78 PSWF 18.50
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