A image reconstruction algorithm of transient sources based on combined sparsities of background and variation
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摘要:
针对射电干涉测量通过结合长时间观测的多组可见度数据对静态源进行高空间分辨率成像，但无法得到时变信息的问题，提出了一种基于背景和目标变化的直和空间上稀疏性的稀疏基线综合孔径动态场景图像重建算法。将起始时刻的亮温和相邻时刻的亮温变化作为待求解矢量，不同时刻的亮温表示为它们的和，构造测量方程，并利用起始时刻亮温和相邻时刻亮温的稀疏性进行求解，重建出不同时刻的瞬变源图像。仿真实验结果表明，对于小区域背景下的瞬变源，所提算法与已有方法相当，对于大区域背景下的瞬变源，所提算法优于已有方法。
Abstract:Radio interferometers can achieve high spatial resolution imaging by combining multiple groups of visibility data measured over long periods of time. However, the variable information of temporally variable source is missing. A image reconstruction algorithm of varied sources by sparse baseline aperture synthesis based on sparse constraint on direct sum of background and inter-frame difference is proposed. The brightness temperature at initial moment and the brightness temperature difference of adjacent moments are taken as the vector of solution to seek, and the brightness temperatures at different moments are the sums of them, which leads to the measuring equation of the brightness temperature at initial moment and the difference. Transient source images at different moments are reconstructed by solving the sparsity of brightness temperature at initial moment and brightness temperature difference of adjacent moments. The results of numerical experiments show that the proposed method matches the best on transient source in a local background and outperforms the existing methods on varying source in a global background.
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Key words:
- transient source /
- sparse recovery /
- radio astronomy /
- synthetic aperture imaging /
- interferometer
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图 2 首帧图像和帧间差分图像的像素基系数、小波基系数的分布
Figure 2. Distribution of coefficients of the first frame and difference in pixel and wavelet domainss
图 3 不同方法对小区域背景下瞬变源的重建结果
Figure 3. Reconstruction results of a transient source on a small region of background by different methods
图 4 小区域背景下，迭代次数增加时不同方法对瞬变源重建结果相对均方根误差的变化
Figure 4. RMSE of reconstruction results of transient source on a small region of background by different methods as number of iteration increasing
图 5 小区域背景下，迭代次数增加时不同方法对运动且强度变化的瞬变源重建结果相对均方根误差的变化
Figure 5. RMSE of reconstruction results of transient source which is moving and varying in intensity on a small region of background by different methods as number of iteration increasing
图 6 不同方法对暗背景下瞬变源的重建结果
Figure 6. Reconstruction results of transient source with dark background by different methods
图 7 暗背景下，每帧可见度函数采样数增加时不同方法对瞬变源重建结果相对均方根误差的变化
Figure 7. RMSE of reconstruction results of transient source with dark background by different methods as number of sampling of visibility increasing
图 8 不同方法对大区域背景下瞬变源的重建结果
Figure 8. Reconstruction results of transient source on a big region of background by different methods
图 9 大区域背景下，每帧可见度函数采样数增加时不同方法对瞬变源重建结果相对均方根误差的变化
Figure 9. RMSE of reconstruction results of transient source on a big region of background by different methods as number of sampling of visibility increasing
图 10 大区域背景下，强度变化率增加时diff-ℓ1算法对瞬变源重建结果相对均方根误差的变化
Figure 10. RMSE of reconstruction results of transient source on a big region of background by diff-ℓ1 algorithm as intensity varying rate increasing
图 11 大区域背景下，信噪比增加时diff-ℓ1算法对瞬变源重建结果相对均方根误差的变化
Figure 11. RMSE of reconstruction results of transient source on a big region of background by diff-ℓ1 algorithm as SNR increasing
图 12 不同方法对VLA的FRB测量数据的重建结果
Figure 12. Reconstruction results of measurement data of FRB on VLA by different methods
表 1 首帧图像和帧间差分图像的像素基系数、小波基系数的ℓ0范数
Table 1. ℓ0 norm of coefficients of the first frame and difference in pixel and wavelet domains
图像 像素基系数ℓ0范数 小波基系数ℓ0范数 首帧图像 1024 338 第2帧图像与首帧图像差分图像 30 208 
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