DoG-HiT：一种新的VLBI多尺度成像方法
DoG-HiT: A novel VLBI Multiscale Imaging Approach
摘要：
从甚长基线干涉测量（VLBI）数据重建图像与稀疏采样的傅立叶域（紫外覆盖）构成一个不适定的反卷积问题。它需要应用鲁棒算法，最大限度地提高从所有采样空间尺度中提取的信息，并最大限度地减少未采样尺度对图像质量的影响。本文提出了一种新的多尺度小波反卷积算法DoG-HiT，该算法将高斯小波差分（DoG）和硬图像阈值（HiT）相结合，用于稀疏采样的干涉数据的成像。基于DoG-HiT，我们提出了一个多步成像流水线的干涉数据分析。DoG-HiT通过采用灵活的DoG小波字典将压缩感知方法应用于成像，该小波字典被设计为平滑地适应UV覆盖。它使用封闭属性作为数据的保真度条款，只有最初和执行非凸，非光滑的优化，通过一个振幅守恒和总流量守恒的硬阈值分裂。DoG-HiT计算多分辨率支持作为副产品。最终的重建是通过自校准循环和成像与振幅和相位信息的多分辨率支持只适用于细化。我们证明了DoG-HiT的稳定性，并将其性能与使用合成数据的CLEAN和正则化最大似然（RML）方法进行的图像重建进行了基准测试。比较表明，DoG-HiT与RML重建实现的超分辨率相匹配，并超过了CLEAN实现的对扩展发射的灵敏度。应用正则化极大似然方法配备灵活的多尺度小波字典成像的干涉数据匹配的性能，最先进的凸优化成像算法，需要较少的先验和用户定义的约束。
英文摘要：
Reconstructing images from very long baseline interferometry (VLBI) data with sparse sampling of the Fourier domain (uv-coverage) constitutes an ill-posed deconvolution problem. It requires application of robust algorithms maximizing the information extraction from all of the sampled spatial scales and minimizing the influence of the unsampled scales on image quality. We develop a new multiscale wavelet deconvolution algorithm DoG-HiT for imaging sparsely sampled interferometric data which combines the difference of Gaussian (DoG) wavelets and hard image thresholding (HiT). Based on DoG-HiT, we propose a multi-step imaging pipeline for analysis of interferometric data. DoG-HiT applies the compressed sensing approach to imaging by employing a flexible DoG wavelet dictionary which is designed to adapt smoothly to the uv-coverage. It uses closure properties as data fidelity terms only initially and perform non-convex, non-smooth optimization by an amplitude conserving and total flux conserving hard thresholding splitting. DoG-HiT calculates a multiresolution support as a side product. The final reconstruction is refined through self-calibration loops and imaging with amplitude and phase information applied for the multiresolution support only. We demonstrate the stability of DoG-HiT and benchmark its performance against image reconstructions made with CLEAN and Regularized Maximum-Likelihood (RML) methods using synthetic data. The comparison shows that DoG-HiT matches the superresolution achieved by the RML reconstructions and surpasses the sensitivity to extended emission reached by CLEAN. Application of regularized maximum likelihood methods outfitted with flexible multiscale wavelet dictionaries to imaging of interferometric data matches the performance of state-of-the art convex optimization imaging algorithms and requires fewer prior and user defined constraints.
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