AI 中文总结
研究针对射电干涉仪缺失短间距问题，引入CDD方法将图像分解为多尺度分量，通过实验发现干涉滤波响应可解耦，提出CDD-erf框架直接在图像域预测干涉图像，为模型与观测搭建定量桥梁。
AI 中文摘要
射电干涉仪存在缺失短间距问题，导致丢失大尺度弥散发射，这会低估气体质量并影响关键指标。目前量化这种尺度相关损失依赖计算密集的模拟观测，缺乏解析图像域框架。我们引入约束扩散分解（CDD）方法将输入图像分解为n个连续尺度空间分量，并应用于模拟的阿塔卡马大型毫米波/亚毫米波阵列（ALMA）对英仙座分子云的观测。发现干涉空间滤波响应可数学解耦，尺度相关通量恢复分数遵循一维误差函数。所提出的CDD-erf框架直接在图像域预测空间滤波干涉图像，绕过可见性模拟，为模型与干涉观测提供定量桥梁。
英文摘要
Radio interferometers suffer from the missing short-spacing problem, losing large-scale diffuse emission. This missing flux underestimates gas mass and biases key metrics like star formation efficiency. Quantifying this scale-dependent loss currently relies on computationally intensive mock observations, lacking an analytical image-domain framework. We introduce the Constrained Diffusion Decomposition (CDD) method to decompose an input image ($I_{\mathrm{in}}$) into $n$ continuous scale-space components, denoted as $I_l = \mathrm{CDD}_l(I_{\mathrm{in}})$ for $l \in [1, n]$, and apply it to simulated Atacama Large Millimeter/submillimeter Array (ALMA) observations of the Perseus molecular cloud across multiple array configurations. We find that the interferometric spatial filtering response can be mathematically decoupled: the scale-dependent flux recovery fraction follows a one-dimensional error function (\texttt{erf}), defined as $R(l) = \frac{B}{2} \left[ 1 - \mathrm{erf}\left( \frac{l - c_{\mathrm{recover}}}{w} \right) \right]$, where compact structures are effectively recovered, while extended emission decays monotonically as scales approach the maximum recoverable scale. The proposed CDD--\texttt{erf} framework predicts the spatially filtered interferometric image $I_{\mathrm{pred}}$ directly in the image domain, bypassing visibility simulations, mapping the true sky brightness distribution via the equation $I_{\mathrm{pred}} = \sum_{l=1}^{n} [ \mathrm{CDD}_l(I_{\mathrm{in}}) \times R(l)]$. This provides a quantitative bridge between model and interferometric observations.
CommentsAccepted by APJS comments welcome
