The ``Residual-to-Residual DNN series for high-Dynamic range imaging'' (R2D2)
approach was recently introduced for Radio-Interferometric (RI) imaging in
astronomy. R2D2's reconstruction is formed as a series of residual images,
iteratively estimated as outputs of Deep Neural Networks (DNNs) taking the
previous iteration's image estimate and associated data residual as inputs. In
this work, we investigate the robustness of the R2D2 image estimation process,
by studying the uncertainty associated with its series of learned models.
Adopting an ensemble averaging approach, multiple series can be trained,
arising from different random DNN initializations of the training process at
each iteration. The resulting multiple R2D2 instances can also be leveraged to
generate ``R2D2 samples'', from which empirical mean and standard deviation
endow the algorithm with a joint estimation and uncertainty quantification
functionality. Focusing on RI imaging, and adopting a telescope-specific
approach, multiple R2D2 instances were trained to encompass the most general
observation setting of the Very Large Array (VLA). Simulations and real-data
experiments confirm that: (i) R2D2's image estimation capability is superior to
that of the state-of-the-art algorithms; (ii) its ultra-fast reconstruction
capability (arising from series with only few DNNs) makes the computation of
multiple reconstruction samples and of uncertainty maps practical even at large
image dimension; (iii) it is characterized by a very low model uncertainty.

这篇研究论文使用 Residual-to-Residual DNN（R2D2）方法进行高动态范围成像，通过集成学习的方式生成多个 R2D2 实例，从而提供了一种同时估计和量化不确定性的功能。结果表明，R2D2 的图像估计能力优于现有算法，计算多个重建样本和不确定性图在大图像尺寸下也非常实用，并且模型的不确定性非常低。

无线电天文学中带有模型不确定性量化的 R2D2 图像重建

R2D2 image reconstruction with model uncertainty quantification in radio  astronomy

Radio-interferometric (RI) imaging entails solving high-resolution
high-dynamic range inverse problems from large data volumes. Recent image
reconstruction techniques grounded in optimization theory have demonstrated
remarkable capability for imaging precision, well beyond CLEAN's capability.
These range from advanced proximal algorithms propelled by handcrafted
regularization operators, such as the SARA family, to hybrid plug-and-play
(PnP) algorithms propelled by learned regularization denoisers, such as AIRI.
Optimization and PnP structures are however highly iterative, which hinders
their ability to handle the extreme data sizes expected from future
instruments. To address this scalability challenge, we introduce a novel deep
learning approach, dubbed ``Residual-to-Residual DNN series for high-Dynamic
range imaging'. R2D2's reconstruction is formed as a series of residual images,
iteratively estimated as outputs of Deep Neural Networks (DNNs) taking the
previous iteration's image estimate and associated data residual as inputs. It
thus takes a hybrid structure between a PnP algorithm and a learned version of
the matching pursuit algorithm that underpins CLEAN. We present a comprehensive
study of our approach, featuring its multiple incarnations distinguished by
their DNN architectures. We provide a detailed description of its training
process, targeting a telescope-specific approach. R2D2's capability to deliver
high precision is demonstrated in simulation, across a variety of image and
observation settings using the Very Large Array (VLA). Its reconstruction speed
is also demonstrated: with only few iterations required to clean data residuals
at dynamic ranges up to 105, R2D2 opens the door to fast precision imaging.
R2D2 codes are available in the BASPLib library on GitHub.

通过引入一种深度学习方法，命名为 “高动态范围成像的残差到残差 DNN 系列”，解决了高分辨率高动态范围反问题的可扩展性挑战，同时提供了快速精确成像的能力。

R2D2 深度神经网络系列模型用于射电天文学中的快速精确成像

The R2D2 deep neural network series paradigm for fast precision imaging  in radio astronomy

We present a novel AI approach for high-resolution high-dynamic range
synthesis imaging by radio interferometry (RI) in astronomy. R2D2, standing for
"{R}esidual-to-{R}esidual {D}NN series for high-{D}ynamic range imaging", is a
model-based data-driven approach relying on hybrid deep neural networks (DNNs)
and data-consistency updates. Its reconstruction is built as a series of
residual images estimated as the outputs of DNNs, each taking the residual
dirty image of the previous iteration as an input. The approach can be
interpreted as a learned version of a matching pursuit approach, whereby model
components are iteratively identified from residual dirty images, and of which
CLEAN is a well-known example. We propose two variants of the R2D2 model, built
upon two distinctive DNN architectures: a standard U-Net, and a novel unrolled
architecture. We demonstrate their use for monochromatic intensity imaging on
highly-sensitive observations of the radio galaxy Cygnus~A at S band, from the
Very Large Array (VLA). R2D2 is validated against CLEAN and the recent RI
algorithms AIRI and uSARA, which respectively inject a learned implicit
regularization and an advanced handcrafted sparsity-based regularization into
the RI data. With only few terms in its series, the R2D2 model is able to
deliver high-precision imaging, significantly superior to CLEAN and matching
the precision of AIRI and uSARA. In terms of computational efficiency, R2D2
runs at a fraction of the cost of AIRI and uSARA, and is also faster than
CLEAN, opening the door to real-time precision imaging in RI.

用于射电干涉测量中高分辨率、高动态范围综合成像的一种新的人工智能方法。该方法基于混合深度神经网络（DNN）和数据一致性更新，通过将重建视为一系列以前一次迭代的残差脏图像作为输入的 DNN 的输出的残差图像来建立。该方法能够以较少的项提供高精度成像，并且在计算效率上比其他算法更快。