Analysis and synthesis are key steps of the radio-interferometric imaging process, serving as a bridge between visibility and sky domains. They can be expressed as partial Fourier transforms involving a large number of non-uniform frequencies and spherically-constrained spatial coordinates. Due to the data non-uniformity, these partial Fourier transforms are computationally expensive and represent a serious bottleneck in the image reconstruction process. The W-gridding algorithm achieves log-linear complexity for both steps by applying a series of 2D non-uniform FFTs (NUFFT) to the data sliced along the so-called $w$ frequency coordinate. A major drawback of this method however is its restriction to direction-cosine meshes, which are fundamentally ill-suited for large field of views. This paper introduces the HVOX gridder, a novel algorithm for analysis/synthesis based on a 3D-NUFFT. Unlike W-gridding, the latter is compatible with arbitrary spherical meshes such as the popular HEALPix scheme for spherical data processing. The 3D-NUFFT allows one to optimally select the size of the inner FFTs, in particular the number of W-planes. This results in a better performing and auto-tuned algorithm, with controlled accuracy guarantees backed by strong results from approximation theory. To cope with the challenging scale of next-generation radio telescopes, we propose moreover a chunked evaluation strategy: by partitioning the visibility and sky domains, the 3D-NUFFT is decomposed into sub-problems which execute in parallel, while simultaneously cutting memory requirements. Our benchmarking results demonstrate the scalability of HVOX for both SKA and LOFAR, considering state-of-the-art challenging imaging setups. HVOX is moreover computationally competitive with W-gridder, despite the absence of domain-specific optimizations in our implementation.

翻译：摘要：分析与综合是射电干涉成像过程中的关键步骤，充当可见度域与天域之间的桥梁。它们可表示为涉及大量非均匀频率及球面约束空间坐标的偏傅里叶变换。由于数据的非均匀性，这些偏傅里叶变换计算代价高昂，成为图像重建过程中的主要瓶颈。W网格算法通过对沿所谓w频率坐标切片的数据应用一系列二维非均匀快速傅里叶变换（NUFFT），实现了两步计算的线性对数复杂度。然而，该方法的主要缺陷在于其仅适用于方向余弦网格，而此类网格从根本上不适合大视场观测。本文提出HVOX网格化算法，一种基于三维NUFFT的分析/综合新算法。与W网格算法不同，该算法兼容任意球面网格（例如球面数据处理的流行方案HEALPix）。三维NUFFT允许用户最优选择内部FFT的尺寸（尤其是W平面数量），从而形成性能更优且自动调优的算法，并提供由逼近理论强结果支持的严格精度保证。为应对下一代射电望远镜的挑战性规模，我们进一步提出分块评估策略：通过划分可见度域与天域，将三维NUFFT分解为可并行执行的子问题，同时显著降低内存需求。我们的基准测试结果展示了HVOX在SKA和LOFAR上的可扩展性，考量了当前最具挑战性的成像配置。尽管我们的实现中未包含领域特定优化，HVOX在计算性能上仍与W网格算法具有竞争力。