[Paper Review] HVOX: Scalable Interferometric Synthesis and Analysis of Spherical Sky Maps

Sepand Kashani, Joan Rué‐Queralt+2 more|arXiv (Cornell University)|Jun 9, 2023

Radio Astronomy Observations and Technology4 citations

TL;DR

HVOX introduces a novel 3D non-uniform FFT (NUFFT)-based gridder for scalable interferometric analysis and synthesis on arbitrary spherical meshes, such as HEALPix, enabling high-accuracy imaging with controlled error bounds. It achieves runtime competitiveness with W-gridding and relative accuracy up to 10⁻⁹ in double precision, while supporting chunked parallel processing to reduce memory use.

ABSTRACT

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.

Motivation & Objective

• To address the computational bottleneck of interferometric analysis and synthesis in wide-field radio astronomy, especially for large-scale telescopes like SKA and LOFAR.
• To overcome the limitations of W-gridding, which relies on direction-cosine meshes and fails to support arbitrary spherical pixelizations like HEALPix.
• To enable accurate, scalable, and memory-efficient image production directly on HEALPix and other spherical meshes with guaranteed error control.
• To develop a software framework that integrates seamlessly into existing pipelines like RASCIL, enabling drop-in replacement for current DCOS-based gridders.
• To provide a foundation for future methods in sparse imaging, calibration, and stochastic optimization on spherical sky maps.

Proposed method

• HVOX employs a type-3 non-uniform FFT (NUFFT) in three dimensions to perform analysis and synthesis, allowing direct mapping between visibility and sky domains on arbitrary spherical meshes.
• The algorithm decouples the 3D FFT size from the image resolution, enabling optimal selection of inner FFT dimensions and improved performance and accuracy.
• A chunked evaluation strategy partitions visibility and sky data into sub-problems, enabling parallel execution and reducing memory requirements by processing only local data chunks.
• The method leverages strong theoretical guarantees from approximation theory to ensure controlled accuracy, achieving relative errors up to 10⁻⁹ in double precision.
• The implementation uses the FINUFFT library and the PyData stack, providing a high-level, user-friendly API for integration into radio astronomy software like RASCIL.
• The framework supports arbitrary spherical meshes, including HEALPix, and avoids interpolation-induced accuracy loss common in W-gridding when mapping to non-DCOS grids.

Experimental results

Research questions

• RQ1 Can a 3D-NUFFT-based approach achieve high-accuracy interferometric synthesis and analysis on arbitrary spherical meshes like HEALPix, without relying on direction-cosine grids?
• RQ2 How does the HVOX method compare in computational performance and memory efficiency to W-gridding, especially for extreme-scale imaging tasks?
• RQ3 To what extent can chunked evaluation strategies reduce memory usage and enable parallelization in interferometric imaging pipelines?
• RQ4 Can HVOX maintain accuracy guarantees (e.g., 10⁻⁹ relative error) across different mesh types and imaging configurations, including sparse fields and extreme baselines?
• RQ5 What is the feasibility of using HVOX as a drop-in replacement for existing gridders in major software frameworks like RASCIL?

Key findings

• HVOX achieves relative accuracy up to 10⁻⁹ in double precision, significantly outperforming W-gridding when interpolating to HEALPix meshes, which suffer from uncontrolled error accumulation.
• For SKA and LOFAR imaging setups with over 100 million pixels and extreme baselines, HVOX demonstrates strong scalability and runtime competitiveness with W-gridding, despite lacking domain-specific optimizations.
• The chunked evaluation strategy reduces memory requirements by processing only local data chunks, enabling efficient execution on limited-memory systems.
• HVOX enables direct imaging on HEALPix meshes, eliminating the need for interpolation from DCOS grids and preserving accuracy in downstream processing like deconvolution and harmonic analysis.
• The method outperforms W-gridding in sparse field scenarios by leveraging the chunked structure to optimize computation per region.
• HVOX is released as a CPU-based, open-source software library with a high-level API, enabling seamless integration into RASCIL and other radio astronomy pipelines.