用随机投影压缩射电干涉数据，显著降低存储需求。
MROP: Modulated Rank-One Projections for compressive radio interferometric imaging
- 通过调制秩一投影在采集阶段压缩数据，减少冗余。
- 压缩后数据量降至图像大小量级，远低于传统方法。
- 适合大规模射电阵列实时数据处理与低资源成像。
新一代射电干涉阵列将实现更高灵敏度与分辨率的天图成像，导致单频观测数据量随天线数Q和时间分段数B呈$/mathcal{O}(Q^2B)$增长，亟需高效降维技术。本文提出一种新型采集阶段压缩方法——调制秩一投影（MROP），将$Q\times Q$的批次协方差矩阵压缩为$P$个随机秩一投影，并通过$M$个随机调制实现跨时间压缩，以$B$换$M$。首先，从随机波束成形或后相关压缩双重视角理解MROP；其次，分析其噪声统计特性，证明投影使各测量值噪声均匀，不受可见度加权方案影响；第三，详细对比了采集与重建阶段的内存与计算开销，优于现有降维方法；最后，在模拟与真实数据上验证了单色强度成像效果，使用uSARA优化算法，结果表明：采用MROP所需数据量可降至图像尺寸量级，远低于原始数据与基线依赖平均（BDA）方法。
原文摘要 · Abstract (English)
The emerging generation of radio-interferometric (RI) arrays are set to form images of the sky with a new regime of sensitivity and resolution. This implies a significant increase in visibility data volumes, which for single-frequency observations will scale as $\mathcal{O}(Q^2B)$ for $Q$ antennas and $B$ short-time integration intervals (or batches), calling for efficient data dimensionality reduction techniques. This paper proposes a new approach to data compression during acquisition, coined modulated rank-one projection (MROP). MROP compresses the $Q\times Q$ batchwise covariance matrix into a smaller number $P$ of random rank-one projections and compresses across time by trading $B$ for a smaller number $M$ of random modulations of the ROP measurement vectors. Firstly, we introduce a dual perspective on the MROP acquisition, which can either be understood as random beamforming, or as a post-correlation compression. Secondly, we analyse the noise statistics of MROPs and demonstrate that the random projections induce a uniform noise level across measurements independently of the visibility-weighting scheme used. Thirdly, we propose a detailed analysis of the memory and computational cost requirements across the data acquisition and image reconstruction stages, with comparison to state-of-the-art dimensionality reduction approaches. Finally, the MROP model is validated for monochromatic intensity imaging both in simulation and from real data, with comparison to the classical and baseline-dependent averaging (BDA) models, and using the uSARA optimisation algorithm for image formation. Our results suggest that the data size necessary to preserve imaging quality using MROPs is reduced to the order of image size, well below the original and BDA data sizes.
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