Information Repackaging via Multiresolution Transforms

AST-0434413Szapudi这项研究将开发新的技术来表征大型天文数据集中的空间聚集。主要目标是一种新的边缘校正的带状双谱估计器，其基于独特的思想组合：i)仔细分析和充分利用底层对称性，ii)校正像素空间中的对称破缺和噪声，iii)使用边缘校正的、具有启发式加权的近乎最优的估计器，iv)使用快速、分层的计算算法v)使用正则化的、分层的(多分辨率)变换技术从像素空间估计器恢复最优统计。数学、统计学、计算机科学和天文学的这种不同寻常的广泛协同将导致空间集群的速度和绘制完整配置空间的能力的巨大飞跃。由此产生的技术是实用的，适用于其他统计数据和许多不同的大型数据集。结果将反馈到一个新的高级统计班级，并将广泛传播。

AST-0434413SzapudiThis research will develop new techniques to characterize spatial clustering in large astronomical datasets. The principal goal is a new edge-corrected, banded bispectrum estimator based on a unique combination of ideas: i) carefully analyze and fully exploit the underlying symmetries, ii) correct for symmetry breaking by the window and noise in pixel space, iii) use edge corrected, nearly optimal estimators with heuristic weighting, iv) use fast, hierarchical computing algorithms v) use regularized, hierarchical (multi-resolution) transform techniques to recover the optimal statistics from pixel space estimators. This unusually broad synergy of mathematics, statistics, computer science, and astronomy will result in a quantum leap in speed and ability to map the full configuration space of spatial clustering. The resultant techniques are practical and applicable to other statistics and to many different large data sets. Results will feed back into a new advanced statistics class, and will be broadly disseminated.