Information Repackaging via Multiresolution Transforms

AST-0434413 Szapudi这项研究将开发新的技术来表征大型天文数据集的空间聚类。 主要目标是一个新的边缘校正，带状双谱估计基于一个独特的想法组合：i）仔细分析并充分利用潜在的对称性，ii）校正像素空间中的窗口和噪声造成的对称性破坏，iii）使用边缘校正的、具有启发式加权的接近最优的估计器，iv）使用快速的分层计算算法，v）使用正则化的，分层（多分辨率）变换技术，以从像素空间估计器恢复最佳统计。 数学、统计学、计算机科学和天文学的这种异常广泛的协同作用将导致绘制空间集群的完整配置空间的速度和能力的飞跃。 由此产生的技术是实用的，适用于其他统计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，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.