Construct information-preserving summaries for BNT-transformed higher-order statistics

Construct a summary statistic for BNT-transformed weak-lensing maps that captures the information carried by cross-map correlations, including the correlated shape-noise structure induced by the linear BNT mixing, so that nulling can be applied effectively to map-based higher-order statistics.

Background

The BNT transform preserves field-level information but mixes tomographic maps and thereby correlates their shape noise. In the analysis, starlet peak counts and the starlet \ell_1-norm are measured independently on each transformed map, omitting cross-map components. This omission causes substantial contour inflation and prevents the map-based higher-order statistics from exploiting the transform’s nominal information-preserving property. The unresolved task is to construct summaries that retain the cross-map information generated by BNT.