Tile-Based Quality Reconstruction for DSO

Tile-Based Quality Reconstruction for Short-Exposure Deep-Sky Imaging — Mathematical Specification v3.3.9 Tile-Based Quality Reconstruction (TBQR) is a stacking methodology for short-exposure deep-sky datasets that replaces binary best-frame selection with a continuous spatio-temporal quality model. Every usable frame contributes to the final result; per-pixel, per-tile reconstruction weights are derived from a multiplicative combination of a global atmospheric quality index and a local structural quality index. Version 3.3.9 refines the mathematical core established in v3.3.6 with six substantive changes: Decoupled photometric normalization — additive background subtraction and multiplicative photometric scaling are now explicit separate steps, preventing sky brightness from acting as a proxy for photometric scale. Soft star-support blend — the hard STAR/STRUCTURE tile switch is replaced by a continuous blend factor η_t, eliminating discontinuities at the star-count threshold. Neighborhood-aware metric normalization — per-tile z-scores are pooled over a spatial tile neighborhood, improving robustness for tiles with limited per-frame samples. Edge-aware spatial regularization — local quality scores are smoothed on the tile-neighborhood graph with affinity weights, preventing neighboring tiles from diverging into incompatible weight regimes. Support-aware overlap-add (OLA) — a per-pixel support mask replaces per-tile median/MAD renormalization, avoiding amplification of tiles dominated by extended emission. Mass-preserving cluster aggregation — the final stacking weight for each synthetic cluster incorporates the total atmospheric mass of that cluster, preventing small high-quality clusters from dominating when the majority of atmospheric mass lies elsewhere. The paper consolidates the mathematical definitions, constraint tables, and function catalog used by the tile_compile implementation, documents the delta from v3.3.6 in a structured comparison table, and grounds the methodology in a concrete M31 example run. The example run processes 645 short exposures on a 3926×2322 canvas, produces 209 adaptive reconstruction tiles, and achieves a median output FWHM of 5.108 px from a median seeing of 12.351 px (58.6% improvement). Downstream post-processing includes background gradient extraction (BGE) with extended RBF autotune and photometric color calibration (PCC).