robust op• 資料種類:matrix × signal → table
• 呼叫: import fullseye as fs; fs.ledger.residue_crt(residues, periods, weights=None, lo=0.0, hi=None) -> 'dict'(要直接呼叫實作,import residue; residue.residue_crt(residues, periods, weights=None, lo=0.0, hi=None) -> 'dict';從台帳取用則 opsresidue.get("residue_crt"))
針對實數週期的加權強健中國剩餘定理 -> dict。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
Solve v ≡ residues[i] (mod periods[i]) for v in [lo, hi). residues has the band axis first, shape (N,) or (N, ...) — every trailing element is solved independently (one pixel, one sample). weights (same shape, or (N,)) say how much each band is trusted — typically the product of the two amplitudes the phase came from, so a band with no contrast gets no vote.
Method: every candidate v = r_ref + k p_ref of the longest period inside the range is scored by phasor agreement sum_i w_i cos(2 pi (v - r_i)/p_i) (the maximum-likelihood criterion for von-Mises phase noise); the best one is refined by the inverse-variance-weighted mean of the signed residuals.
Returns {"value", "score", "margin", "residual", "n_candidates", "unambiguous_range"}: score in [-1, 1] (1 = all bands agree exactly), margin = best minus runner-up score (small = the answer was a near tie — treat as unreliable), residual per band in the units of v. hi defaults to lo + the least common multiple of the periods (when they are commensurate); a range wider than that is refused, because two values in it would have identical residues.
Exactness: integer residues of pairwise-coprime integer periods reproduce residue_integer_crt exactly. Robustness: with periods Γ M_i (M_i coprime integers) a value is recovered exactly whenever every residue error is below Γ/4 (Wang & Xia's bound); beyond it the margin collapses first.
• 範例資料目錄(下載 URL / 授權) —— 2-D 用 skimage.data(BSD/公有領域)加合成圖,3-D 給出真實資料源(Stanford/PDS 等)的下載 URL。
• 運算子來歷與參考文獻 —— 該運算子族所依據的研究/方法出處。
• 演算法的正典(作者、年份)與用途見上面的族使用指南。
• poc_residue_crt — py -3.11 examples/poc_residue_crt.py
table 作為輸入)—
robust)*Provenance: residue.py — RESIDUE 運算子登記表。本條目由 tools/opdocs.py md 自動產生(請勿手動編輯)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.