robust op• Datenarten: matrix × signal → table
• Aufruf: import fullseye as fs; fs.ledger.residue_crt(residues, periods, weights=None, lo=0.0, hi=None) -> 'dict' (die Implementierung direkt: import residue; residue.residue_crt(residues, periods, weights=None, lo=0.0, hi=None) -> 'dict'; aus dem Register: opsresidue.get("residue_crt"))
Gewichteter robuster chinesischer Restsatz über reelle Perioden -> dict.
> Die ausführliche Beschreibung unten ist der Originaltext — Zusammenfassung und Überschriften sind übersetzt.
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.
• Katalog der Beispieldaten (Download-URLs / Lizenzen) — 2-D nutzt skimage.data (BSD/Public Domain) plus synthetische Bilder, 3-D nennt Download-URLs echter Datenquellen (Stanford, PDS, …).
• Herkunft und Literatur der Operatoren — die Quellen der Forschung/Verfahren, auf denen diese Operatorfamilie beruht.
• Der kanonische Algorithmus (Autor, Jahr) und seine Anwendungen stehen im Familienleitfaden oben.
• poc_residue_crt — py -3.11 examples/poc_residue_crt.py
table als Eingabe)—
robust)*Provenance: residue.py — RESIDUE Operator-Registry. Diese Notiz wird von tools/opdocs.py md erzeugt (nicht von Hand bearbeiten).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.