fullseye

beam_hardening_apply — TOMOGRAPHY artifact op

• データ種: sinogram → sinogram
• 呼び出し: import fullseye as fs; fs.ledger.beam_hardening_apply(sinogram, high_energy_fraction=0.5, attenuation_ratio=0.4) (実装を直接呼ぶなら import tomography; tomography.beam_hardening_apply(sinogram, high_energy_fraction=0.5, attenuation_ratio=0.4)、台帳から引くなら opstomography.get("beam_hardening_apply"))

使い方

Turn a monochromatic sinogram into a polychromatic one — cupping.

A real X-ray tube emits a spectrum, and low-energy photons are absorbed more, so the beam that survives a thick path is harder (higher mean energy) and therefore attenuated less per unit length than the beam that survives a thin one. The line integral stops being linear in path length, and the reconstruction of a uniform object comes back with a depressed centre: the cupping artefact.

The two-spectrum model used here is the smallest one that is physics and not a curve::

I/I0    = (1-w) exp(-p) + w exp(-k p)
p_meas  = -ln(I/I0)

with w the fraction of the beam at the high energy and k < 1 its relative attenuation. It is exact at p = 0, concave everywhere, and monotone — so it is invertible, which is what :func:beam_hardening_correct inverts.

Measured on a uniform disc (radius 60 px in 256 px, density 1/60 so the peak line integral is 2.0) at w = 0.5, k = 0.4: the FBP reconstruction’s centre-to-rim ratio drops to 0.9312, against 0.9981 before hardening, and :func:beam_hardening_correct returns it to 0.9981 — the clean value in all four digits. (The clean ratio is 0.9981 rather than exactly 1 because of the detector sampling discussed in :func:filtered_backprojection. The cupping is the 6.7-point drop, not the 0.2-point one.)

:param sinogram: (n_angles, n_detectors) monochromatic line integrals, which must be >= 0. :param high_energy_fraction: w, in [0, 1). 0 is a monochromatic beam and the operator is then the identity. :param attenuation_ratio: k, in (0, 1). 1 is again monochromatic. :returns: (n_angles, n_detectors) float64 hardened sinogram. :raises ValueError: on a negative sinogram (a negative line integral is not a measurement this model can harden — the logarithm of the transmitted intensity has already gone wrong upstream), or parameters outside range.

参考(サンプルデータ・文献)

• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。
• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。
• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。

実行できる例(この op を実際に呼ぶ検証済みサンプル)

• ct_reconstruction — py -3.11 examples/ct_reconstruction.py
• poc_battery_ct_degradation — py -3.11 examples/poc_battery_ct_degradation.py

型が繋がる次の op(sinogram を入力に取れる)

backproject_sinogram · filtered_backprojection · sart_reconstruct · beam_hardening_correct · ring_artifact_apply · ring_artifact_remove · metal_trace_interpolate · sinogram_center_of_rotation

同カテゴリ(artifact)

beam_hardening_correct · ring_artifact_apply · ring_artifact_remove · metal_trace_interpolate

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Provenance: tomography.py — TOMOGRAPHY operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。

© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.

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