beam_hardening_correct — TOMOGRAPHY artifact op

• データ種: sinogram → sinogram

• 呼び出し: import tomography; tomography.beam_hardening_correct(sinogram, high_energy_fraction=0.5, attenuation_ratio=0.4, poly_coeffs=None, n_table=4096) (または opstomography.get("beam_hardening_correct"))

使い方

Undo cupping — either the exact model inverse, or a calibrated polynomial.

Two routes, and the difference between them is what you are allowed to claim:

• Model inverse (default). :func:beam_hardening_apply is a monotone

scalar function of the line integral, so it has an exact inverse; this

builds it by interpolating the forward curve on *n_table* nodes. Round-trip

error on the disc phantom: 1.6e-08 absolute and 8.0e-09 relative to

the peak line integral — the table resolution and nothing else.

This is a *simulation* tool — it needs the same `w and k` the

hardening used, which on real data nobody has.

• Polynomial (*poly_coeffs*). `p_corr = c1 p + c2 p^2 + ...`, the

water-correction of every clinical scanner, whose coefficients come from

scanning a uniform water phantom and fitting for a flat reconstruction.

This is what applies to real data, and it is only as good as the assumption

that everything in the field of view attenuates like water.

The honest limitation is the same one every scanner has: the correction is

material-specific. A water calibration applied to a slice containing bone

or metal over-corrects the dense material and leaves dark bands between dense

objects, and nothing in the sinogram says which case you are in.

:param sinogram: `(n_angles, n_detectors)` hardened line integrals.

:param high_energy_fraction: *w* used by the forward model.

:param attenuation_ratio: *k* used by the forward model.

:param poly_coeffs: `(c1, c2, ...)`; when given, the polynomial route is

used and *w* / *k* are ignored.

:param n_table: nodes of the inverse table, `64 .. 1048576`.

:returns: `(n_angles, n_detectors)` float64 corrected sinogram.

:raises ValueError: as :func:beam_hardening_apply, plus an empty or

non-finite *poly_coeffs*.

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

型が繋がる次の op(sinogram を入力に取れる)

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

同カテゴリ(artifact)

beam_hardening_apply · ring_artifact_apply · ring_artifact_remove · metal_trace_interpolate

*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.