artifact op• Data kinds: sinogram → sinogram
• Call: import tomography; tomography.beam_hardening_correct(sinogram, high_energy_fraction=0.5, attenuation_ratio=0.4, poly_coeffs=None, n_table=4096) (or opstomography.get("beam_hardening_correct"))
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*.
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• ct_reconstruction — py -3.11 examples/ct_reconstruction.py
sinogram as input)backproject_sinogram · filtered_backprojection · sart_reconstruct · beam_hardening_apply · ring_artifact_apply · ring_artifact_remove · metal_trace_interpolate · sinogram_center_of_rotation
artifact)beam_hardening_apply · ring_artifact_apply · ring_artifact_remove · metal_trace_interpolate
*Provenance: tomography.py — TOMOGRAPHY operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.