fullseye

backproject_sinogram — TOMOGRAPHY reconstruct op

• データ種: sinogram → image2d
• 呼び出し: import fullseye as fs; fs.ledger.backproject_sinogram(sinogram, angles_deg=None, size=None, span_deg=None) (実装を直接呼ぶなら import tomography; tomography.backproject_sinogram(sinogram, angles_deg=None, size=None, span_deg=None)、台帳から引くなら opstomography.get("backproject_sinogram"))

使い方

Plain, un-filtered back-projection — the blurred baseline.

Smear each projection back along the rays it came from and sum. The result is the true slice convolved with 1/|r|, so it is correct in the large and wrong everywhere in detail.

Two numbers, because only one of them is the interesting one. Raw, on the Shepp-Logan phantom with 180 views, this operator’s values run 0.768 to 2.493 where the truth runs 0.0 to 0.0167 — the 1/|r| kernel has no finite integral, so an un-filtered back-projection has no meaningful absolute scale at all and its normalised RMS error against the truth is 104. After the best least-squares rescaling onto the truth — which is what any display with an auto window does for you, silently — the error is 0.168 against 0.0246 for :func:filtered_backprojection, a factor of 6.8. That second number is the ramp filter’s real contribution; the first is a warning that a picture which looks approximately right after auto-windowing can be off by a factor of 100 in the numbers underneath it.

It is a registered operator and not a private helper because the blur is the lesson, and because it is the correct starting point for iterative methods.

Not to be confused with :func:fullseye.backproject, which lifts pixels into 3-D using a depth map and a camera model; that one is projective geometry, this one is an integral transform, and the only thing they share is a word.

:param sinogram: (n_angles, n_detectors), rows = angles. :param angles_deg: view angles; None -> uniform [0, 180). :param size: output side; None -> the inscribed square, n_det/sqrt2 rounded down to an odd number. :param span_deg: angular range used for the d(theta) weight; None -> inferred from angles_deg (or 180 for the default scan). :returns: (size, size) float64 image. :raises ValueError: as :func:filtered_backprojection.

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_ct_fidelity — py -3.11 examples/poc_ct_fidelity.py

型が繋がる次の op(image2d を入力に取れる)

radon_transform

同カテゴリ(reconstruct)

filtered_backprojection · sart_reconstruct

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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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