fullseye

sart_reconstruct — TOMOGRAPHY reconstruct op

• データ種: sinogram → image2d
• 呼び出し: import fullseye as fs; fs.ledger.sart_reconstruct(sinogram, angles_deg=None, size=None, n_iter=10, relaxation=0.3, initial=None, nonnegative=True) (実装を直接呼ぶなら import tomography; tomography.sart_reconstruct(sinogram, angles_deg=None, size=None, n_iter=10, relaxation=0.3, initial=None, nonnegative=True)、台帳から引くなら opstomography.get("sart_reconstruct"))

使い方

SART — simultaneous algebraic reconstruction, one angle at a time.

An iterative solver for A x = p where A is the projector: for each view in turn, project the current estimate, take the residual, and back-project it with the row and column sums of A as normalisers::

x <- x + lambda * BP_theta( (p_theta - FP_theta(x)) / rowsum_theta )
                  / colsum_theta

rowsum is the length of each ray through the grid and colsum is how many rays touched each pixel, so the update is dimensionally a density and does not depend on the grid size. One “iteration” is one pass over all views.

Why it exists next to :func:filtered_backprojection: FBP inverts an integral transform and therefore needs the transform to have been sampled; SART solves a linear system and merely does worse when the system is underdetermined. Measured, it is better at every view count tested (the table in :func:filtered_backprojection), by 1.43x at 180 views and 2.9x at 8.

The cost is honest and it is the reason this is not the default: 10 sweeps over 180 views is 1800 forward and 1800 back-projections against FBP’s 180 back-projections, measured at 37.7 s against 0.12 s for a 256-px reconstruction — a factor of 312. At 8 views it is 2.14 s against 0.01 s, the same ratio applied to a much smaller number.

nonnegative=True clips the estimate at zero after every sweep. Attenuation coefficients cannot be negative, so this is a genuine constraint and not a cosmetic clip, and it carries a large part of the advantage above — measured on the analytic Shepp-Logan sinogram, normalised RMS with the constraint against without:

views     with     without
  180    0.0175    0.0300
   45    0.0353    0.0626
    8    0.1257    0.1428

so at 180 views the constraint alone is worth 1.7x, and it is the only reason SART leads FBP there at all (FBP scores 0.0250, between the two).

: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. :param n_iter: sweeps over the full angle set, 1 .. 500. :param relaxation: step size lambda, (0, 2). Over 1 the iteration can oscillate; over 2 it provably diverges, and is refused. :param initial: starting estimate, (size, size); None -> zeros. :param nonnegative: clip to >= 0 after each sweep. :returns: (size, size) float64 image. :raises ValueError: as :func:filtered_backprojection, plus a relaxation outside (0, 2) and an initial whose shape is not (size, size).

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(image2d を入力に取れる)

radon_transform

同カテゴリ(reconstruct)

backproject_sinogram · filtered_backprojection

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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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