reconstruct op• データ種: sinogram → image2d
• 呼び出し: import tomography; tomography.sart_reconstruct(sinogram, angles_deg=None, size=None, n_iter=10, relaxation=0.3, initial=None, nonnegative=True) (または opstomography.get("sart_reconstruct"))
SART —— 同時代数再構成を 1 角度ずつ。
> 以下の詳細説明は原文のままです —— 要約と見出しは訳出済み。
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)`.
• 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。
• ct_reconstruction — py -3.11 examples/ct_reconstruction.py
image2d を入力に取れる)reconstruct)backproject_sinogram · filtered_backprojection
*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.