reconstruct op• Data kinds: sinogram → image2d
• Call: import tomography; tomography.backproject_sinogram(sinogram, angles_deg=None, size=None, span_deg=None) (or opstomography.get("backproject_sinogram"))
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.
• 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
• poc_ct_fidelity — py -3.11 examples/poc_ct_fidelity.py
image2d as input)reconstruct)filtered_backprojection · sart_reconstruct
*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.