ellipse_sinogram — TOMOGRAPHY `forward` op

• Data kinds: none → sinogram (an op determined by its arguments alone — it takes no image or data input)

• Call: import tomography; tomography.ellipse_sinogram(size=256, ellipses=None, angles_deg=None, n_detectors=None) (or opstomography.get("ellipse_sinogram"))

Usage

The closed-form Radon transform of a sum of uniform ellipses.

The ground truth this module is tested against, and a usable operator in its

own right: a sinogram with no discretisation error to feed a reconstruction,

so that any error in the picture belongs to the reconstruction and not to the

projector.

For one ellipse with centre `(x0, y0), semi-axes (a, b)`, rotation

`phi and density rho, the line integral along `x cos(t) + y sin(t) =

s`` is::

A(t)^2 = a^2 cos^2(t - phi) + b^2 sin^2(t - phi)

s' = s - (x0 cos t + y0 sin t)

p = 2 rho a b sqrt(A^2 - s'^2) / A^2 for |s'| < A, else 0

which for a disc (`a = b = r, rho = 1`) collapses to the chord length

`2 sqrt(r^2 - s^2)`. Densities add, so a sum of ellipses projects to a sum

of these.

The result is in the same pixel units as :func:radon_transform applied

to :func:ellipse_phantom at the same *size*: the normalised half-width is

`size/2` pixels, and a line integral scales with length, so the closed form

is multiplied by `size/2`. Getting that factor wrong is invisible in the

picture — a sinogram has no absolute scale — and shows up only as a

reconstruction whose density is off by a constant, which is why it is pinned

by a test rather than by a comment.

:param size: the pixel grid the units refer to (as in :func:ellipse_phantom).

:param ellipses: as :func:ellipse_phantom; `None -> :data:SHEPP_LOGAN`.

:param angles_deg: view angles; `None -> `linspace(0, 180, 180,

endpoint=False)``.

:param n_detectors: detector bins; `None` -> enough to cover the diagonal.

:returns: `(n_angles, n_detectors)` float64 sinogram.

:raises ValueError: on a degenerate ellipse or a sinogram over

:data:MAX_SINOGRAM_ELEMENTS.

References (sample data, literature)

• 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.

Runnable examples (verified samples that actually call this op)

• ct_reconstruction — py -3.11 examples/ct_reconstruction.py

Ops the type connects to (they accept `sinogram` as input)

backproject_sinogram · filtered_backprojection · sart_reconstruct · beam_hardening_apply · beam_hardening_correct · ring_artifact_apply · ring_artifact_remove · metal_trace_interpolate

Same category (`forward`)

ellipse_phantom · radon_transform

*Provenance: tomography.py — TOMOGRAPHY operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

ellipse_sinogram — TOMOGRAPHY forward op