fourier op• Data kinds: qimage → qimage
• Call: import fullseye as fs; fs.ledger.iqft2(spectrum, side, mu=None) -> 'np.ndarray' (to call the implementation directly, import quatimage; quatimage.iqft2(spectrum, side, mu=None) -> 'np.ndarray'; from the registry, opsquat.get("iqft2"))
Inverse quaternion Fourier transform of a centred spectrum. → (H, W, 4).
The exact inverse of qft2 for the same side and the same mu:
measured round-trip error 2.22e-15 for both sides on a standard-normal (32, 32, 4) field. The kernel is exp(+mu * 2*pi*(...)) applied on the side named, and the 1/(H*W) normalisation is carried here, as in numpy.fft.ifft2.
Using the wrong side does not raise. iqft2(qft2(q, "left"), "right") returns a finite, plausible quaternion image that is simply not q:
measured max|err| = 1.113 on a random colour image whose own range is 0.9994 (another seed: 1.063 against 1.0), and — the dangerous case — only 0.054 against a range of 1.076 on a grey-axis-dominated one, which is small enough to survive a look at the picture. The side argument is required at both ends for exactly this reason, and the two calls must agree: nothing in the data records which transform produced it, so nothing downstream can catch the mismatch for you.
Raises ValueError: *spectrum* is not a valid (H, W, 4) field; *side* is not 'left' / 'right'; *mu* is not a finite non-zero 3-vector.
• quaternion_monogenic family guide
• 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.
• quaternion_monogenic — py -3.11 examples/quaternion_monogenic.py
qimage as input)quaternion_to_rgb · quat_norm · quat_conjugate_image · quat_normalize_image · quat_image_multiply · monogenic_amplitude · monogenic_phase · monogenic_orientation
fourier)*Provenance: quatimage.py — QUAT 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.