Frequency-domain artifacts in generated images

Transposed convolution and upsampling operate on a fixed grid, and a fixed grid imposes a periodic component on the output. In a two-dimensional Fourier transform that component appears as regularly spaced peaks away from the centre. Photographs have a smooth, roughly power-law spectrum with no such peaks, which makes the difference visible without any trained model.

Where the periodicity comes from

Generative architectures build an image by repeatedly increasing resolution. A transposed convolution inserts zeros between input samples and convolves; a nearest or bilinear upsample repeats or interpolates on a fixed lattice. Either way, the operation treats positions differently depending on where they fall relative to a grid.

That grid dependence is periodic by construction, with a period set by the upsampling factor. Periodic structure in the spatial domain is exactly what a Fourier transform concentrates into isolated peaks. Stack several upsampling stages and you get several periods, and therefore several sets of peaks at related spacings.

The effect is not a bug that better training removes. It is a property of building an image on a lattice, and it is why the topic has a decade of literature behind it.

Seeing it without a detector

The check is short enough to write from memory: read the image, convert to greyscale, take numpy.fft.fft2, centre it with fftshift, take the log of the magnitude, and display.

A photograph produces a bright centre with energy decaying outward, plus whatever the scene contributes - strong axis-aligned energy from buildings, diagonal energy from repeating fabric. It is smooth in the sense that matters: there are no isolated bright points sitting in otherwise empty regions.

A generated image frequently shows a symmetric arrangement of those isolated points. Once seen, they are hard to unsee, and no threshold or trained classifier is needed to notice them.

What compression does to them

JPEG divides high-frequency coefficients by the largest values in its quantization table, so aggressive compression attenuates exactly the region where these peaks live. This leads people to conclude that saving at low quality solves the problem.

It attenuates rather than removes, and it costs visible quality in the process. An image compressed hard enough to flatten the peaks looks compressed. The approach also leaves a file whose compression is inconsistent with what its metadata claims, trading one measurable oddity for another.

Why the radial average hides things

A common shortcut is to reduce the spectrum to a one-dimensional radial profile by averaging over all orientations at each distance from the centre. It makes comparison across images easy and it throws away the thing being looked for.

Grid periodicity is axis-aligned. Its energy sits at a small number of specific coordinate pairs, and averaging over orientation spreads that concentration across an entire ring, diluting a sharp peak into a bump that may not clear the noise. A defect living at one location becomes a barely visible rise.

The practical consequence is that a pipeline judged only on radial profiles can look like it removed something it merely smeared. Looking at the full two-dimensional magnitude image, unaveraged, is the check that does not lie to you, and it takes one extra line of code.

The same reasoning applies in reverse to correction. A filter defined radially cannot selectively address a defect that lives at one coordinate pair, because a radial filter treats every orientation identically by construction.

What a low-pass filter does instead

The pipeline applies a radial low-pass filter at 0.88 of the Nyquist frequency. That attenuates the band where the periodic component sits, without notching individual peaks - a spectrum with surgical holes in it is its own signature, and easier to spot than the peaks were.

The sensor stage runs first, adding grain at intensity 0.018, which matters here for a reason beyond noise floors: broadband noise raises the spectrum's high-frequency floor, so residual peaks stand less far above their surroundings.

Lateral chromatic aberration reaching 1.25 px at the corners contributes too, by making the channels disagree slightly about where edges are. Perfect inter-channel registration is itself a regularity, and one that a spectrum computed per channel will show.

There is a limit worth stating. Attenuation is not removal, and a classifier trained on the residue after this kind of filtering can still find some of it. The setting sits at 0.88 because lowering it removes more structure and starts costing visible sharpness - a trade measured on real images rather than chosen for how it sounds.

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