Understanding regularization

5 panel of a crop with various settings of deconvolution applied.
Left: No deconvolution. 2nd left: "ideal" stable solution. Middle: Moderate error diffusion. 2nd right: Aggresive error diffusion. Right: Unstable (too high Error Diffusion). Notice that at 100% zoom, the intelligent error diffusion is barely noticeble, however introduces subtly more detail and tighter stars (middle).

Deconvolution is exceptionally sensitive to noise; without something discerning between newly recovered detail and artefact, the compounding effect of multiple iterations of deconvolving noise will quickly end up in a noisy, artefacting mess. The process that discerns between artefact and detail is regularization.

In general, as opposed to any other software, regularization (and deconvolution as a whole) in StarTools is extremely adept at detecting and mitigating noise and artifact propagation, thanks to signal evolution Tracking. Regularization in StarTools is wholly driven by per-pixel SNR statistics gathered as you processed the image, thereby avoiding artefact development in low SNR areas, while guaranteeing maximum detail in higher SNR areas. In fact, this ability makes applying deconvolution later in your processing a good idea, as Decon will have more "up to date" SNR statistics to work with. The closer your image is to completion, the more settled per-pixel SNR measurements will be. The latter settled SNR-measurements can than be taken into account by the Regularization algorithm to yield the most appropriate results for your image.

5-panel at 200% zoom.
At 200% zoom, the error diffusion is revealed as a subtle noise/dithering pattern around the enhanced detail (middle), breaking the pyschovisual effect.

Throughout all this, Deconvolution still operates on the linear data, even though the end result is calculated for your stretched and (possibly) heavily processed image; eberything you did to the image is taken into account and compensated for. The mechanism responsible for this mathematical tour de force is signal evolution Tracking; decisions based on your stretched image are back propagated to the dataset when it was linear, re-calculated, then forward propagated to the heavily processed state your dataset is now in.

You can think of this procedure as undoing all changes you made since you started with linear data until the dataset is linear again, then making a modification to the dataset in its linear state, then redoing all those changes you made again - this time starting from modified linear data. It's a little bit like time travel and changing the past using knowledge about the future. This unique approach to regularization means that deconvolution in StarTools converges to an optimal solution that fits the detected noise levels - it will not - by default - destabilise with more iterations as often seen in other software.

Psychovisual trickery

A further innovation in StarTools' deconvolution algorithm, is its ability to tightly control destabilisation. It is possible to artificially limit StarTools' default advanced regularization stabilisation behaviour, by increasing the 'Error Diffusion' parameter from 0%. This will cause the deconvolution algorithm to cleverly exploit a quirk of the human visual system, which makes it so that noise in areas of high detail are harder to discern. By allowing the solution to destabilise only in those areas, more perceptual detail can be eeked out, without causing destabilisation to become noticeable. It should be noted that at zoom levels higher than 100%, the illusion falls apart, and the human eye will start detecting the diffused grain for what it is; destabilisation artefacts.