Understanding regularization

A three-panel comparison of a deep space object being deconvolved.
If pushed to introduce noise to gain more detail, the regularization algorithm employs the same psychovisual tricks as found in the noise grain equalization denoise module. Top left; regularization set to 1.0 (no grain introduced). Top right; regularization set to 0.85 (grain is introduced in such a way that it is nearly invisible at native resolution). Bottom; a 200% zoom of the top right image (breaking the illusion and showing the noise grain).

The 'Regularization' parameter controls the balance between newly recovered detail and noise grain propagation. 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 'Regularization' in StarTools is automatically set to a baseline that should yield a good balance between detail recovery and artefact/noise suppression. However, there are instances where you may wish to deviate somewhat from the baseline to show more detail. The way this detail is introduced at the expense of noise, is very similar to how the Noise Grain Equalization Denoise module works; noise grain is allocated/'allowed' in such a way that it is still hard to detect by humans if the image is viewed at 100% zoom or below. Zoom levels above 100% break the illusion, however and noise grain allocation becomes visible.

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.

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. The mechanism responsible for this mathematical tour de force is 'Tracking Propagation'; 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.

There are two modes for 'Tracking Propagation'. The first, 'Post-decon (fast)', default mode, only back and forward propagates the final result of the deconvolution operation and uses an approximation for the intermediary iterations. This was the default mode before StarTools 1.6. The second mode, 'During Regularization (Quality)' back and forward propagates the results constantly for every iteration. The second option is slower but more precise than the first, however may allow you to push the dataset a little more, especially in conjunction with 'Regularization' values lower than the default balanced 1.0.