Hi DO (your actual name?)
Welcome to PixInsight Forum.
I understand your complains, and trust me that I can feel your pain, especially if your images are very large. There is no bug here, but actually a limitation of some of the algorithms involved.
The global deringing algorithm in Deconvolution (and in a few other tools that share the same deringing techniques, as ATrousWaveletTransform, HDRWaveletTransform, UnsharpMask and RestorationFilter) works, as its name suggests, by analyzing data from the whole image. But this isn't, by itself, the actual problem. After all, we could analyze data from a preview's parent image "behind the scenes" to provide an accurate representation of the final result. Some tools already do this in PixInsight. The problem is that ringing is a very complex phenomenon which we cannot predict, especially ringing generated during sophisticated procedures such as deconvolution and HDR wavelet transforms. So we are unable to know what the ringing would be if the same process were applied to the preview's parent image, without actually applying the whole process, which obviously isn't an option.
So what we are facing here is, strictly speaking, a non-previewable algorithm. That said, the situation is usually much better than what you are experiencing. In most cases, a small preview can be used to fine tune deringing parameters very accurately. For example, I've just made a test with a nice image of the M81/M82 region by Oriol Lehmkhul and Ivette RodrÃguez:
http://forum-images.pixinsight.com/legacy/decon-previews/01.jpgAs you see, Preview01 is our small preview (some 600x600 px), where we can try out deconvolution very quickly. Preview02 is a nearly full-size preview, but note how I haven't included the dark border artifacts that result from partial coverage after registration, especially the black column at the left edge. These dark artifacts can cause a lot of problems with many algorithms that depend on image statistics, and in general must be avoided or cropped.
This is the small preview before deconvolution:
http://forum-images.pixinsight.com/legacy/decon-previews/02.jpgNote the strong STF being applied, since the image is of course linear (or Deconvolution wouldn't make any sense). This is the small preview after deconvolution, including global deringing:
http://forum-images.pixinsight.com/legacy/decon-previews/03.jpgIn this case deringing could be improved with a (very easy to build) star mask used as a local deringing support, especially to get rid of those residual rings around bright stars within M81. Anyway, let's stay on-topic; this is the large preview after the same deconvolution:
http://forum-images.pixinsight.com/legacy/decon-previews/04.jpgCan you see any difference between 03 and 04? Virtually none, neither in deringing nor in deconvolution regularization. This happens because both previews share the same image structures, from a multiscale point of view. More simply put, both previews comprise the same range of brightness at the same scales. M81 is the largest and brightest structure in this image, and it is present in both previews. On the other hand, the small preview contains stars that are nearly as bright as the brightest stars in the image (stars are critical for deringing).
Previews are extremely useful tools in PixInsight, but they are not perfect, nor can they work accurately in all situations. This is especially true with algorithms that depend on large-scale properties, such as some multiscale algorithms, and algorithms that depend on global brightness distributions. If your image is giving you more problems than the example I've put above, then now you know the cause: your small previews are not representative of the image at large scales. If we could see the image in question, we could try to further help you, and we could also learn from your particular problem, which is of great help to improve our implementations.