Please read the
documentation for interpolation algorithms I wrote some years ago.
In the comparison you've posted, the right-hand image is severely blurred. This result is typical of poor pixel interpolations (bilinear or some oversmoothing higher order algorithm, such as cubic b-spline), possibly combined with inaccurate image registration.
The small artifacts around some stars in the left-hand image are ringing artifacts caused by Lanczos or bicubic spline interpolation. Normally they should be eliminated by statistical rejection during image integration. If necessary, they can also be controlled with the interpolation clamping threshold parameter of StarAlignment. This may be necessary with weak (or low-SNR) data. In this case try reducing this parameter from its default value of 0.3 to something between 0.2 and 0.1 (but bear in mind that too low of a clamping threshold will degrade interpolation performance).
Using the Parameter "NearestNeighbour" in PixelInterpolation of StarAlignement solves this issue and get you round stars.
Nearest neighbor should never be used with correctly sampled or undersampled data, as it lacks subpixel registration accuracy. It cannot be used either with rotated frames for the same reason. With very few and special exceptions, there's no reason to use nearest neighbor interpolation in PixInsight IMO, since Lanczos is always better in virtually all practical cases. This is described in the documentation linked above.
The default parameter Auto did the pixel interpolation with Lancoz (regarding to the Process Console) and this results in my case in square stars .. strange
Not strange at all. Square stars are just the correct result that can be expected from well acquired undersampled data. For example, see
this document, specifically the Sampling section, to learn why this happens.
Not sure if Bicubic B-Spline is the very best for my setting but maybe this finding will help others with similar problems.
Bicubic B-spline is one of the worst options for pixel interpolation with deep-sky images. Actually, this algorithm is retained in our implementation mainly for completeness and historic reasons. This interpolation method has very poor aliasing characteristics.
If the small artifacts are really a problem for you, and you can't control them with pixel rejection and/or the clamping threshold parameter and Lanczos interpolation, try with bicubic spline interpolation, where ringing is less problematic.
