If you do a post filtering or not depends on what you want. Modern PSF reconstructions will enhance your contrast and special resolution (at least they are told to) but it is known that they are more infulenced by noise (e.g. gibbs artefacts). No post filter is good for sharp images but if you use the maximal pixel value (SUVmax) it will be less reproducible than with post filtering. For quantitative measurements post filtering could help. If you do not want post filtering you could use the mean pixel value of an threshold segmentet area or the mean of a fixed area around the max pixel. These values are more stable concerning noise.
TOF reconstructions should reduce noice, but I can't quantivy that reduction.
A common setting for post filtering is a Gaussian filter with 5mm FWHM
In Siemens PET/CTs nowadays monstly the TrueX algorithm (PSF) is used with no post filtering (Allpass). If the "Iterativ" algorithm (without PSF) is used mostly a 5mm FWHM Gaussian filter is used.
GE is using VUE POINT HD or TF(meaning TOF) and you can switch the PSF on and off (SHARP IR on/off). GE uses a Gaussian post filter. I think the recommended FWHM is 6.3mm (entered in the field Cut Off). The Z-Axis filter is a Axial 1:N:1 filter with N=2 (Heavy), N=4 (Standard), N=6 (Light).
For Philips i don't know a common setting. I didn't solve the mysteries of the examination cards till now but i am looking forward that i will somewhen.
The question post filtering or not can't be answert.
The importent thing is that post filtering is changing your measurements. You should be always aware that every change in recon setting or filter setting will influence the outcome. Therefor the choice of settings should be made in accordance with the things (measurements) you want to compare to.
E.g. if you want to monitor therapy response, you must not change the settings between the two studies because you would get values which are not comparable.
Not necesary. One can use different filtration methods or even more advance techniques like waveletes but in clinical routine we do not denoise PET images before reconstruction.