Thanks for the tips and some more input.
After reading the ICC Profile Specs doc I think that I need to refine my terminology a bit.
The scanner supplies image data in Device RGB. Scanner software takes that data and converts into CIELAB by applying the scanner's input profile. The resulting image that is now in CIELAB is saved as a TIFF.
What I am looking for is to find a way to convert my scans that are currently stored in CIELAB TIFFs back into Device RGB TIFFs, knowing the scanner input profile (or the measurement data that profile was built upon).
The profile contains both TRC curves as well as cLUT A2B tables.
It is clear to me that for converting from Device RGB into CIELAB the scanner SW was applying cLUT based conversion.
According to the ICC Profile Specs, TRCs is mandatory element of an input profile and if present can be used for converting into CIEXYZ as a PCS, while cLUT A2B should be used converting into CIELAB as a PCS.
6.3.1.2 RGB Input Profiles
The three tone reproduction curves linearize the raw values with respect to the luminance (Y) dimension of the CIEXYZ encoding of the profile connection space. The 3x3 matrix converts these linearized values into XYZ values for the CIEXYZ encoding of the profile connection space
...
Only the CIEXYZ encoding of the profile connection space can be used with matrix/TRC models. A multidimensional table tag must be included if the CIELAB encoding of the profile connection space is to be used.
Does this mean that data contained in the profile sufficient for a CMS to use either Matrix or cLUT to convert from Device RGB into other color spaces(just in theory)?
In my case cLUT was used for conversion, but did TRCs elements participate in the conversion as well, or were they ignored by the CMS engine during the conversion from Device RGb into CIELAB?
Some more info about the TRCs in my profile:
Although all 3 TRCs are comprised of 511 element arrays each, upon further examination the actual values in all 3 curves are identical and resemble a simple gamma 2.2 curve
Part of Argyll package is
revfix utility that allows for "Regenerate a CLUT device profiles B2A table data by inverting the A2B table". Can it be used to built a B2A cLUT based upon the data contained in my scanner profile ?
I have tried it but it rejected to work with my profile. Do I need to add some tag elements into my profile to make it work? If needed I think I should be able to do it without breaking the integrity of scanners profile.
Apologies for so many questions and thanks again for your help,
SergeyT