I have TIF files that I would like to compress without losing any data, do you know the best tool for that? The data is very important. The data file looks like this: I have thousands of them. (It's X-ray data and it's black and white. )
Your example image in png format seems to only have two states. The png is already losslessly compressed, albeit in full color mode, at 16.5 Kbytes.
Thresholding the image to pure Black and White and using GIF indexed color mode produces a 10.3 Kbyte file, roughly 2/3 size.
---------Edit to try to answer OP's additional questions
Loading the linked original image into GIMP, the image appears to be completely BLACK.
Note that it is 8-bit Integer Indexed Color.
Now opening up the Histogram function in Gimp.
and exporting a CSV file of the Histogram, we see:
0,1002001.0 1,40674.0 2,0.0 3,0.0 4,0.0 5,0.0 ... 255,0.0
So the image has a million zeros, 40 thousand one's, and nothing else.
Last but not least is the EXIF data from Gimp / Image / Metadata / View Metadata
You can see the LZW compression here.
I actually extracted the LZW information using a different tool that examined the file format, but this is easier if EXIF is available.
Programs normally offer LZW compression for TIFF image files, which is 100% lossless. You should first make sure that your program that opens and views them can handle opening LZW compression (try one first), but LZW is very common for images.
Document files (text page archives, and fax) typically use TIFF with one of the CCITT compressions, also lossless, but which is not normally found in image programs, so that is not a good choice for your images.