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I am using texmaker and is writing a thesis where I have many different images. These images needs to have a pixel perfect accuracy so the results are not incorrect. I have many png images I would like to use. How is the images stored or compressed upon building into a pdf-file? How can I change such method in the event of my conversion being incorrect?

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For bitmap images (such as png) the files are copied as-is (and there is no way to change them in any way) and wrapped in a PDF object. Compression is done on-top as for other objects in a PDF file with the usual losless file compression of PDF. This is true for pdftex and xetex and probably still true for luatex.

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The closest answer I found to this question was through this: https://tug.org/TUGboat/tb26-1/hoeppner.pdf

It does not explicitly state what I was asking but it says that PNG is supported through pdflatex. Read it for further details for your own specific problem.

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After generating the pdf, you can use ghostscript to compress the images. Ex:

gs -sDEVICE=pdfwrite -dCompatibilityLevel=1.5 -dNOPAUSE -dQUIET -dBATCH -dEmbedAllFonts=true -dSubsetFonts=true -dDetectDuplicateImages -dPDFSETTINGS=/prepress -sOutputFile=${DOC}-compress.pdf ${DOC}.pdf

After that I use exiftool to maintain tags. Ex:

exiftool -overwrite_original -all= -tagsFromFile ${DOC}.pdf ${DOC}-compress.pdf

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