I suppose this is it, with docs how: GitHub - JuliaIO/JpegTurbo.jl: Julia interface to libjpeg-turbo
It’s the fastest option/backend (also faster then MATLAB and Python/OpenCV): benchmark results against other backends · Issue #15 · JuliaIO/JpegTurbo.jl · GitHub
In case you looked no further than Julia’s docs, then that’s usually a mistake, it provides e.g. LinearAlgebra and some other math, but look at juliahub.com for most other stuff, also googling e.g. JPEG Julia would have worked.
FYI: This is probably the first package for JPEG/image decoding/encoding, and supports all kinds of formats including PNG you need: GitHub - JuliaIO/ImageMagick.jl: Thin Wrapper for the library ImageMagick
I doubt you find pure Julia code for JPEG (unlike e.g. available for the simpler GIF format), but the non-pure dependencies shouldn’t be any problem.
There might be one or more packages for this, be aware of FileIO.jl and Images.jl, but I think this is all you need to know.