I am wondering if there is any way to compress a specific sections of an image and preserve other sections. For example I want the background of a large image compressed but the title and description text laid over the background to be crisp.
This would be pretty cool. Short answer (no).
Long Answer. JPEG and PNG. Do the background with JPEG and save this off as a separate file. Then do the title and description as a PNG with transparency.
In what every you are making (website, app) you will then be able to overlay these images and since the PNG has transparency it will appear as part of the original image.
At the end of the day we only have a few technologies we can work with ant that is jpg, gif, png, tiff, bmp, (svg some things dont support this) for image decoding for the end user.
Neither of these technologies do what you want well. PNG is awesome, but it the file size will be pretty huge compared to JPG. JPG wont give you crisp text when you have an image in the background.
I wouldnt be surprised if someone has written an encoder for what you want to do but being able to send this file to someone or something. They wont be able to decode it easily without your encoder and hence this is why we stick to the standard formats.