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Preferred without loss of quality. Something like the WSQ (however, this is only for images up to 500 ppi).
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There is no difference of algorithms that depend on the resolution of the image. Resolution is just a parameter that maps the number of pixels in the image to physical units of measurement - typically speaks of "300 dpi" (meaning 300 ppi pixels per inch and not Dots-per-inch) in "images for printing".
2500 PPI is a resolution lady - possibly used in color slide movies. Even the craziest LCD displays are below or around 500 PPI resolution.
So if you have an image to appear in 2 x 1 inches at 2500 PPI it will still be a 5000x2500px -image and it’s that number of pixels that you have to compress. The resolution being 2500 PPI, or 1 pixel per meter (in which case this same image would extend by 5km of landscape), does not differ in anything the algorithmic treatment on the pixels. The resolution is a single field of few bytes in the final file, which serves as a "tip" of the final size for some of the preview/print programs.
I saw now that this WSQ standard was developed to handle digital print image storage - hence we have an idea of your domain and types of images you need to store. It may be that WSQ is great for storing the details of a fingerprint that appear on the 500PPI scale - and lose on others - but this has to do with the type of image and type of details specific to your domain of work. If WSQ is not good at other resolutions, and you want something lossless, use PNG files yourself - which is good enough for generic images - if they get too big for your application, a format like Webpp from Google can work better.
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The ideal is for you to provide your references on the subject (links, documentation, tools you use, etc). In fact, what your question has to do with programming?
– brasofilo
I need to know the best method to implement in an application developed for Android, in which it captures the image through the camera itself and compresses using some method(this q I’m looking for).
– Lucas Moreira