Yes you can do this, new app called Onavo, that compresses your mobile data to help you save up to 80% on your data bill and get more out of your data plan.
Onavo compresses your mobile data through its servers while running in the background of your iPhone or iPad. Unfortunately, Onavo will not compress any streaming data, video or audio, so that any streaming will continue to consume large chunks of your data plan.
Onavo generates detailed reports that display your monthly data usage of all your applications, as well as how much you saved using the service. It’s also possible to turn Onavo‘s compression off while still benefiting from their data reports.
The app will automatically turn itself off when you connect yourself to a WiFi network and lets you easily toggle the compression on and off. You can also decided what is compressed and when under the application settings.
Onavao claims to take their user’s privacy very seriously by storing the only barre minimum to generate its reports on savings and app usage. Onavo explicitly stated that they did not store the content of the data; all they record is the metadata.
At the moment, Onavo is free as a special-time limited offer following their launch, but in the future, their service will not be free. It currently works for iPhone and iPad users on AT&T and they are working on expanding the service to Verizon Wireless customers.