BF4 uses your system default input and output for audio.
Open your sound properties panel (on Win10 right click the speaker icon in your taskbar and choose Sounds) and make sure your headset mic and speakers are set as Default Device and Default Communications Device.
If that doesn't work, reinstall ESN Sonar (the software BF4 uses for VOIP).
Usually it installs alongside of BF4 at installation time but can be found in your BF4 installation directory under ..\Battlefield 4\__Installer\customcomponent\webplugin\battlelog-web-plugins.exe