There are several ways you can do it.
Option 1:
Create different perfect images for different dpi and place them in related drawable folder. Then set
android:background=”@drawable/your_image
Option 2:
Add a single large image. Use FrameLayout. As a first child add an ImageView. Set the following in your ImageView.
android:src="@drawable/your_image" android:scaleType = "centerCrop"
References
https://stackoverflow.com/questions/16135984/full-screen-background-image-in-an-activity