I had this problem when setting a high resolution image as an activity background, and I was able to solve it using the following Java code from the Activity method onCreate().
BitmapFactory.Options myOptions = new BitmapFactory.Options();
myOptions.inDither = true;
myOptions.inScaled = false;
myOptions.inPreferredConfig = Bitmap.Config.ARGB_8888;
myOptions.inDither = false;
myOptions.inPurgeable = true;
Bitmap preparedBitmap = BitmapFactory.decodeResource(yourAppName.getSharedApplication().getResources(),
R.drawable.yourImage, myOptions);
Drawable background = new BitmapDrawable(preparedBitmap);
((LinearLayout) findViewById(R.id.yourLayoutId))
.setBackgroundDrawable(background);
xml, . , AndroidManifest.xml
<supports-screens android:largeScreens="true"
android:normalScreens="true" android:smallScreens="true"
android:anyDensity="true" />
, !!!