Use SharedPreferences to persist changes even after your App is closed.
Save resource image path to a key in SharedPrefernces. Use it at the image load time(when onCreate() gets called).
SharedPreferences sharedPreferences = getSharedPreferences("Name", <Mode>);
int imageResource = sharedPreferences.getInt("KEY_NAME", <default value>);
image.setImageResource(imageResource);
On Button click, save the changes in SharedPreferences:
SharedPreferences.Editor spEditor = sharedPreferences.edit();
spEditor.putInt("KEY_NAME", <image resource>).commit();