Why can't you just invoke the image method inside your class?

Dunno much about such endeavors. Just some wild guesses!

By encapsulation you mean you're making a 3rd-party library?

If it's an isolated one, instead of a nested PApplet class, I believe
you have to import Processing's library and also extend your class with it.

Warning: Dunno nothing about it yet! 
But I intend to learn about it in the near future!!!  

import processing.core.*;

final class zzz extends PApplet {

  PApplet pa;

  zzz(PApplet sketch) {
    pa = sketch;
  }

  void test() {
    pa.image( pa.get(), 0, 0 );
  }
}

There request is vague (or my brain need the coffee brewing downstairs...).
" Since image is not a static method of PGraphics"
Not sure if you are using "static" in the proper Java way.
Why would it be static?
PGraphics has an image() method, that works like the main one. It is not static, so it needs an instance of the PGraphics class to be invoked.

The vagueness is where you need to draw the image. If that's directly on the main sketch area, just use image() in the class. If that's on a separate PGraphics, just do as you shown, pg.image(i, x, y).

Perhaps you can show a simplified, minimalistic sketch to illustrate your problem, so we can suggest a solution.

Thanks guys for the ideas.

king_lemon: I tried just invoking image and got a NullPointerException.

GoToLoop: your idea worked! All I needed was to pass the sketch instance to my class's constructor. This gave me
an instance of PApplet (pa) and invoking pa.image(...) did the trick.

PhiLho: I keep switching between C++ on my Arduino and Java (Processing) on my host. Switching between the two every few minutes is giving me brain gas. I was using static in the sense that image is an instance method as opposed to a class method. Yes, I am drawing in the main sketch, so passing "this" from the sketch to my class's constructor was all that was needed.

Again, guys, thanks.