Hints:
1) You know the Rectangle which displays the image
2) MouseEvent has the capability to provide you the x and y co-ordinates of the mouse click
3) Rectangle can tell if if a particular Point is inside/outside that rectangle
it is pretty simple really. one of your classes(usually the one you are drawing on) needs to implement MouseListener(or extend MouseAdapter) and override the mouseClicked method. here is an example.
i didnt use mouseClicked in this example but it should give you the idea. you have to implement all the methods of MouseListener even if they do nothing.
i forgot to mention in your constructor you have to add the MouseListener. in the example it looks like this:
addMouseListener(this);
another suggestion is to use mousePressed instead of mouseClicked.