If you had some ink bleeds you could just put them over the picture and change the pictures track matte to "Luma Matte".
From there I would precompose both layers and bring them into my final composition. If you are using a camera to move around, just hit the 3d switch and place your precomp where you need it.
If you are moving the background texture with position keyframes, just parent the precomp to the background texture. Adjusting the transfer mode will also help to sell the effect.
Finally you can easily create your own ink bleeds. Drag your picture on to the create new comp button. Add a comp sized solid above your picture and turn off it's opacity. Now on the solid layer create a rough mask around the area that you want revealed.
Turn the solids opacity back on and increase the feather to 80 to start(adjust to taste) and over 1 second animate the math expansion property from a negative number large to make your entire solid disappear to a full reveal.
Add the effect Stylize > Roughen Edges and change the settings to Roughen Color, Border to around 50, Edge Sharpness to .1 and Complexity to 1. You might want to add keyframes the evolution property as the mask expands.
Now change the picture track matte to alpha and you should be good to go. I uploaded an example project showing the process: 3394_inkbleedexamplesfolder.zip