You will definitely want to use the GPU. I would recommend that you use a render to texture step and HLSL. HLSL is pretty easy to pick up, and I do believe there's a sample for rendering to a texture. (you could do multiple passes too if you pass it back in again)
Here's a good blog on HLSL using XNA 4: http://digitalerr0r.wordpress.com/2011/12/12/xna-4-0-shader-programming-1intro-to-hlsl-ambient-light/
Here's an example of render-to-texture in XNA 4: http://www.riemers.net/eng/Tutorials/XNA/Csharp/Series3/Render_to_texture.php
Basically speaking, render targets in XNA are textures and can be used just like one.