Firstly, understand that by the nature of its operation, the processor will create noise. Also understand that your measurement technique might be fooling you - the magic ground lead from your probe is a nice antenna - you can prove this by earthing the probe tip to the earth clip with it near the processor whilst its powered - can you see any noise?? Then there's the wiring and the regulator circuit. Your 220uF cap on the input serves as bulk filtering - it will do little for the high frequency noise the processor creates, nevertheless, you still need it. What is also critical is the capcitors on the 5V side of the regulator - some 100nF ceramics and a 10uF tant will certainly help. The wiring between the regulator and the processor may also contribute to the problem - at high frequencies the wire looks like an inductor! The pcb layout is also critical - a nice ground plane implemented on the pcb helps immensly - of course we're talking of a two or more layer pcb here.

Anyway, at a guess, I'd say your measurement technique is fooling you. And don't expect the output signals to be perfect squarewaves!