Compare and contrast; The atkins diet and starving.?

Well I want to lose weight fast. I'm formally eating disordered and I gained a little weight and now I am freaking out about it. I don't want to spiral back into my anorexia and starve myself. I chose the atkins diet and it is my second day on it. If I did let myself slip and starve myself eating little to nothing for weeks at a time would I lose more weight in the same period of time- lets say 2 months, then I would if I chose the atkins? Because the atkins makes you burn off of your own body fat while starving feeds off of your muscle and fat... so I want to do the right thing for myself but I want to lose weight and I need alot of guidance and information. Please help me.