1. A method of producing an image with a magnetic resonance imaging system, the method comprising: acquiring an image data set with the magnetic resonance imaging system, forming an in-phase image component and an out-of-phase image component from the acquired image data set, each component comprising first and second signal information; compensating for a chemical shift artifact by: a) setting a second signal to initial values using said in-phase image component and said out-of-phase image component, b) generating a first signal using a first signal correction factor based on the second signal, c) generating a second signal using a second signal correction factor based on the first signal, d) repeating steps (b) and (c) until a predefined criterion is fulfilled; and producing, based on the first signal and/or the second signal, at least one resulting image representing at least one of: a first signal image, a second signal image, and a joint image representing both the first and the second signal.