MRI - "IDEAL" MRI: Weighted Least-squares Water-Fat Separation

A method of separating signals from at least two species in a body using echo-coherent time magnetic resonance imaging is provided. A plurality of echo signals is acquired at acquisition times optimized based on the noise properties of images with different variance with possibly correlated noise resulting in possibly asymmetrically positioned images with respect to an echo time. The plurality of echo signals is combined iteratively by using a maximum likelihood decomposition algorithm for non-identically distributed noise.