A method of complex image reconstruction from partially acquired data in two or more dimensions is presented. This method uses an iterative multidimensional transformation to reconstruct a magnetic resonance image. The method of this invention abandons the theory that complex conjugation is necessary to reconstruct a complex image from partially acquired data and, instead, utilizes a phase constraint to make the solution determinable using a multidimensional transformation technique. This method of image reconstruction allows magnetic resonance images to be reconstructed by acquiring only one-half of the k-space data.