An apparatus and method process magnetic resonance image (MRI) data and other data from a subject, including image data corresponding to at least one of angiographic data, four-dimensional blood flow, neurological blood flow, abdominal blood flow, and peripheral blood flow in the subject, and applies a compressed sensing (CS) reconstruction method utilizing a complex difference of the image data as a sparsifying transform for imaging of at least one of blood flow and magnetic resonance angiography to output a reconstructed image of the blood flow and magnetic resonance angiography, in the subject with increased processing speed and having high accuracy. The apparatus receives the MRI data of the fluid flow from an MRI device. The processor operates predetermined software, receives the MRI data, and applies the CS reconstruction method to generate the reconstructed image. An output device outputs the reconstructed image of the fluid flow.
