Magnitude detection of complex images in magnetic resonance imaging (MRI) is immune to the effects of incidental phase variations, although in some applications information is lost or images are degraded. Synchronous detection or demodulation, a technique commonly applied to detection of amplitude-modulated signals in communication systems, can be used in MRI systems in place of magnitude detection to provide complete suppression of undesired quadrature components, to preserve polarity and phase information, and to eliminate the biases and reduction in SNR and contrast in low SNR images. The incidental phase variations in an image are removed through the use of a homodyne demodulation reference, a reference that is derived from the image or the object itself. Synchronous homodyne detection has been applied to the detection of low SNR images, the reconstruction of partial k-space images, the simultaneous detection of water and lipid signals in quadrature, and the preservation of polarity in inversion-recovery images.