Reconstructed MRI images must ideally be real and positive, since they correspond to density distributions of objects, which by definition are real, positive quantities. In practice however, most reconstructed images become complex due to a shift in data from the nominal origin in k space. In some situations such as constant readout gradient, these phase shifts do not affect the magnitude of the reconstructed images, and can therefore be easily determined and eliminated. However, when the readout gradient is sinusoidal and the frequency plane is scanned with data reversal on alternate lines, time delays between the start of data acquisition and the start of the readout pulse become different for even and odd lines, and result in a ghost separated by half the image size. In this paper, we describe ghost cancellation algorithms for restoration of MRI images in medical applications. Our approach is to model the effect of the time delays and the asymmetry of the sinusoidal readout gradient for even and odd lines by two phase functions relating the actual object density to even and odd parts of the observed image. We then exploit a priori information about the phase functions in order to estimate the true object density. Examples of application of this ghost cancellation approach to liver and heart images will be presented.