# Why is the image complex in magnetic resonance imaging? (and how does partial Fourier imaging work?)

The MRI image is reconstructed using inverse Fourier transform from k-space data measured during a pulse sequence. According to some online sources the resulting image is complex-valued and usually (for structural images) the magnitude of this image is used in medicine. Since MRI measures the distribution of the magnetization vector in the x-y plane in a particular time point, it is intuitive that we have a complex result at the end with a magnitude and a phase in each voxel.

In partial Fourier imaging however, only approximately half of the k-space is sampled and reconstruction is based on the assumption that the k-space has Hermitian symmetry. This implies that the resulting image after FFT will have zero imaginary parts. If I understand correctly, this also implies that the magnetization vector is parallel to one of the coordinate axes in the x-y plane (or the axis of the "real" reciever coil if we have quadrature detection).

My questions are:

Are all the magnetization vectors aligned parallel to one of the axes in x-y plane when we use a partial Fourier imaging method?

How is this achieved? Is this generally the case, or does it require some special techniques?

If it is generally true, then why do we get complex images from reconstructions working with all the k-space data? (other than noise)

Are all the magnetization vectors aligned parallel to one of the axes in x-y plane when we use a partial Fourier imaging method?

For the most part, yes. There can be small nonzero phases due to noise and other artifacts, but in pulse sequences where the Hermitian symmetry is used, those contributions are necessarily small.

How is this achieved? Is this generally the case, or it requires some special techniques?

The usual way is with a spin echo. Spin echoes refocus all static inhomogeneities so that the magnetization is all properly aligned.

If it is generally true, then why do we get complex images from reconstructions working with all the k-space data? (other than noise)

It is not generally true. In fact, in the sequences where there is a substantial variation in the phase the Hermitian symmetry cannot be used for partial Fourier. Partial Fourier with Hermitian symmetry is a technique that cannot always be used for the reasons that you already touched on.

• Thank you for the edits and the answer. – David Sep 23 '19 at 13:04