quadrature detection for MRI
It depends on a sequence used. For simple cases:

You have to keep in mind that the signal received by NRI receiver is frequency domain signal. So it is converted to spatial domain by FFT. FFT is a complex transformation. It needs phase of each frequency component on its input. Wrong or missing phase on FFT input leads to bad artifacts, actually, it damages the image.

In most simple cases, the phase information is dropped out after FFT.