# Relation between two k-spaces phase-frequency and spatial frequencies in

When I see MRI explained, two types of 2D k-space images seem to be described as if they were the same.

1. Axes are the two spatial frequencies. This images is directly fourier-transformed into the final image.

2. Axes are phase and frequency (temporal, I assume). The data read through the RF coil is put directly into this matrix.

What is the relation between 1 and 2? Are they the same?

Example with spatial frequencies:

Example with phase and frequency, which seems to be the "raw data":

"k-phase" and "k-readout", which I think is identical to phase and frequency.

In MRI the term $k$-space usually means that you have spatial frequencies in a matrix. The Fourier Transformation of this matrix is the image.
The terms readout and frequency correspond to each other; they mean the same. The readout direction is a logical direction, along which a gradient is applied during signal acquisition, i.e. during readout. This gradient field causes a frequency spread of the excited magnetization along the direction of this gradient, hence the second name readout for this direction and for the corresponding signal axis in $k$-space.
Of course you are right: The coil that measures the signal does measure it in a time-domain. Keep in mind, that you additionally switch magnetic gradient fields. These fields act upon the magnetization and hence alter the measured signal. Since the temporal behavior of those gradient fields is known and chosen carefully (to fulfill certain criteria such as the Sampling Theorem, etc.), there is a simple relation between the time $t$ of the measured signal and the corresponding $k$-space position: $\vec{k}(t) = \frac{\gamma}{2\pi}\int_0^t \vec{G}(\tau)\,\textrm{d}\tau$.