Trajectory Definition in Monalisa
=================================

What is a Trajectory? Basic Usage
----------------------------------

The raw MRI signal does not contain information about where in k-space each measurement was taken. It only contains `nSamp` complex-valued values. To reconstruct an image accurately, we must know the **spatial k-space location** of each sample. This sampling pattern is referred to as the **trajectory**.

In **Monalisa**, a trajectory is represented as a double-precision array:

.. code-block:: matlab

    t  % size [frDim, nPt]

Each **column** of `t` corresponds to a single k-space point (sample), and each **row** corresponds to a spatial dimension (e.g., `kx`, `ky`, `kz`).

.. note::

    All trajectories must be defined in **physical units**, consistent with the scanner’s true input Field of View (FoV). We do **not** support arbitrary units (e.g., [-0.5, 0.5] unit cube).

Example: Let's say your acquisition FoV is ``[200, 300]`` mm. Then:

- The step size along `kx` must be `1 / 200` (in `1/mm`)
- The step size along `ky` must be `1 / 300` (in `1/mm`)

Similarly, for a radial trajectory with FoV of ``[360, 360]`` mm, the spacing between points on each spoke must be `1 / 360`.

.. image:: ../images/mitosius/trajectory_ct_radial.png
   :alt: Example of a radial trajectory in k-space


Monalisa provides a selector function to generate standard trajectories:

.. code-block:: matlab

    t = bmTraj(mriAcquisitionNode)

This function supports various predefined trajectories, including those extracted directly from PulSeq `.seq` files. This allows easy integration of vendor-neutral sequence designs into Monalisa reconstructions.

However, please note:

.. warning::

    Even when using the same nominal trajectory (e.g., radial), different sequence implementations or vendors may produce **slightly different actual coordinate sets**. Always verify that the trajectory used in reconstruction **matches the one used during acquisition**.

.. _customTrajectories:

Custom Trajectories
-------------------

You may provide a custom trajectory, but coordinates must be in **physical units** matching the **true acquisition FoV** (e.g., `1/mm`).

For instance, if you have a trajectory defined in a unit cube (e.g., scaled between `-0.5` and `+0.5`), you can rescale it with:

.. math::

    [k_x, k_y, k_z] \rightarrow \left[
        k_x \cdot \frac{aN_x}{aL_x}, \quad
        k_y \cdot \frac{aN_y}{aL_y}, \quad
        k_z \cdot \frac{aN_z}{aL_z}
    \right]

Where:

- :math:`aN_x, aN_y, aN_z` = matrix size in each direction (e.g., 256 × 256)
- :math:`aL_x, aL_y, aL_z` = true FoV in each direction (in `mm`)

Alternatively, if your trajectory is scaled from `-aN/2` to `aN/2 - 1`, apply:

.. math::

    [k_x, k_y, k_z] \rightarrow \left[
        \frac{k_x}{aL_x}, \quad
        \frac{k_y}{aL_y}, \quad
        \frac{k_z}{aL_z}
    \right]

Need More Help?

- `Open an issue on GitHub <https://github.com/mattechlab/monalisa/issues>`_