make_centric_order

pypulseqpp.make_centric_order()

Echo-train ordering of Cartesian views in centric order.

The views are ranked by their distance from the origin (the k-space centre), ties broken by polar angle, and the ranking is cut into train_length consecutive bands of ceil(N / train_length) views. Band e is acquired at echo e, one view per shot, dealt across the shots in angle order. The first echo of every shot therefore acquires a view near the centre: the conventional centric ordering of segmented gradient-echo and MPRAGE acquisitions.

Parameters:

• coords (array_like) – Centred coordinates of the selected views: an (N, 2) array of (ky, kz) or an (N,) array of ky, relative to the k-space centre, which is the origin. Encoded view indices (y, z) on an (n_y, n_z) grid convert as views - (n_y // 2, n_z // 2). Distances and angles are evaluated in the units supplied. Boolean masks are not accepted.

• train_length (int) – Echo-train length, at least 1. The number of shots is ceil(N / train_length).

• center_echo (int or None, default=None) – Echo at which the innermost band is acquired, in [0, train_length). None acquires it at echo 0; an integer rotates the band order, which moves the effective echo time without changing the train membership.

• pad (bool, default=False) – Pad every train to train_length with None, so that the position in a train is the echo index. With False the None entries are removed.

Returns:

trains – trains[s][e] is the row index into coords of the view acquired at echo e of shot s. The values are indices, not coordinates; every row of coords appears exactly once. With pad=True, None marks an echo that acquires no view. Empty coords give [].

Return type:

list of list of int

Raises:

• TypeError – If coords is a boolean mask or not numeric.

• ValueError – If coords does not have shape (N,) or (N, 2), train_length is not a positive integer, or center_echo is outside [0, train_length).

See also

make_radial_order

centre-out order within angular wedges.

make_radial_adaptive_order

distance order folded about a target echo.

Examples

Five centred ky views in shots of two echoes:

>>> import pypulseqpp as pp
>>> views = [-2, -1, 0, 1, 2]
>>> trains = pp.make_centric_order(views, 2)
>>> trains
[[2, 4], [3, 0], [1]]
>>> [[views[i] for i in train] for train in trains]
[[0, 2], [1, -2], [-1]]

Echo 0 acquires the three views nearest the centre, one per shot, and echo 1 the two outer views. The third shot has no second view.