Phantom tool
------------

For more options see

bart phantom -h


x-space and k-space simulation
------------

The user can create x-space and k-space magnetization data
of simple shapes with the bart phantom library.

Shepp-Logan phantom in x-space:

2d: 		bart phantom x
3d: 		bart phantom -3 x
2d, 256 px: 	bart phantom -x 256 x

The magnetization functions are represented by indicator functions
over the shape geometry

m(x) = 1_S(x)

For computation of the k-space magnetization data, a *continuous*
Fourier transform of the magnetization function m is used as the
forward model.

Shepp-Logan phantom in k-space on Cartesian trajectory:

2d: 		bart phantom -k ksp
3d: 		bart phantom -3 -k ksp
2d, 256 px: 	bart phantom -x 256 -k ksp

Compare k-space and x-space simulation:

		bart fft -i 7 ksp r
		bart saxpy -- -1 r x diff


Multi-coil x-space and k-space simulation
------------

The user can obtain multi-coil x-space and k-space magnetization data
by using the internal sensitivity map model (trigonometric polynomial).

8-coil x-space and k-space Shepp-Logan data:

		bart phantom -s 8 x8
		bart phantom -s 8 -k ksp8

Compare multi-coil k-space and x-space simulation:

		bart nlinv ksp8 r8
		bart saxpy -- -1 r8 x8 diff8


Multi-coil k-space simulation on arbitrary trajectory
------------

The user can provide any trajectory to the phantom tool to obtain
multi-coil k-space data on the trajectory. Since the forward model
uses the *continuous* Fourier transform, the k-space value on the
trajectory is exact and *not* interpolated.

8-coil k-space Shepp-Logan data on radial trajectory:

		bart traj -r tr
		bart phantom -s 8 -k -t tr ksp8_tr
		bart nlinv -t tr ksp8_tr r8_tr


Multi-coil k-space simulation of arbitrary 3d shapes
------------

Arbitrary 3d shapes/volumes can be described by a triangulation of the
volume surface in the stl-fileformat which is commonly used in 3D-printing.

Create tetrahedron in stl-fileformat and simulate 50-coil k-space data by
using the first 50 channel from the internal 3d 64-channel head coil on a Cartesian grid:

		bart stl --model TET tet.stl
		bart phantom -k --stl tet.stl -s 50 --coil HEAD_3D_64CH ktet50
		bart fft -i 7 ktet50 xtet50
