tfmri.sampling.estimate_density

estimate_density(points, grid_shape, method='jackson', max_iter=50)[source]

Estimate the density of an arbitrary set of points.

Parameters

  • points – A Tensor. Must be one of the following types: float32, float64. The coordinates at which the sampling density should be estimated. Must have shape [..., M, N], where M is the number of points, N is the number of dimensions and ... is an arbitrary batch shape. N must be 1, 2 or 3. The coordinates should be in radians/pixel, ie, in the range [-pi, pi].

  • grid_shape – A tf.TensorShape or list of ints. The shape of the image corresponding to this k-space.

  • method – A str. The estimation algorithm to use. Must be "jackson" or "pipe". Method "pipe" may be more accurate but it is slower.

  • max_iter – Maximum number of iterations. Only relevant if method is "pipe".

Returns

A Tensor of shape [..., M] containing the density of points.

References

1

Jackson, J.I., Meyer, C.H., Nishimura, D.G. and Macovski, A. (1991), Selection of a convolution function for Fourier inversion using gridding (computerised tomography application). IEEE Transactions on Medical Imaging, 10(3): 473-478. https://doi.org/10.1109/42.97598

2

Pipe, J.G. and Menon, P. (1999), Sampling density compensation in MRI: Rationale and an iterative numerical solution. Magn. Reson. Med., 41: 179-186. https://doi.org/10.1002/(SICI)1522-2594(199901)41:1<179::AID-MRM25>3.0.CO;2-V