I have sparsely sampled slices of data which are aligned to a 3d volume (medical imaging volume). The slices are all parallel planes to one another. I want to perform a linear interpolation of the values between the planes however using existing solutions like scipy's LinearNDInterpolator are too slow given the size of my volume. I also can not treat my data like a regular grid since the data on the slice (a brain) only takes up a portion of the image (the rest being empty space). The values outside the brain are masked to deal with this but this then makes the data no longer a regular grid.
Is there a solution which would specifically take advantage of the fact that my slices are all parallel? is there any way of leveraging this fact to perform a faster interpolation?