pypft 0.0.4

Polar Fourier Transform for Reconstruction of Polar MR images

PyPFT

Polar Fourier Transform for Reconstruction of Polar MR images in Python using Numpy

Assuming you have raw kspace data in polar coordinates $F\left( {\rho ,\varphi } \right)$, if you want to reconstruct the image in the spatial domain with polar coordinates $f\left( {r,\theta } \right)$, you can follow these steps:

$F\left( {\rho ,\varphi } \right)\mathop \leftrightarrow \limits^{FF{T_\varphi }} {F_n}\left( \rho \right)\mathop \leftrightarrow \limits^{{H_n}} {f_n}\left( r \right)\mathop \leftrightarrow \limits^{IFF{T_\theta }} f\left( {r,\theta } \right)$

Meaning that you need to take two FFTs and one Hankel Transform. FFT is already implemented in numpy.fft.fft. However, hankel transform is not implemented. Also, in general, there is no package to handle this type of data natively in Python. This package serves as a toolkit to reconstruct polar MR images using PFT and handle the images after that.

Based on:

Golshani, S., & Nasiraei‐Moghaddam, A. (2017). Efficient radial tagging CMR exam: A coherent k‐space reading and image reconstruction approach. Magnetic resonance in medicine, 77(4), 1459-1472. https://doi.org/10.1002/mrm.26219

Dependencies

"matplotlib>=2.0",
"joblib>=1.5",
"opencv-python>=4.12",
"platformdirs>=4.4",
"scipy>=1.16"

Installing

Optional: Create a conda environment

conda create -n PyPFT python=3.13

Then, once the environment is activated, install it using pip

pip install pypft

You can run a sample test with this command:

python -m pypft test