algotom.rec.reconstruction

Module of FFT-based reconstruction methods in the reconstruction stage: - Filtered back-projection (FBP) method for GPU (using numba and cuda) and CPU. - Direct Fourier inversion (DFI) method. - Wrapper for Astra Toolbox reconstruction (optional) - Wrapper for Tomopy-gridrec reconstruction (optional)

Functions:

algotom.rec.reconstruction.apply_ramp_filter(sinogram, ramp_win=None, filter_name=None, pad=None, pad_mode='edge')[source]

Apply the ramp filter to a sinogram with the option of adding a smoothing filter.

Parameters

  • sinogram (array_like) – 2D rray. Sinogram image.

  • ramp_win (complex ndarray or None) – Ramp window in the Fourier space.

  • filter_name (*{None, “hann”, “bartlett”, “blackman”, “hamming”, “nuttall”,*) – “parzen”, “triang”} Name of a smoothing window used.

  • pad (int or None) – To apply padding before the FFT. The value is set to 10% of the image width if None is given.

  • pad_mode (str) – Padding method. Full list can be found at numpy.pad documentation.

Returns

array_like – Filtered sinogram.

algotom.rec.reconstruction.astra_reconstruction(sinogram, center, angles=None, ratio=1.0, method='FBP_CUDA', num_iter=1, filter_name='hann', pad=None, apply_log=True)[source]

Wrapper of reconstruction methods implemented in the astra toolbox package. https://www.astra-toolbox.com/docs/algs/index.html Users must install Astra Toolbox before using this function.

Parameters

  • sinogram (array_like) – 2D array. Sinogram image.

  • center (float) – Center of rotation.

  • angles (array_like) – 1D array. List of angles (radian) corresponding to the sinogram.

  • ratio (float) – To apply a circle mask to the reconstructed image.

  • method (str) – Reconstruction algorithms. for CPU: ‘FBP’, ‘SIRT’, ‘SART’, ‘ART’, ‘CGLS’. for GPU: ‘FBP_CUDA’, ‘SIRT_CUDA’, ‘SART_CUDA’, ‘CGLS_CUDA’.

  • num_iter (int) – Number of iterations if using iteration methods.

  • filter_name (str) – Apply filter if using FBP method. Options: ‘hamming’, ‘hann’, ‘lanczos’, ‘kaiser’, ‘parzen’,…

  • pad (int) – Padding to reduce the side effect of FFT.

  • apply_log (bool) – Apply the logarithm function to the sinogram before reconstruction.

Returns

array_like – Square array.

algotom.rec.reconstruction.back_projection_cpu(sinogram, angles, xlist, center)

Implement the back-projection algorithm using CPU.

sinogramarray_like

2D array. (Filtered) sinogram image.

anglesarray_like

1D array. Angles (radian) corresponding to the sinogram.

xlistarray_like

1D array. Distances of the integration lines to the image center.

centerfloat

Center of rotation.

Returns

recon (array_like) – Square array. Reconstructed image.

algotom.rec.reconstruction.dfi_reconstruction(sinogram, center, angles=None, ratio=1.0, filter_name='hann', pad_rate=0.25, pad_mode='edge', apply_log=True)[source]

Apply the DFI (direct Fourier inversion) reconstruction method to a sinogram image (Ref. [1]). The method is a practical and direct implementation of the Fourier slice theorem (Ref. [2]).

Parameters

  • sinogram (array_like) – 2D array. Sinogram image.

  • center (float) – Center of rotation.

  • angles (array_like) – 1D array. List of angles (in radian) corresponding to the sinogram.

  • ratio (float) – To apply a circle mask to the reconstructed image.

  • filter_name (*{None, “hann”, “bartlett”, “blackman”, “hamming”, “nuttall”,*) – “parzen”, “triang”} Apply a smoothing filter.

  • pad_rate (float) – To apply padding before the FFT. The padding width equals to (pad_rate * image_width).

  • pad_mode (str) – Padding method. Full list can be found at numpy.pad documentation.

  • apply_log (bool) – Apply the logarithm function to the sinogram before reconstruction.

Returns

array_like – Square array. Reconstructed image.

References

1

https://doi.org/10.1364/OE.418448

2

https://doi.org/10.1071/PH560198

algotom.rec.reconstruction.fbp_reconstruction(sinogram, center, angles=None, ratio=1.0, ramp_win=None, filter_name='hann', pad=None, pad_mode='edge', apply_log=True, gpu=True)[source]

Apply the FBP (filtered back-projection) reconstruction method to a sinogram image.

Parameters

  • sinogram (array_like) – 2D array. Sinogram image.

  • center (float) – Center of rotation.

  • angles (array_like, optional) – 1D array. List of angles (in radian) corresponding to the sinogram.

  • ratio (float, optional) – To apply a circle mask to the reconstructed image.

  • ramp_win (complex ndarray, optional) – Ramp window in the Fourier space. It will be generated if None is given.

  • filter_name (*{None, “hann”, “bartlett”, “blackman”, “hamming”, “nuttall”,*) – “parzen”, “triang”} Apply a smoothing filter.

  • pad (int, optional) – To apply padding before the FFT. The value is set to 10% of the image width if None is given.

  • pad_mode (str, optional) – Padding method. Full list can be found at numpy.pad documentation.

  • apply_log (bool, optional) – Apply the logarithm function to the sinogram before reconstruction.

  • gpu (bool, optional) – Use GPU for computing if True.

Returns

array_like – Square array. Reconstructed image.

algotom.rec.reconstruction.generate_mapping_coordinate(width_sino, height_sino, width_rec, height_rec)[source]

Calculate coordinates in the sinogram space from coordinates in the reconstruction space (in the Fourier domain). They are used for the DFI (direct Fourier inversion) reconstruction method.

Parameters

  • width_sino (int) – Width of a sinogram image.

  • height_sino (int) – Height of a sinogram image.

  • width_rec (int) – Width of a reconstruction image.

  • height_rec (int) – Height of a reconstruction image.

Returns

  • r_mat (array_like) – 2D array. Broadcast of the r-coordinates.

  • theta_mat (array_like) – 2D array. Broadcast of the theta-coordinates.

algotom.rec.reconstruction.gridrec_reconstruction(sinogram, center, angles=None, ratio=1.0, filter_name='shepp', apply_log=True, pad=True, ncore=1)[source]

Wrapper of the gridrec method implemented in the tomopy package: https://tomopy.readthedocs.io/en/latest/api/tomopy.recon.algorithm.html Users must install Tomopy before using this function.

Parameters

  • sinogram (array_like) – 2D array. Sinogram image.

  • center (float) – Center of rotation.

  • angles (array_like) – 1D array. List of angles (radian) corresponding to the sinogram.

  • ratio (float) – To apply a circle mask to the reconstructed image.

  • filter_name (str) – Apply a smoothing filter. Full list is at: https://github.com/tomopy/tomopy/blob/master/source/tomopy/recon/algorithm.py

  • apply_log (bool) – Apply the logarithm function to the sinogram before reconstruction.

  • pad (bool) – Apply edge padding to the nearest power of 2.

Returns

array_like – Square array.

algotom.rec.reconstruction.make_2d_ramp_window(height, width, filter_name=None)[source]

Make the 2d ramp window (in the Fourier space) by repeating the 1d ramp window with the option of adding a smoothing window.

Parameters

  • height (int) – Height of the window.

  • width (int) – Width of the window.

  • filter_name (*{None, “hann”, “bartlett”, “blackman”, “hamming”, “nuttall”,*) – “parzen”, “triang”} Name of a smoothing window used.

Returns

complex ndarray – 2D array.

algotom.rec.reconstruction.make_smoothing_window(filter_name, width)[source]

Make a 1d smoothing window.

Parameters

  • filter_name (*{“hann”, “bartlett”, “blackman”, “hamming”, “nuttall”,*) – “parzen”, “triang”} Window function used for filtering.

  • width (int) – Width of the window.

Returns

array_like – 1D array.