Log-Polar 3D (ToMoBAR)

Description

The Log-Polar method is especially useful for implementing filtered back-projection (FBP) and Fourier-based reconstruction techniques via Fourier Slice Theorem aka Projection-Slice Throrem. It is normally the fastest reconstruction method, as it allows Fast Fourier Transform (FFT) computations. Instead of working in standard Cartesian coordinates, the projection data (Radon transform) is mapped into log-polar coordinates, where scaling and rotation become simpler transformations, see more [1]. The method is implemented in ToMoBAR software [5] using CuPy API and exposed in HTTomolibGPU. It also optimised to work with the 3D projection data, hence the name of the method.

Where and how to use it:

It is the fastest direct method in the library compared to FBP3D (ToMoBAR) and FBP2D (ASTRA-Toolbox), but also the most memory-hungry one. The Log-Polar accuracy is comparable to FBP if the data is well-sampled and evenly spaced. However, for poor/uneven-sampled projection data it is generally to recommend to use FBP methods to avoid interpolation errors during coordinate transformation. Arguably, the reconstruction errors (artifacts) can be minor and generally not visible. The Log-Polar can be used as a first choice method for fast reconstruction followed by FBP3D (ToMoBAR).

What are the adjustable parameters:

Most of parameters are self-explanatory from the method’s API httomolibgpu.recon.algorithm.LPRec3d_tomobar, so we will mention only the ones that potentially need more explanation.

• detector_pad This parameter is responsible for padding of both (left/right) sides of the horizontal detector of each radiograph. This type of padding extend the edge assuming the sample outside the field of view is approximately similar. This should be used in cases when the sample is larger than the field of view or when the halo-type artifacts should be minimised.

Fig. 37 Reconstruction using Log-Polar method without detector padding detector_pad=0.

Fig. 38 Using detector padding detector_pad=300 leads to the halo artifacts removed.

• recon_mask_radius This applies the circular mask to the reconstructed volume by zeroing all data outside a certain radius.

Fig. 39 Reconstruction with the mask recon_mask_radius=2.0.

Fig. 40 Reconstruction with the mask recon_mask_radius=0.78.

• filter_type and filter_freq_cutoff control the type of filter and the cut-off frequency applied. Different results therefore can be achieved, for instance, when noise is either accentuated or suppressed.

Fig. 41 Reconstruction using filter_type = 'hann' and filter_freq_cutoff=1.0.

Fig. 42 Reconstruction using filter_type = 'parzen' and filter_freq_cutoff=1.0.