adding info on the log-polar method

Author: dkazanc

docs/source/_static/figures/reconstructions/lprec_recon_filter_hann.png

@@ -1,12 +1,12 @@
 .. _method_FBP2d_astra:
 
-FBP using ASTRA-Toolbox
-^^^^^^^^^^^^^^^^^^^^^^^
+FBP2D (ASTRA-Toolbox)
+^^^^^^^^^^^^^^^^^^^^^
 
 **Description**
 
 This module performs Filtered-Back-projection direct reconstruction using `ASTRA-Toolbox <https://astra-toolbox.com>`_. It is an implementation of parallel-beam 
-`FBP <https://astra-toolbox.com/docs/algs/FBP.html>`_ reconstruction method by ASTRA with the related parameters exposed (see the adjustable parameters bellow).
+`FBP_CUDA <https://astra-toolbox.com/docs/algs/FBP_CUDA.html>`_ reconstruction method by ASTRA with the related parameters exposed (see the adjustable parameters bellow).
 
 
 .. note:: This is the slowest direct reconstruction method in the library and it is recommended to use other methods, such as, :ref:`method_FBP3d_tomobar` or :ref:`method_LPRec3d_tomobar`.

docs/source/_static/figures/reconstructions/lprec_recon_filter_parzen.png

@@ -5,12 +5,64 @@ 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 <https://en.wikipedia.org/wiki/Projection-slice_theorem>`_.
+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 :cite:`andersson2016fast`. The method is implemented in `ToMoBAR <https://dkazanc.github.io/ToMoBAR>`_ software :cite:`kazantsev2020tomographic` 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 :ref:`method_FBP3d_tomobar` and :ref:`method_FBP2d_astra`. 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 :ref:`method_FBP3d_tomobar`.
 
 **What are the adjustable parameters:**
 
+Most of parameters are self-explanatory from the method's API :mod:`httomolibgpu.recon.algorithm.LPRec3d_tomobar`, so we will mention only the ones that need more explanation.
 
-**Practical example:**
+* :code:`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.
 
+.. list-table::
+
+
+    * - .. figure:: ../../../_static/figures/reconstructions/lprec_recon_no_pad.png
+           :width: 300px
+
+           Reconstruction using Log-Polar method without detector padding :code:`detector_pad=0`.
+
+      - .. figure:: ../../../_static/figures/reconstructions/lprec_recon_pad.png
+           :width: 300px
+
+           Reconstruction using detector padding :code:`detector_pad=300`. See that the halo artifacts were removed.
+
+
+* :code:`recon_mask_radius` This applies the circular mask to the reconstructed volume by zeroing all data outside a certain radius. 
+
+.. list-table::
+
+
+    * - .. figure:: ../../../_static/figures/reconstructions/lprec_recon_no_pad.png
+           :width: 300px
+
+           Reconstruction with the mask  :code:`recon_mask_radius=2.0`.
+
+      - .. figure:: ../../../_static/figures/reconstructions/lprec_recon_mask.png
+           :width: 300px
+
+           Reconstruction with the mask  :code:`recon_mask_radius=0.78`.
+
+
+* :code:`filter_type` and :code:`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.  
+
+.. list-table::
+
+
+    * - .. figure:: ../../../_static/figures/reconstructions/lprec_recon_filter_hann.png
+           :width: 300px
+
+           Reconstruction using :code:`filter_type = 'hann'` and :code:`filter_freq_cutoff=1.0`.
+
+      - .. figure:: ../../../_static/figures/reconstructions/lprec_recon_filter_parzen.png
+           :width: 300px
+
+           Reconstruction using :code:`filter_type = 'parzen'` and :code:`filter_freq_cutoff=1.5`.

docs/source/_static/figures/reconstructions/lprec_recon_mask.png

@@ -4,9 +4,9 @@ Image reconstruction methods
 ****************************
 
 Methods from :mod:`httomolibgpu.recon.algorithm` module are required to reconstruct the projection data, i.e., converting the set of sinograms into a reconstructed volume.
-The reconstruction methods can be divided into two groups: Direct methods and Iterative methods. 
+The reconstruction methods can be divided into two groups: Direct (analytical) methods and Iterative methods. 
 The former are faster and suitable for the majority of well-sampled and well-exposed data. 
-The latter are more complex and slower methods suitable for erroneuos or/and undersampled data. 
+The latter are more complex and slower methods suitable for erroneous or/and undersampled data. 
 
 .. toctree::
    :maxdepth: 2

docs/source/_static/figures/reconstructions/lprec_recon_no_pad.png

@@ -18,7 +18,7 @@
 # Created By  : Tomography Team at DLS <[email protected]>
 # Changes relative to ToMoBAR 2024.01 version
 # ---------------------------------------------------------------------------
-"""Module for tomographic reconstruction"""
+"""Module for tomographic reconstruction. For more detailed information see :ref:`image_reconstruction_module`"""
 
 import numpy as np
 from httomolibgpu import cupywrapper
@@ -71,8 +71,7 @@ def FBP2d_astra(
     """
     Perform Filtered Backprojection (FBP) reconstruction slice-by-slice (2d) using ASTRA toolbox :cite:`van2016fast` and
     ToMoBAR :cite:`kazantsev2020tomographic` wrappers.
-    This is a 2D recon using ASTRA's API for the FBP method, see for more parameters ASTRA's documentation here:
-    https://astra-toolbox.com/docs/algs/FBP_CUDA.html.
+    This is a 2D recon using ASTRA's API for the FBP_CUDA method, see more in :ref:`method_FBP2d_astra`.
 
     Parameters
     ----------
@@ -153,7 +152,8 @@ def FBP3d_tomobar(
     """
     Perform Filtered Backprojection (FBP) reconstruction using ASTRA toolbox :cite:`van2016fast` and
     ToMoBAR :cite:`kazantsev2020tomographic` wrappers.
-    This is a 3D recon from the CuPy array directly and using a custom built SINC filter for filtration in Fourier space.
+    This is a 3D recon from the CuPy array directly and using a custom built SINC filter for filtration in Fourier space, 
+    see more in :ref:`method_FBP3d_tomobar`.
 
     Parameters
     ----------
@@ -216,7 +216,7 @@ def LPRec3d_tomobar(
     """
     Fourier direct inversion in 3D on unequally spaced (also called as Log-Polar) grids using
     CuPy array as an input. This implementation follows V. Nikitin's CUDA-C implementation and TomoCuPy package.
-    :cite:`andersson2016fast`.
+    :cite:`andersson2016fast`, see more in :ref:`method_LPRec3d_tomobar`.
 
     Parameters
     ----------
@@ -231,7 +231,7 @@ def LPRec3d_tomobar(
     filter_type : str
         Filter type, the accepted strings are: none, ramp, shepp, cosine, cosine2, hamming, hann, parzen.
     filter_freq_cutoff : float
-        Cutoff frequency parameter for a filter. The higher values increase the resolution but also amplify the noise.
+        Cutoff frequency parameter for a filter.
     recon_size : int, optional
         The [recon_size, recon_size] shape of the reconstructed slice in pixels.
         By default (None), the reconstructed size will be the dimension of the horizontal detector.