95 lines
3.1 KiB
ReStructuredText
95 lines
3.1 KiB
ReStructuredText
.. AMBER documentation master file, created by
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sphinx-quickstart on Fri Apr 11 10:48:14 2025.
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You can adapt this file completely to your liking, but it should at least
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contain the root `toctree` directive.
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AMBER documentation
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===================
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This is the documentation for the **A** lgorithm for **M** ultiplexing spectrometer
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**B** ackground **E** stimation with **R** otation-independence **AMBER** which is a method to estimate and background within 3D data sets.
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This software is the result of the collaboration between the instrument responsible at the `CAMEA <https://www.psi.ch/en/sinq/camea>`_ beamline at SINQ, at the
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`Paul Scherrer Institut <https://psi.ch/>`_ with the `Swiss Data Science Center <https://www.datascience.ch/>`_ through the "Data Science for Multiplexing Spectrometers" (DS4MS) project supported by
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the fifth call for Collaborative Research Data Science Projects.
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Badges
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------
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.. image:: https://gitea.psi.ch/lass_j/AMBER/actions/workflows/test.yaml/badge.svg
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:width: 200
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:alt: Test Status
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Installation
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------------
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Installation can be done through PyPI using
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.. code-block::
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python -m pip install AMBER
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Alternatively, the newest version can be installed directly from the source repository through
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.. code-block::
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python -m pip install git https://gitea.psi.ch/lass_j/AMBER.git@master
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General Introduction
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--------------------
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**AMBER** has been developed with multiplexing neutron spectrometers in mind, i.e. a novel version of the triple axis instrument which acquires multiple data points simultaneously.
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However, the algorithm is more general and can be utilized on data with other origins.
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The main requirements of the data are
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#. Rotation independence of the background in two out of three directions.
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#. Smooth change of background along all directions
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#. The signal is sparse but continuous in all directions
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**AMBER** minimizes the following cost function for the signal and background given the set of parameters :math:`\lambda`, :math:`\beta`, and :math:`\mu` on a voxelated data set:
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.. math::
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\min_{X,b} \frac{1}{2}\lVert Y-X-\mathcal{R}b\rVert_{2}^2+\lambda\vert| X |\vert_{1} +\frac{\beta}{2} \mathrm{Tr} \left( b^T L_{b} b \right) +\frac{\mu}{2} \boldsymbol{1}_{n_x}^TX^T L_{\omega} X\boldsymbol{1}_{n_y}
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where :math:`Y`, :math:`X`, and :math:`b` are the measured signal, the subtracted signal and the rotation independent background, respectively. :math:`\mathcal{R}` is a rotation operator taking
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the radial :math:`b` to the full space. These three parameters constitute the fitting term while the rest are denoted penalty terms. :math:`\lambda` controls the weighing of sparcity of the subtracted signal gauge through the L-1 norm
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:math:`\vert| X |\vert_{1}`, :math:`\beta` controls the smoothness of the background while :math:`\mu` the smoothness of the subtracted signal.
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For further details, see the the paper.
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Documentation & Tutorials
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-------------------------
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For **AMBER** the following tutorials have been created
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.. toctree::
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:maxdepth: 2
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:caption: Contents:
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tutorials/index.rst
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Contribute
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----------
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Contact
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-------
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