OMEGA

Open-source MATLAB/GNU Octave Emission and Transmission Tomography Software

Purpose

The purpose of OMEGA is twofold. First it is designed to allow easy, fast and efficient reconstruction of any positron emission tomography (PET) and computed tomography (CT) data, including simulated GATE data. Secondly, it is intended for easy algorithmic development as it allows easy matrix-free implementation of the forward (A * x) and backward (A' * y) projections.

Introduction

OMEGA is a software for MATLAB and GNU Octave to reconstruct data obtained with a positron emission tomography or CT scanner. This software also allows to easily reconstruct ASCII, LMF or ROOT data obtained from GATE PET simulations and imageCT projections for CT. See Features section below for more information on available features and Known Issues and Limitations for software limitations. If you wish to add your own code (e.g. reconstruction algorithm) see Contributing code to OMEGA.

The algorithms implemented so far are:

• Improved Siddon's ray tracer algorithm for the system matrix creation (code for regular Siddon available, but not used) [1,2]
• Orthogonal distance-based ray tracer [3]
• Volume of intersection ray tracer (THOR) [28].
• Maximum Likelihood Expectation Maximization (MLEM) [4,5]
• Ordered Subsets Expectation Maximization (OSEM) [6]
• Complete-data Ordered Subsets Expectation Maximization (COSEM) [7]
• Enhanced COSEM (ECOSEM) [8]
• Accelerated COSEM (ACOSEM) [9]
• Row-Action Maximum Likelihood Algorithm (RAMLA) [10]
• Relaxed OSEM (ROSEM)
• Rescaled Block-Iterative EM (RBI) [11]
• Dynamic RAMLA (DRAMA) [12]
• Modified RAMLA (MRAMLA), aka modified BSREM-2 [13]
• Block Sequential Regularized Expectation Maximization (BSREM) [14]
• One-step-late algorithm (OSL) [15]
• Preconditioned Krasnoselskii-Mann algorithm (PKMA) [29]
• Quadratic prior (Gibbs prior with quadratic potential function)
• Median Root Prior (MRP) [16]
• L-filter (MRP-L) prior [17]
• Finite Impulse Response Median Hybrid (MRP-FMH) prior [17,18]
• Weighted mean prior [19,20]
• Total variation (TV) [21, 22, 23]
• Total generalized variation (TGV) [24]
• Anisotropic diffusion (AD) Median Root Prior
• Asymmetric parallel levels sets prior (APLS) [22]
• Non-local means prior (NLM), including non-local TV [25,26,27]
• Relative difference prior [30]

Installation

For additional install help, see installation help on the wiki.

You're going to need a C++ compiler in order to compile the MEX-files and use this software. Visual Studio and GCC have been tested to work and are recommended depending on your platform (Visual Studio on Windows, GCC on Linux, clang should work on MacOS). Specifically, Visual Studio 2015, 2017 and 2019 have been tested to work on Windows 7/10 and as well as G++ 5.5, 6.4, 7.3 and 9.3 on Ubuntu 16.04/18.04/20.04. MinGW++ also works though it is unable to compile ArrayFire OpenCL reconstructions (implementation 2) on Windows. Octave supports only MinGW++ on Windows and as such implementation 2 on Windows is only supported if you manually compile ArrayFire from source with MinGW (for instructions, see here).

MinGW++ for MATLAB can be downloaded from here.

Visual studio can be downloaded from here.

On Ubuntu you can install g++ with sudo apt install build-essential.

To install the OMEGA software, either simply extract the release/master package, download the MATLAB toolbox file from releases (OMEGA.-.Open-source.MATLAB.emission.tomography.software.mltbx) or obtain the source code through git:
git clone https://github.com/villekf/OMEGA and then add the OMEGA folder and subfolders to MATLAB/Octave path (this is done automatically if you install with the mltbx-file). Finally, run install_mex in the source folder to build the necessary MEX-files. Both ROOT and OpenCL support will be installed, if the corresponding files are found. ROOT is, however, only supported on Linux and MacOS platforms. Possible compilation errors can be seen with install_mex(1). OpenCL include and library paths, ArrayFire path and ROOT path can also be set manually with install_mex(0, OpenCL_include_path, OpenCL_lib_path, AF_PATH, ROOT_PATH). OpenCL_include_path should be the folder where cl.h is located, OpenCL_lib_path the folder where OpenCL.lib/libOpenCL.so (Windows/Linux) is located, AF_PATH the path to ArrayFire installation location and ROOT_PATH to ROOT installation location.

Certain features on Octave (such as normalization calculation) require packages io and statistics. You can install them from the Octave user interface with the following commands (io has to be installed first):

pkg install -forge io

pkg install -forge statistics

and then you need to load the statistics package:

pkg load statistics

In order to enable OpenCL support (implementations 2 and 3), you're going to need an OpenCL SDK/library and (for implementation 2) ArrayFire (see below). On Linux you can alternatively just install the OpenCL headers and library. Below examples are for Ubuntu, but the packages should exist for other distros as well.

Headers: sudo apt-get install opencl-headers

and then the library:
sudo apt-get install ocl-icd-opencl-dev

Alternative libraries in case the above one fails: sudo apt-get install nvidia-opencl-dev or sudo apt-get install intel-opencl-icd

In case the above doesn't work or you use Windows then you need to obtain an OpenCL SDK. The SDK can be any (or all) of the following: CUDA Toolkit, Intel OpenCL SDK, OCL-SDK, AMD APP SDK. On all cases, the OpenCL library and header files need to be on your system's PATH. By default, the install_mex-file assumes that you have installed CUDA toolkit (Linux and Windows), AMD APP SDK v3.0 (Linux and Windows), OCL-SDK (Windows), AMD GPU Pro drivers (Linux) or Intel SDK (Linux and Windows). If you get an error message like "CL/cl.h: No such file or directory", the headers could not be found. You can manually add custom OpenCL paths with install_mex(0, '/path/to/cl.h', '/path/to/libOpenCL.so'). On Ubuntu you can use command find / -iname cl.h 2>/dev/null to find the required cl.h file and find / -iname libOpenCL.so 2>/dev/null to find the required library file. See install_mex.m for further details.

All library paths needs to be on system path when running the mex-files or otherwise the required libraries will not be found.

Links:
https://software.intel.com/en-us/intel-opencl
https://developer.nvidia.com/cuda-toolkit
https://github.com/GPUOpen-LibrariesAndSDKs/OCL-SDK/releases

Once you have the header and library files, you need drivers/OpenCL runtimes for your device(s). If you have GPUs/APUs then simply having the vendor drivers should be enough. For Intel CPUs without an integrated GPU you need CPU runtimes (see the link below).

For AMD CPUs it seems that the AMD drivers released around the summer 2018 and after no longer support CPUs so you need an older driver in order to get CPU support or use an alternative runtime. One possibility is to use POCL http://portablecl.org/ and another is to try the Intel runtimes (link below).

Intel runtimes can be found here: https://software.intel.com/en-us/articles/opencl-drivers

This software also uses ArrayFire library for the GPU/OpenCL implementation. You can find AF binaries from here:
https://arrayfire.com/download/ and the source code from here:
https://github.com/arrayfire/arrayfire

On Windows you should install Visual Studio 2015 (x64) runtime libraries first before installing ArrayFire.

Installing/building ArrayFire to the default location (C:\Program Files\ArrayFire on Windows, /opt/arrayfire/ on Linux/MacOS) should cause install_mex to automatically locate everything. However, in both cases you need to add the library paths to the system PATH. On Windows you will be prompted for this during the installation, for Linux you need to add /opt/arrayfire/lib (bulding from source) or /opt/arrayfire/lib64 (installer) to the library path (e.g. sudo ldconfig /opt/arrayfire/lib64/). Alternatively, on Linux, you can also build/install it directly into the /usr/local/ folder.

Using CUDA code instead of OpenCL requires the CUDA toolkit. On both cases the CUDA folder should be on the system path. install_mex always attempts to build the CUDA code as well so no additional input is required from the user if all the header and library data is found. By default install_mex looks for CUDA in /usr/local/cuda/ on Linux. On Windows, CUDA location is determined from the environmental variables (PATH).

For additional install help, see installation help on the wiki.

Getting Started

First you should build the required mex-files by running install_mex. In case you have trouble compiling the mex-files, you can also try using the precompiled files available on the releases (MATLAB only) page.

GATE PET users should use the gate_main.m file to reconstruct GATE data. For any PET data, the file you should start with is main_PET.m. For computing the forward and/or backward projections use forward_backward_projections_example.m. For custom (gradient-based) priors, use custom_prior_test_main.m. A more simplified main-file for GATE data (simple OSEM reconstruction) is available in gate_main_simple.m. Inveon PET data should be used with Inveon_PET_main.m while Biograph mCT data can be used with Biograph_mCT_main.m and Biograph Vision with Biograph_Vision_main.m.

A GATE PET example with GATE macros is available in exampleGATE-folder. Simply run the GATE macros as a GATE simulation (the GATE material database needs to be in the same folder as the macros) and then input correct path for the GATE output data in gate_main.m (options.fpath). After this simply run gate_main.m to load and reconstruct the data. By default, ASCII data is used for compatibility.

Example PET MAT-files for non-GATE situation can be found from . These files are based on the above GATE-example. The original simulated GATE PET data can be found from .

Open preclinical PET data measured with Siemens Inveon PET can be found from and .

For CT data, GATE data example is shown with gate_CT_main.m. µCT example (along with a link to open data) is provided with walnut_CT_main.m (2D case is shown in walnut2D_CT_main.m. Inveon CT data can be read and reconstructed with Inveon_CT_main.m.

Preclinical phantom CT data can be found from .

For more information see the wiki.

Sinograms created with v0.9 need to be transposed for them to work.

Features

The following features are currently present:

• Supports both MATLAB and Octave
• Reconstruct any PET sinogram/list-mode data
• Reconstruct any CT projection data
• Reconstruction with MLEM, OSEM, COSEM, ECOSEM, ACOSEM, RAMLA, MRAMLA, RBI, ROSEM, BSREM, MBSREM, DRAMA, PKMA, MRP, Quadratic prior, L-filter, FMH, weighted mean, TV, TGV, AD, APLS, NLM, RDP algorithms in MATLAB/Octave (OpenCL support in addition to traditional C++)
• Import GATE PET LMF, ASCII or ROOT data into MATLAB/Octave and either reconstruct them in their list-mode format, in the OMEGA specific raw data format, or in the user specified sinogram format (see Known issues and limitations for LMF and ROOT limitations)
• Import GATE imageCT data and reconstruct the data
• Extract GATE PET scatter, randoms and/or trues data and optionally reconstruct it
• Compare the reconstructed image with the actual "true" GATE PET source image (i.e. error analysis)
• Matrix-free reconstruction possible, with a pure CPU version (OpenMP parallelization), pure OpenCL version (multidevice support, e.g. multiple GPUs or heterogenous computing) or OpenCL version utilizing ArrayFire libraries
• Preliminary CUDA support available
• Include PET attenuation correction, normalization, scatter correction and/or randoms correction into the reconstruction (either user-made or OMEGA made data)
• Compute PET normalization coefficients from measured/simulated data
• Perform variance reduction and/or smoothing on randoms/scatter data
• Perform GATE PET Monte Carlo scatter correction
• Perform corrections either to the measurement data (excluding attenuation) or during the reconstruction phase (ordinary Poisson)
• Optionally allows to obtain only the system/observation matrix used in PET/CT reconstruction
• All the data (e.g. sinograms, system matrix) can be used with your own algorithms
• Supports scanners with pseudo detectors
• Supports sinogram gap filling in pseudo detector case
• Parallel and matrix free forward and back projection functions
• Ready-made function for custom gradient-based priors
• Three different projectors available, one being the improved Siddon's algorithm with user-specified number of transaxial and axial rays, one being the orthogonal distance-based ray tracer (2.5D or 3D mode) and one a volume of intersection ray tracer.
• Point spread function (PSF) support
• Optional deblurring available to PSF reconstruction
• Support for dynamic (time-varying) imaging (time-series of images)
• Several different subset selection methods, including random sampling, golden angle sampling, every nth measurement, etc.
• Support for Siemens Inveon PET list-mode, attenuation and scatter data
• Support for Siemens Biograph mCT and Vision list-mode data
• Support for Siemens Inveon CT projection data and any (µ)CT using tiff, bmp or binary projection images
• (Preliminary) Support for TOF data, both simulated and measured

Additional features

These features can be used as independent functions without any input needed from any other OMEGA files

• Save images (matrices) in MATLAB/Octave in NIfTI, MetaImage, Interfile, Analyze 7.5, DICOM and raw binary formats (saveImage.m)
• Import NIfTI, MetaImage, Interfile, Analyze 7.5, DICOM and raw binary formats into MATLAB/Octave (importData.m)
• Save images (matrices) in MATLAB/Octave in Interfile (saveInterfile.m) or MetaImage formats (saveMetaimage.m)
• Convert CT-attenuation coefficients into 511 keV attenuation coefficients (attenuationCT_to_511.m)
• (Experimental) Convert CT-attenuation coefficients directly from CT DICOM images into 511 keV attenuation coefficients (create_atten_matrix_CT.m)
• Convert COO (Coordinate list) sparse matrix row indices into CSR (Compressed sparse row) indices (coo_to_csr.m)
• Convert voxelized phantoms/sources into GATE compatible files (Voxelized_phantom_handle.m, Voxelized_source_handle.m)

System Requirements

MATLAB R2009a or later is mandatory. Following versions are guaranteed to work: 2017a, 2017b, 2018b, 2019a, 2019b and 2020a.

For Octave, 5.1 and 5.2 works. 4.4 should also work but is untested. io and statistics packages are required for some features.

C++11 compiler is required.

For Windows Visual Studio 2019 or 2017 is recommended with "Desktop development with C++", no other options are required. https://visualstudio.microsoft.com/

For Linux it is recommended to use GCC which usually comes bundled with the system.

On MacOS Xcode is required https://apps.apple.com/us/app/xcode/id497799835?mt=12.

OpenCL SDK/headers/library are required for OpenCL functionality.

ArrayFire is required for implementation 2.

For OpenCL, an OpenCL 1.2 compatible device is required. For CUDA, compute capability of 2.0 or higher is required.

The following third-party MATLAB codes are NOT required, but can be useful as they can be optionally used:
https://se.mathworks.com/matlabcentral/fileexchange/27076-shuffle (Shuffle, used by random subset sampling) https://se.mathworks.com/matlabcentral/fileexchange/22940-vol3d-v2 (vol3d v2, used for 3D visualization)
https://github.com/stefanengblom/stenglib (FSPARSE, used when creating sparse matrices. Recommended only for R2019b and eaerlier.) https://www.mathworks.com/matlabcentral/fileexchange/8797-tools-for-nifti-and-analyze-image (Tools for NIfTI and ANALYZE image, to load/save Analyze files and also NIfTI files in absence of image processing toolbox).

Known Issues and Limitations

MATLAB & Octave

Raw data with non-GATE data is still experimental (i.e. the data needs to be formatted in the same way as done in OMEGA).

Multi-device/GPU reconstruction only supports OSEM and MLEM.

Implementation 4 (OpenMP CPU) supports only one prior/algorithm at a time.

LMF output currently has to contain the time stamp (cannot be removed in GATE) and detector indices. The source location needs to be included if it was selected in the main-file, same goes for the scatter data. If you have any other options selected in the LMF output in GATE, then you will not get any sensible detector data. Source locations and/or scatter data can be deselected. LMF data, with different format than in GATE, are not supported.

LMF source information is a lot more unreliable than the ASCII or ROOT version.

Scanners with more detectors than 65536 will not work with the raw data format of OMEGA.

Due to the same reason as above, maximum number of counts per sinogram pixel is 65535 (applies only to GATE PET data).

Moving bed is not supported at the moment (needs to be step-and-shoot and the different bed positions need to be handled as separate cases).

Only cylindrical symmetric scanners are supported inherently, for other types of scanners the user has to input the detector coordinates.

For CT, only cone beam flat panel scanners are supported. For other types of scanners, the user has to input the detector coordinates.

ROOT or ASCII data is not yet supported with GATE CT data.

Attenuation correction can be applied only with attenuation images (e.g. CT images scaled to 511 keV).

ECAT geometry is supported only with ASCII data. ROOT data might also work (untested).

If you are experiencing crashes when using implementation 2, it might be caused by the graphics features of ArrayFire. In this case I recommend renaming/removing the libforge.so files from the ArrayFire library folder (e.g. /opt/arrayfire/lib64/). Alternatively you can install the no-gl AF:
http://arrayfire.s3.amazonaws.com/index.html (3.6.2 is the latest). Finally, you can also simply build AF from source, preferably without building Forge. This seems to apply only to Linux and affects both MATLAB and Octave.

MATLAB

If you get GLIBCXX_3.4.XX/CXXABI_1.3.XX not found error or an error about "undefined reference to dlopen/dlclose/dlsomethingelse" when building or running files, this should be fixed with one of the methods presented here:
https://se.mathworks.com/matlabcentral/answers/329796-issue-with-libstdc-so-6

Or see the solutions in installation help.

If you are using ROOT data with ROOT 6.16.00 or newer you might receive the following error message: "undefined symbol: _ZN3tbb10interface78internal20isolate_within_arenaERNS1_13delegate_baseEl". This is caused by the libtbb.so.2 used by MATLAB (located in /matlabroot/bin/glnxa64). Same solutions apply as with the above case (e.g. renaming the file). See installation help for details.

ROOT data import is unstable in MATLAB R2018b and earlier versions due to a library incompatibility between the Java virtual machine in MATLAB and ROOT. On Linux you will experience MATLAB crashes when importing ROOT data. There is a workaround for this by using MATLAB in the no Java mode (e.g matlab -nojvm), though you won't have any GUI or graphic features. MATLAB R2019a and up are unaffected. It is recommended to use nojvm for data load only (set options.only_sinos = true to load only the data).

ROOT is not supported on Windows, though it should, theoretically, work if you use ROOT with 32-bit MATLAB, but this is untested.

Octave

Implementation 2 (ArrayFire matrix free OpenCL) can only be enabled by manually building ArrayFire with Mingw. Instructions are provided here.

Almost all MATLAB-based code runs significantly slower compared to MATLAB (this is due to the slowness of loops in Octave). Reconstructions are unaffected.

MAT-files that are over 2 GB are not supported by Octave and such large data sets cannot be saved in Octave at the moment.

Upcoming Features

Here is a list of features that should appear in future releases:

• Support for SPECT data
• Support for "list-mode" GATE CT data (ROOT and ASCII)
• New projectors

Reporting Bugs and Feature Requests

For any bug reports I recommend posting an issue on GitHub. For proper analysis I need the main-file that you have used and if you have used GATE data then also the macros. Preferably also all possible .mat files created, especially if the problem occurs in the reconstruction phase.

For feature requests, post an issue on GitHub. I do not guarantee that a specific feature will be added in the future.

Citations

If you wish to use this software in your work, cite this paper: V-V Wettenhovi et al 2021 Phys. Med. Biol. 66 065010. The peer reviewed (open access) paper on OMEGA can be found from https://doi.org/10.1088/1361-6560/abe65f.

Acknowledgments

Original versions of COSEM, ACOSEM, ECOSEM, RAMLA, MRAMLA, MRP, L-filter, FMH, weighted mean, quadratic prior, sinogram coordinate and sinogram creation codes were written by Samuli Summala. Normalization coefficient and variance reduction codes were written by Anssi Manninen. Initial work on TOF was done by Jonna Kangasniemi. All other codes were written by Ville-Veikko Wettenhovi. Some pieces of code were copied from various websites (Stack Overflow, MATLAB Answers), the original sources of these codes can be found in the source files.

This work was supported by a grant from Jane and Aatos Erkko foundation, Instrumentarium Science Foundation and Jenny and Antti Wihuri Foundation. This work has been supported by University of Eastern Finland, Planmeca Group and Academy of Finland.

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