New Reconstruction Toolsuite powered by inversion algorithms
In 1976, Keller formulated the following very general definition of inverse problems:
“We call two problems inverses of one another if the formulation of each involves all or part of the solution of the other. Often, for historical reasons, one of the two problems has been studied extensively for some time, while the other is newer and not so well understood. In such cases, the former problem is called the direct problem, while the latter is called the inverse problem.”
Inverse problems appear in many fields such as physics, engineering and electrical tomography (ERT/ECT). For the electrical tomography software developed by ITS, inversion algorithms are used to convert the sensor measurement into conductivity/permittivity images. Over the past few decades, the ‘linear back projection’ (LBP) algorithm has been the only standard reconstruction method for commercialized ERT/ECT systems because of its high-speed feature and simplicity, which is essential for monitoring industrial processes in real-time.
However, there are other algorithms that may be more suitable for some specific applications. For the past few years therefore, ITS has been working on improving tomography inversion techniques by developing our new Reconstruction Tool-Suite Package, which collects several reconstruction methods for industrial users to compare and select the most suitable algorithm for their applications (see the image above for an example of how different algorithms render different objects).
All of the new algorithms included in the Reconstruction Tool-Suite Package have gone through several verification processes in order to ensure the inverse solvers are developed correctly, so can be of maximum benefit for users. In creating this software package, the following steps have been taken by ITS developers:
- Step 1: Each reconstruction method is first designed and implemented using MATLAB, and validated using ITS measurement database.
- Step 2: The MATLAB prototype reconstruction model is examined by the Engineering Tomography Laboratory (ETL) at University of Bath.
- Step 3: Once the model is verified, the MATLAB code is implemented into ITS Tool-Suite using the linear algebraic libraries.
- Step 4: After the MATLAB code is implemented into Tool-Suite, the reconstruction result is cross-checked with our previously designed MATLAB model, to make sure no error is made in the conversion process.
ITS’s Reconstruction Tool-Suite Package is the first commercial software to introduce non-LBP methods to industrial users. The ‘Super Jacobian scheme’ is implemented in the software so that all the single step inverse algorithms can be executed as fast as the LBP method. ITS R&D Engineer Kent Wei remarked:
“We believe that this Reconstruction Tool-Suite can offer a platform for our clients to explore our pioneering tomography techniques in greater depth. This software package collects some of the most popular mathematical algorithms for users to compare and investigate the quality improvement of reconstructed images. All of this means that Reconstruction Tool-Suite will enable users to gain more accurate insights into their applications.”
ITS’s Reconstruction Tool-Suite will be released in May, 2014.