A Deep Residual Neural Network for Image Reconstruction in Biomedical 3D Magnetic Induction Tomography

Abstract

In recent years, it has become increasingly popular to solve inverse problems of various tomography methods with deep learning techniques. Here, a deep residual neural network (ResNet) is introduced to reconstruct the conductivity distribution of a biomedical, voluminous body in magnetic induction tomography (MIT). MIT is a relatively new, contactless and noninvasive tomography method. However, the ill-conditioned inverse problem of MIT is challenging to solve, especially for voluminous bodies with conductivities in the range of biological tissue. The proposed ResNet can reconstruct up to two cuboid perturbation objects with conductivities of 0.0 and 1.0 S/m in the whole voluminous body, even in the difficult-to-detect centre. The dataset used for training and testing contained simulated signals of cuboid perturbation objects with randomised lengths and positions. Furthermore, special care went into avoiding the inverse crime while creating the dataset. The calculated metrics showed good results over the test dataset, with an average correlation coefficient of 0.87 and mean squared error of 0.001. Robustness was tested on three special test cases containing unknown shapes, conductivities and a real measurement that showed error results well within the margin of the metrics of the test dataset. This indicates that a good approximation of the inverse function in MIT for up to two perturbation objects was achieved and the inverse crime was avoided.

Magnetic Induction Tomography: Separation of the Ill-Posed and Non-Linear Inverse Problem into a Series of Isolated and Less Demanding Subproblems

“…The method can be applied to a recently realized 3D MIT scanner [ 19 , 20 , 27 ], where essentially only two sinusoidally alternating eddy current fields, J φ and J ψ , provide the basis for all signals S . The approach appears less suitable for commonly published and circular MIT setups with multiple excitation coils ( Figure 1 a) and more eddy current fields, where the number of independent and unknown moments can considerably exceed the number of searched conductivities.…”

“…Approaches to 3D scenarios following Figure 3 are currently being investigated. The principles are not fundamentally different, and since successful 3D reconstructions have already been demonstrated with other algorithms using this scanner [ 19 , 20 , 27 ], the structural information is definitely present in the signals. However, in addition to the greater error-proneness of a 3D code, the difficult visualization of 3D vector fields also makes the tracking of possible errors more difficult.…”

“…Moreover, the process does not allow for simple and instructive insights, as deriving handy conclusions for favorable measures is difficult from this type of integral strategy. This is even truer for the MIT inversions using machine learning, which was also studied for this particular MIT setup [ 27 ]. On the one hand, machine learning can provide fast and good solutions for ill-posed inverse problems in imaging [ 28 ].…”

Influence on Sample Determination for Deep Learning Electromagnetic Tomography

“…This is the change in sample size used in 21 randomly selected papers on DL-ET in recent years [ 16 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 ]. In Figure 1 , the size of each point represents the size of the sample set used in an article, while different colors are assigned to them for easy distinction.…”

“…The signals were stored as one-dimensional vectors with a dimension of 1236. This dataset was meticulously designed [ 30 ]. The design of the samples in these studies is usually based on experience, with few research efforts optimizing the number and composition of samples based on data and algorithms.…”