Abstract

The main goal of the research presented in this paper was to develop a refined machine learning algorithm for industrial tomography applications. The article presents algorithms based on logistic regression in relation to image reconstruction using electrical impedance tomography (EIT) and ultrasound transmission tomography (UST). The test object was a tank filled with water in which reconstructed objects were placed. For both EIT and UST, a novel approach was used in which each pixel of the output image was reconstructed by a separately trained prediction system. Therefore, it was necessary to use many predictive systems whose number corresponds to the number of pixels of the output image. Thanks to this approach the under-completed problem was changed to an over-completed one. To reduce the number of predictors in logistic regression by removing irrelevant and mutually correlated entries, the elastic net method was used. The developed algorithm that reconstructs images pixel-by-pixel is insensitive to the shape, number and position of the reconstructed objects. In order to assess the quality of mappings obtained thanks to the new algorithm, appropriate metrics were used: compatibility ratio (CR) and relative error (RE). The obtained results enabled the assessment of the usefulness of logistic regression in the reconstruction of EIT and UST images.

Highlights

  • Tomography is a non-invasive method of identifying the interior of objects [1]

  • In order to compare cases of reconstruction of electrical impedance tomography (EIT) and ultrasound transmission tomography (UST), data generated by simulation were used

  • A pattern image was assigned to each analyzed case, and the performed reconstructions were divided into three variants differing with the applied coefficient l: l = 0.6, l = 0.5 and l = 0.4

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Summary

Introduction

Tomography is a non-invasive method of identifying the interior of objects [1]. The non-destructive nature of this method is both its advantage and disadvantage. Lack of the necessity of damaging or total destruction of the examined object is burdened with the necessity to solve the inverse problem, which is an immanent feature of every type of tomography [2,3,4]. If the problem is not well-posed, it should be reformulated in a way that allows the use of a numeric algorithm [9]. In such cases, additional assumptions are usually applied, e.g., a smoothness of the solution. Additional assumptions are usually applied, e.g., a smoothness of the solution Regularization of linear problems is usually carried out by Tikhonov regularization

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