Image reconstruction by solving the inverse problem in ultrasonic transmission tomography system

Abstract

Purpose

The purpose of this study is to develop a reconstruction and measurement system for data analysis using ultrasonic transmission tomography. The problem of reconstruction from the projection is encountered in practical implementation, which consists in reconstructing an image that is an estimation of an unknown object from a finite set of projection data. Reconstructive algorithms used in transmission tomography are based on linear mathematical models, which makes it necessary to process non-linear data into estimates for a finite number of projections. The application of transformation methods requires building a mathematical model in which the projection data forming the known and unknown quantities are functions with arguments from a continuous set of real numbers, determining the function describing the unknown quantities sought in the form of inverse relation and adapting it to operate on discrete and noisy data. This was done by designing a tomographic device and proprietary algorithms capable of reconstructing two-dimensional images regardless of the size, shape, location or number of inclusions hidden in the examined object.

Design/methodology/approach

The application consists of a device and measuring sensors, as well as proprietary algorithms for image reconstruction. Ultrasonic transmission tomography makes it possible to analyse processes occurring in an object without interfering with the examined object. The proposed solution uses algorithms based on ray integration, the Fermat principle and deterministic methods. Two applications were developed, one based on C and implemented on the embedded device, while the other application was made in Matlab.

Findings

Research shows that ultrasonic transmission tomography provides an effective analysis of tested objects in closed tanks.

Research limitations/implications

In the presented technique, the use of ultrasonic absorption wave has been limited. Nevertheless, the effectiveness of such a solution has been confirmed.

Practical implications

The presented solution can be used for research and monitoring of technological processes.

Originality/value

Author’s tomographic system consisting of a measuring system and image reconstruction algorithms.

Citation

Rymarczyk, T., Kania, K., Gołąbek, M., Sikora, J., Maj, M. and Adamkiewicz, P. (2021), "Image reconstruction by solving the inverse problem in ultrasonic transmission tomography system", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 40 No. 2, pp. 238-266. https://doi.org/10.1108/COMPEL-01-2020-0045