Optimization Approach for Image Forming in Ultrasound Transmission Tomography (UTT): Real Data Case

Tomasz Rymarczyk,Jan Sikora

doi:10.1155/2019/9126136

Abstract

Effective image reconstruction algorithm that could be used in Ultrasound Transmission Tomography (UTT) is presented in this paper. The reconstruction process was bringing over to the solution of the inverse problem which was converted to the optimization task. The optimization parameters were selected as follows: a position vector defining the position of the obstacle centre (the length of the position vector and its angle) and the internal radius of the test objects (obstacles). In this case, sixteen trial objects were selected, which gives 48th optimization parameters (three parameters for each trial object). During the optimization process some of them could diminish to zero; the others would change the position and dimensions in such a way that the calculated signal become as close as possible to the measured one. The objective function and linear inequality constrain were defined. The optimization process is very sensitive how far away from the optimal solution the starting point was defined. That is why three cases of the selection of the starting point to the optimization process were considered.

Highlights

The idea of optimization approach, among the others [1–8], is very popular for the inverse problem’s solution [9,10,11,12,13,14]and could be successfully applied in ultrasonic image reconstruction
Effective image reconstruction algorithm that could be used in Ultrasound Transmission Tomography (UTT) is presented in this paper
For the case when the starting point was determined by analysis of measured signal and for the hybrid approach the results of reconstruction are presented in

Summary

Introduction

Could be successfully applied in ultrasonic image reconstruction. This is not a new idea [2, 9, 15, 16] and as a matter of fact is very simple. In this work all, simplifying assumption was introduced along with the fact that ultrasound wave is propagated along strait lines [16] Despite such strong simplifying assumptions resulting images are satisfactory with respect to the imaging precision and could be applied in the industry. ART approach makes it possible to cover the existence of a possible object, which would be subject to optimization Both approaches for defining the starting point and those mentioned above have certain disadvantages. A third approach to the optimization process was proposed This third approach was called a generalized starting point. This approach has already been successfully used in nonclassical problems (not X-ray tomography). Tomography (UTT) for industrial processes is able to offer reliable images

One Internal Object Case

The Objective Function Definition

The Linear Inequality Constrains

Results of Reconstruction

Conclusions