Image Reconstruction In Breast Ultrasound Tomography: Computational Analysis And Performance

Breast Cancer is the second leading cause of fatality among all cancers in women. Eachyear39,970women die in united state because of the disease. In UK,48,417new casesdiagnosed each year. WHO stated that Worldwide1.4million new cases have beendiagnosed positively in2008. Developing countries are not an exception and half of theglobally registered cases occurred there. The percentage of breast cancer cases increasedsignificantly in China and Eastern Asia in the last few years, where17.2-25.8out of100,000women have been diagnosed with breast cancer in2008. Many studies haveproven that the detection of cancer in early stages limits the rate of mortality. Severalmodalities are available for breast cancer screening, such as X-ray mammography, OpticalImaging Techniques (OIT), Magnetic Resonance Imaging (MRI), and B-mode UltraSound(B-US). Each of these modalities has many its own advantages and disadvantages.Ultrasound Computes Tomography (USCT) is a powerful and important alternative to theaforementioned modalities, which deals with recovering images of the physical propertiessuch as sound speed distribution, attenuation coefficient, refractive index, etc. Particularly;in this study, we are interested in reconstructing an image of the sound speed of the femalebreast. Therefore, we call such a system as Breast Ultrasound Tomography (B-USCT). Ingeneral, image reconstruction in B-USCT is accomplished in three main steps: mediumparameterization, formulating the forward problem, and defining and solving the inverseproblem.The main purpose of this dissertation is to examine the applicability of the wave equation-based and straight ray-based inversion techniques in USCT. This thesis introduced threedifferent methods for B-USCT. The first part of our exposition deals with the theoreticalaspects and the mathematical formulation of the Diffraction Tomography (DT), whichrelies on the Fourier diffraction tomography. We have showed that straight-ray model isnot appropriate for highly diffracted media. Then, we have showed that exploiting theBorn approximation to simplify the inhomogeneous wave equation we can invent an easyrelationship between the object and its projections in the frequency domain. Our results show that the DT algorithm outperforms the Filtered-Back Projection when usingdiffracted sources such as ultrasound or microwaves.In the second part, we have developed a wave-based tomographic imaging method. In thismethod, there is no approximation made to the wave equation. However, it has two majordrawbacks, which make difficult to be implemented in a practical setting:1) The amountof the acquired data is too large, which makes the inversion process computationallyintensive;2) It is usually ill-conditioned, which means that the convergence is difficult toobtain. In this work, we addressed these two shortcomings by applying the AdjointMethod (ADM) for the first problem, and the second one is solved by utilizing a globallyconvergent method called Homotopy Continuation Method (HCM).The third part introduces an alternative method for B-USCT, namely the travel-timetomography method. This method also tries to image the sound speed distribution withinthe female breast. In this part, we consider the reconstruction problem as a minimizationproblem. Accordingly, we tried to minimize the difference between the measured data andthe simulated data. We applied the Gauss-Newton Method (G-NM) to minimize the costfunction (error) iteratively. Each iteration requires solving a linear system, which can besolved efficiently by combining several available methods. The results showed that theimage quality obtained by this approach beats the other ones (DT and wave-basedtomography).