Seismic imaging is a method for generating images of the subsurface of the Earth without the need to drill down to observe it directly. Using a seismic source, high-amplitude acoustic waves are generated, which propagate through the Earth. When these waves encounter interfaces between different layers, part of their energy is reflected, traveling back upwards. At the surface, these scattered waves are recorded using an array of sensors. These recorded wavefields are then used as input for a seismic imaging algorithm, which attempts to reconstruct an accurate image of the subsurface based on these measurements.
While many different seismic imaging methods exist, this thesis focuses specifically on Full-Wavefield Migration (FWM). FWM is a least-squares migration method, based on iteratively updating the image in order to minimize the misfit between the recorded data and the forward modelled wavefield at the surface. Using this iterative approach, FWM is able to incorporate multiple scattering effects into the imaging process, increasing the accuracy of the resulting images. Also, by using explicit convolutional operators based on the one-way wave equation, the computational cost of FWMis reduced compared to alternative iterative imaging methods based on finite-difference modelling.
In this thesis, we describe a number of recent advancements to the FWM method. Our main focus is the extension of the FWM method to include converted waves. In order to take these effects into account, we need accurate reflection and transmission operators. However, the true, elastic reflection and transmission operators are notoriously non-linear, making them difficult to work with. Therefore, we introduce a novel set of approximations of these operators, which we name the extended Shuey approximations. To benchmark these approximations, we apply them in a simple, 1.5D scenario. This test shows that the extended Shuey approximations yield improved results for forward modelling and imaging, compared to the conventional Shuey approximation.
We then use these extended Shuey approximations to derive accurate reflection and transmission operators for the 2D case. Combining these operators with the existing theoretical framework of FWM we develop a robust imaging algorithm which takes converted waves into account. We then apply this algorithm, which we name elastic FWM, to two synthetic models. We show that, for these models, the elastic FWM method out-performs the conventional, acoustic FWM method. We also demonstrate that, using this method, additional information regarding the elastic medium parameters of the subsurface can be recovered.
Finally, we examine the known issue of slow convergence for the conventional, acoustic FWM algorithm. We introduce a novel preconditioner, based on approximating the pseudo-inverse using Proper Orthogonal Decomposition (POD). Using this preconditioner, we demonstrate improved convergence for the synthetic Marmousi model and a field data set from the Vøring basin in Norway.

This thesis is concerned with the technical, physical and computational challenges regarding
the incorporation of microwave tomography in hyperthermia treatments. Hyperthermia is a
clinical technique in which tumorous tissue is heated to gain therapeutic effect for concurrent
radiotherapy. Hyperthermia by microwaves, as performed at the Erasmus Medical Center,
suffers from uncertainties and lacking control. To relieve the burden of uncertainties regarding
dielectric properties and patient positioning, microwave tomography can be used in hyperthermia systems. This could also improve treatments, as it would offer more possibilities for
controlling the delivery. This work is focused on relieving several practical limitations to the
integration of tomography, rather than researching its possibilities. This thesis is accompanied by the literature research “Advancements in Microwave Tomography and Hyperthermia
Treatments” by the same author.

Imaging by inversion of acoustic or electromagnetic wave fields have applications in a wide variety of areas, such as non-destructive testing, biomedical applications, and geophysical explorations. Unfortunately, each modality suffers from its own application specific limitations, typically being difficulties in distinguishing different materials or tissues from each other in the case of acoustic wave fields and a low spatial resolution in the case of electromagnetic wave fields. To exploit the advantages of both imaging modalities, methods to combine them include image fusion, usage of spatial priors and application of joint or multi-physics inversion methods. The latter can be based on empirical relations between acoustic and electromagnetic medium properties or on structural similarity. In this work, two joint inversion algorithms based on structural similarity are presented. To account for the structural similarity the error-functional of standard Born inversion is extended with an additional penalty term. This additional term is either based on the L2-norm of the cross-gradient (CG), i.e. the cross product of the gradients of the acoustic and electromagnetic contrasts or on the L2-norm of the gradient difference (GD), i.e. the difference between the normalized gradients of both contrasts. To test the proposed methods, two synthetic models are considered; one with the gradients of the contrasts pointing in the same direction and one where the gradients point in opposite directions. Results show that the GD constraint significantly improves the resolution for the electromagnetic reconstruction compared to separate BI. The mean square errors (MSE) of the reconstructed profiles for the separate BI are 0.12 for the acoustic and 0.51 for the electromagnetic case, and for the joint GD inversion, 0.09 for the acoustic and 0.46 for the electromagnetic case. The joint GD inversion fails when using the model with the gradients of the contrasts pointing in opposite directions. The joint CG inversion does not enhance the reconstructed images, but shows similar performances for the different models. In conclusion, joint inversion based on structural constraints is shown to improve the electromagnetic resolution, especially using the GD constraint. Further research needs to be conducted to extend the functionality of the GD constraint to acoustic and electromagnetic contrasts with opposite contrast gradient directions.

This report describes the study on the optimization of the magnetic field generated by a low-field magnetic resonance imaging modality. In the optimization the Genetic Algorithm and a quasi-Newton Algorithm are used.

Breast cancer is the most occurring cancer among women. Detecting it at an early stage enables to significantly reduce the mortality rate. Mammography is the golden standard technique used for screening but it has some disadvantages, among which the difficulty to scan women with dense breasts. Ultrasound is a promising technique enabling a cheap and fast diagnosis. More precisely, waveform inversion reconstructs the 3D speed of sound distribution within the breast, enabling an easier differentiation between healthy and non-healthy tissues.

In this work, two inversion methods are investigated, namely Algebraic Reconstruction Technique (ART) and Born inversion. Born inversion is a non-linear waveform inversion method aiming at solving an integral equation. To increase its performance while keeping the computation time constant, the frequencies used for the reconstruction are chosen randomly over a given bandwidth for each source receiver combination, at the expense of an additional noise in the reconstruction. The sparsity of the reconstruction in the wavelet
domain has been utilized to implement two new regularization methods aiming at reducing this noise. To test and validate the three algorithms (namely ART and Born Inversion with the two regularization methods), a phantom study has been performed with both synthetic and real data. The phantom, made out of agar, is
placed in a square water tank in the centre of a measurement setup designed during this study, allowing to scan the phantom from its four sides.

The results of the methods are presented and discussed. ART does not perform well with real data as the assumption on which it relies is not satisfied at the frequencies used in this study. Born inversion is presented with transmission and reflection data, as well as a combination of the two. With synthetic data, both reflections and transmissions give very satisfying results with the help of the regularization. With real data the phantom is correctly imaged by the reflections but the transmissions do not perform well enough to give an accurate speed of sound map.

The knowledge gathered in this work can help building a better measurement setup, with a phantom closer to the breast geometry and internal structure, with which the reconstruction techniques could be tested and further improved.

Breast cancer is impacting over 1.5 million women each year. Early detection is essential in decreasing the mortality rate. Mammography is currently the golden standard for breast screening. However, this method is not ideal and water-bath ultrasound breast scanning is considered to be a promising screening modality. This type of scanning system is able to obtain ultrasound reflection and transmission data. In this study, a water-cup breast scanning setup is built. The setup consists of a plastic cup with four acoustic windows and four phased array ultrasound probes. The water-cup is used to execute a phantom study. The phantom study gives insight into the operability of the built water-cup. The differences between reflection and transmission data are observed and utilised. One imaging algorithm and two inversion algorithms are employed to reconstruct an image of the phantom. The images of the different algorithms are compared.
Furthermore, a method is proposed that reduces the computation time of a reflection data based Born inversion algorithm. In the end, the water-cup is used to image an ex-vivo human breast. Finally, the limitations of the built water-cup are stated. In addition to manufacturing the water-cup, a pulse-echo-scan of an ex-vivo human breast is made. This pulse-echo-scan is compared with the cross-sectional photograph of the breast. Due to the pudding-like structure of the breast, it is challenging to make a cross-section at the same position as the pulse-echo-scan is made. The pulse-echo-scan is made at the Pathology Department of the Erasmus MC. The ex-vivo human breast study helps to understand what structures are present in the breast. This knowledge can be used to build a new measurement setup and optimize the imaging algorithms for finding tumours.