Ultrasound images are typically generated using the Delay-And-Sum (DAS) method, which assumes a homogeneous propagation medium. When an aberrating layer is situated between the sensor array and the imaging target, this assumption does not hold, and DAS is replaced with model-based methods. These methods are computationally expensive and require to accurately model the aberrations caused by the layer. This thesis investigates novel methods for image formation and aberration estimation. The effect of the layer is described using a set of transfer functions from the sensor array to a virtual array placed after the layer. In the first part, we assume the transfer functions are known, and we propose a new method for image formation. The transfer functions allow to map the signal from the sensor array to the virtual array, and the DAS method is used on the virtual array signal. This technique is equivalent to model-based matched filtering in terms of image quality, without requiring expensive matrix computations. In the second part, the transfer functions are unknown, and a novel technique is introduced for their estimation. Using pulse-echo data, a focus-quality metric is computed to quantify the accuracy of the transfer function estimate. The transfer functions are modeled using a dictionary and the dictionary coefficients are iteratively updated to increase the defined metric. The optimization leads to improved focus quality and sharper images. In the case the layer model requires a limited dictionary, the proposed algorithm generates an accurate estimate of the transfer functions.

The application of Compressive Sampling (CS) in the medical ultrasound has been widely studied in recent years with the growing requirement of reconstructing high-quality images with smaller data size. Most of the current studies with successful CS reconstruction are mainly focusing on the mathematical applications of CS theory in ultrasound imaging. However, the randomized mechanisms in these studies are hard to be fully fulfilled in hardware. In addition, some of the studies try to discover the sparse representation of signals by ignoring a part of information rather than compressing all data. We propose a new compression scheme for fast image acquisition in ultrasound imaging using a method, which is similar in style to CS. Our scheme is based on the formulation of an inverse scattering problem (ISP), where the Born approximation have been used during its derivation. In our system, the ultrasound image are represented by a collection of hypothetical points, what can be called pixels. These points are identified by their unique spatial impulse responses relative to the elements in the transducer. The randomized linear combinations of the spatial impulse responses from the view of elements can be maintained the uniquenesses of these points, which is similar to the coding techniques in data compression. Hence, our compression scheme can be more controllable than the conventional CS, which can achieve the real-time compression of data during the acquisition stage in hardware. We employ L2-regularization to solve the ill-posed ISP rather than the L1-regularization CS since there is no any assumption of signal sparsity. In our work, we finally achieve the acceptable reconstructions by compressing the raw data to 12.5% of its original size. The results are better than 12.5% with multiplexing the received signals from 12.5% elements in the array and almost as good as 25% with multiplexing the received signals from 25% elements in the array.

Understanding the hidden organizational principles existing in the human brain was always one of the great challenges in Neuroscience. To uncover the way the brain functions, advancements in the fields of Medical Imaging and Computational Science have been of great importance. Powerful imaging tools, such as functional magnetic resonance imaging (fMRI) and positron emission tomography (PET), have already enabled scanning the whole brain volume and visualizing the brain functioning, both at rest and during task execution, to a significant degree. However, several limitations especially in spatiotemporal resolution led to the need for further advancements in the field of functional imaging. An alternative technique, that overcomes most of the previously existing problems, is functional ultrasound (fUS). fUS is capable of imaging even the microvasculature blood-flow dynamics in response to brain activation with high spatiotemporal resolution. The wealth of fUS-acquired data calls for advanced data-analytic methods to uncover new information, beyond the well-applied simple univariant correlation method. This is the main goal of this MSc thesis, to use a proper analysis technique, mainly borrowed from the same-principle fMRI technique, in order to produce powerful inferences. For this reason, a detailed literature review regarding fUS imaging and fMRI analysis methods is introduced. Then, the main analysis part is focused on the Independent Component Analysis (ICA) method, trying to segregate the brain into spatially independent components that share a similar activity response. Here, the whole processing pipeline is established, describing all the necessary preprocessing steps along with ICA parameters and approaches (single- and group-ICA) using the ICASSO software package. As a post-processing step, functional images-to-Allen brain atlas registration is also performed in order to identify the different regions represented in the ICA-derived spatial components. The effectiveness of the methods is assessed based on the collected results on different datasets, obtained from 2D visual-stimulation as well as 3D resting-state experiments conducted on mice at the Neuroscience department of the Erasmus MC. As a conclusion, ICA was able to separate different anatomical and functional sub-networks. More specifically, from the visual-stimulation experiments, brain regions such as Lateral geniculate nucleus (LGN) that play a role in the visual pathway are identified, while from the resting-state the spatial continuity of different regions is confirmed.

At the Center for Ultrasound and Brain imaging at Erasmus MC in Rotterdam, a mouse's visual cortex had been imaged using the fUS technique. The mouse had been exposed to different visual stimuli. The stimuli varied in position, size, and shape. We investigate how the measured task-based fUS signals differ depending on the visual stimuli presented to the mouse. For that purpose, we decompose the fUS data with four different methods giving different levels of sparsity. This thesis compares the performance of the four methods, and provides neurological insights obtained with these methods. For modeling the data, we consider four data-driven decomposition methods: ICA and three sDL variants. The methods decompose the data into better interpretable spatial maps and time courses. Every decomposition is further examined by training L1-regularized prediction models that optimize for sparsity. The goal is to predict the presented stimulus based on the decomposed data. Furthermore, the potential of group lasso regularization in prediction models is illustrated. The decompositions extract spatial maps anatomically linked to the visual cortex, superior colliculus and the hippocampus. All decompositions achieve considerable performance in the position prediction but have low success in the size and shape prediction. ICA outperformed the three sDL variants in all prediction tasks. Furthermore, group lasso regularization is found to be a useful tool to obtain discriminatory information in the time dynamics.

Functional ultrasound (fUS) is a neuroimaging modality that offers high spatial and temporal resolution while also providing portability. In this thesis, neuroimaging data acquired with fUS at Center for Ultrasound and Brain imaging at Erasmus MC (CUBE) is processed. Due to the fact that fUS data is inherently multidimensional, we propose using tensor decompositions, tensors here referring to generalizations of matrices, for processing of fUS data. We define two main research questions regarding fUS data analysis. First, for compressing the large-scale raw beamformed fUS data, we apply sequentially truncated multilinear singular value decomposition. This compression method is compared against ensemble averaging used in the conventional pipeline, and shown to provide a higher compression rate while preserving more temporal resolution for specific ranks. Furthermore, it is observed to denoise the data, resulting in a more precise extraction of the active region of Superior Colliculus using correlation maps. Secondly, in order to investigate the advantage of multi-slice processing that incorporates 3-D informa- tion, blind-source separation methods are applied to single slice and two-slice fUS recordings. After applying independent component analysis (ICA) to the matricized data as a benchmark method, block term decompo- sition (BTD) is used as a way of processing the data as it is, in its natural 3-D structure without vectorization. Through a simulation study, it is shown that the method is able to separate two images even when using a rank that is lower than the true rank, as well as in noisy conditions. Subsequently, BTD is applied to real 4-D fUS data formed by concatenation of slices in a new dimension. However, this method is seen to perform worse than single slice ICA in terms of extracting the active regions. In order to amplify common information between slices, a new 3-D data structure is then formed by summing the fUS data of two slices. For extraction of this common information, a BTD is then applied to the aggregate 3-D data. The findings of this decomposition reveal that both taking a longer portion of single slice data and incorporating the second slice helps to achieve better results.

Doppler ultrasound imaging of cerebral blood flow faces challenges arising from a low signal-to-noise ratio (SNR) and a wide dynamic range. Echo signals received from blood cells are significantly weaker compared to surrounding tissues, such as the skull or brain soft tissue, resulting in inhibited visualization of small blood vessels and deep brain areas. To address this issue, this thesis explored the feasibility of employing and improving coded excitation techniques to enhance the SNR of Doppler ultrasound images. Furthermore, an optimized code for Doppler ultrasound imaging is designed, represented by a generalized encoding matrix. The research begins with the definition of a linear signal model that incorporates the encoding matrix. Subsequently, a trace-constraint optimization problem is formulated based on maximizing the Fisher information matrix to find the optimized encoding matrix. The feasibility and performance of the optimized encoding matrix are assessed through simulations on both small and large array settings, which operate above Nyquist sampling frequency and under Nyquist sampling frequency respectively. The imaging results indicate that the optimized code exhibits higher SNR in deep image regions compared to existing coded excitation methods like Barker code while using the same number of transmissions, bit length, and same average transmit energy, albeit with a trade-off of decreased axial resolution. Nonetheless, this resolution degradation can be mitigated through the application of the iterative imaging technique LSQR. Finally, the optimized code is tested in a clinical transducer setting, and a blood flow simulation is conducted. The outcomes showcase the capacity of the proposed optimized code to enable higher SNR in Doppler ultrasound imaging and more accurate and informative clinical assessments.

Previous work [1] has demonstrated the possibility of high resolution imaging through the use of a single element and a aberration mask. This thesis will expand on the previous work by examining the proposed method for errors in the creation of the model. The analysis is preformed by examining the various aspects of the measurements setup and underlying theoretical model, after which measurements are performed to determine their contribution and correctness with regard to the model. Results demonstrated a systematic error of a non-linear frequency scaling and semi-linear phase shift. The origin of the error lies in the unwanted addition of transfer functions of some of the components. A Tikhonov regularized least squares method is proposed to estimate this transfer function and supply compensation based on all the measurements. The results of application of this method on the uncalibrated model are demonstrated through 1D imaging experiments. The result of which show a signicant improvement over the previous uncalibrated results. After which the possibility of calibration due to a singular measurement is explored and a adaptation of the Tikhonov regularized least squares method is proposed for close approximation of the previously found transfer function. Further to obtain an indication of possible remaining hurdles and successes with this method, extensive simulations are preformed to examine the individual impact of various sources of noise and interference.

Detailed imaging of blood flow may improve the understanding of brain functions. The state-of-the-art non-invasive flow imaging of the brain is limited to a one-dimensional Doppler setting. We propose a method to estimate the two-dimensional flow vector in the fine vascular network of the brain by using a speckle tracking technique. The framework of Orthogonal Matching Pursuit is used for speckle tracking and modified to include prior constraints to guide the matching process among two frames, called as Guided Orthogonal Matching Pursuit. Prior constraint is in the form of a directional constraint which determines the probability of vector flow in all the directions according to the orientation of the vessels. The orientation of the vessels is computed using Power Doppler Imaging. In this work, the proposed method for two-dimensional vector estimation is compared with the standard block matching technique of Normalized Cross-Correlation. We see that the variance of the final velocity estimates has reduced when compared to the standard speckle tracking method and the direction of blood flow is found within the curvature of the vessel.