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.

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.