Compensated Row-Column Ultrasound Imaging System

Ultrasound imaging is a valuable tool in many applications ranging from material science to medical imaging. While 2-D ultrasound imaging is more commonly used, 3-D ultrasound imaging offers unique opportunities that can only be found with the help of the extra dimension. Acquiring a 3-D ultrasound image can be done in two main ways: mechanically moving a transducer over a region of interest and using a fixed 2-D transducer. Mechanical motion introduces unwanted artifacts and increases image acquisition time, so a fixed 2-D is usually preferred. However, a fully addressed 2-D array will require a significant amount of connections and data to handle. This motivated the exploration of different simplification schemes to make 2-D arrays for 3-D ultrasound imaging feasible. A method that received a lot of attention for making real-time volumetric ultrasound imaging possible is the row-column method. The row-column method simplifies the fully addressed 2-D array by utilizing a set of 1-D arrays arranged in rows and another set in columns, one set will be responsible for transmit beamforming, while the other for receive beamforming. Using this setup, only $N+N$ connections are needed instead of $N\times N$. This simplification comes at the cost of image quality. Recent advances in row-column ultrasound imaging systems were largely focused on transducer design. However, these imaging systems face a few intrinsic challenges which cannot be addressed through transducer design alone: the issues of sparsity, speckle noise inherent to ultrasound, the spatially varying point spread function, and the ghosting artifacts inherent to the row-column method must all be taken into account. As such, strategies for tackling these intrinsic challenges in row-column imaging would be highly desired to improve imaging quality. In this thesis, we propose a novel compensated row-column ultrasound imaging system where the intrinsic characteristics of the transducer and other aspects of the physical row-column imaging apparatus are leveraged to computationally produce high quality ultrasound imagery. More specifically, the proposed system incorporates a novel conditional random field-driven computational image reconstruction component consisting of two phases: i) characterization and ii) compensation. In the characterization phase, a joint statistical image formation and noise model is introduced for characterizing the intrinsic properties of the physical row-column ultrasound imaging system. In the compensation phase, the developed joint image formation and noise model is incorporated alongside a conditional random field model within an energy minimization framework to reconstruct the compensated row-column ultrasound imagery. To explore the efficacy of the proposed concept, we introduced three different realizations of the proposed compensated row-column ultrasound imaging system. First, we introduce a compensated row-column imaging system based on a novel multilayered conditional random field driven framework to better account for local spatial relationships in the captured data. Second, we incorporated more global relationships by introducing a compensated row-column imaging system based around a novel edge-guided stochastically fully connected random field framework. Third, accounting for the case where the analytical image formation model may not optimally reflect the real-world physical system, we introduce a compensated row-column imaging system based around a data-driven spatially varying point-spread-function learning framework to better characterize the true physical image formation characteristics. While these different realizations of the compensated row-column system have their advantages and disadvantages, which will be discussed throughout this thesis, they all manage to boost the performance of the row-column method to comparable and often higher levels than the fully addressed 2-D array

Randomly-connected Non-Local Conditional Random Fields

Structural data modeling is an important field of research. Structural data are the combination of latent variables being related to each other. The incorporation of these relations in modeling and taking advantage of those to have a robust estimation is an open field of research. There are several approaches that involve these relations such as Markov chain models or random field frameworks. Random fields specify the relations among random variables in the context of probability distributions. Markov random fields are generative models used to represent the prior distribution among random variables. On the other hand, conditional random fields (CRFs) are known as discriminative models computing the posterior probability of random variables given observations directly. CRFs are one of the most powerful frameworks in image modeling. However practical CRFs typically have edges only between nearby nodes. Utilizing more interactions and expressive relations among nodes make these methods impractical for large-scale applications, due to the high computational complexity. Nevertheless, studies have demonstrated that obtaining long-range interactions in the modeling improves the modeling accuracy and addresses the short-boundary bias problem to some extent. Recent work has shown that fully connected CRFs can be tractable by defining specific potential functions. Although the proposed frameworks present algorithms to efficiently manage the fully connected interactions/relatively dense random fields, there exists the unanswered question that fully connected interactions are usually useful in modeling. To the best of our knowledge, no research has been conducted to answer this question and the focus of research was to introduce a tractable approach to utilize all connectivity interactions. This research aims to analyze this question and attempts to provide an answer. It demonstrates that how long-range of connections might be useful. Motivated by the answer of this question, a novel framework to tackle the computational complexity of a fully connected random fields without requiring specific potential functions is proposed. Inspired by random graph theory and sampling methods, this thesis introduces a new clique structure called stochastic cliques. The stochastic cliques specify the range of effective connections dynamically which converts a conditional random field (CRF) to a randomly-connected CRF. The randomly-connected CRF (RCRF) is a marriage between random graphs and random fields, benefiting from the advantages of fully connected graphs while maintaining computational tractability. To address the limitations of RCRF, the proposed stochastic clique structure is utilized in a deep structural approach (deep structure randomly-connected conditional random field (DRCRF)) where various range of connectivities are obtained in a hierarchical framework to maintain the computational complexity while utilizing long-range interactions. In this thesis the concept of randomly-connected non-local conditional random fields is explored to address the smoothness issues of local random fields. To demonstrate the effectiveness of the proposed approaches, they are compared with state-of-the-art methods on interactive image segmentation problem. A comprehensive analysis is done via different datasets with noiseless and noisy situations. The results shows that the proposed method can compete with state-of-the-art algorithms on the interactive image segmentation problem