Toeplitz Covariance Matrix Estimation for Adaptive Beamforming and Ultrasound Imaging

In recent years, adaptive beamformers have been researched more extensively, to be able to use it in the application of medical ultrasound imaging. The adaptive beamformers can provide a higher resolution and better contrasts in the resulting images than non-adaptive, and most commonly used, delay-and-sum beamformer. The difficulties of applying adaptive beamformers to ultrasound imaging can e.g. be numerical complexity, stability of statistics, coherent sources, or the robustness of the beamformer. Methods to handle these types of difficulties have been researched and successfully applied to utilize the performance advantages provided by adaptive beamformers. Why is it important to prevent these types of errors? The beamformer is used in the image formation stage, and errors that occur at this stage are difficult to get rid of even for the most sophisticated imaging software. We have in this thesis investigated methods that attempt to force the estimate of the covariance matrix to become a Toeplitz matrix. A Toeplitz matrix has equal elements along its diagonals, and has several useful properties that are desirable in array processing. Assuming the Toeplitz structure can be achieved, this is because of the spatial stationarity in the received data, it can be applied in medical ultrasound imaging. Three different methods are proposed to reach the desired Toeplitz structure in this thesis; IAAAPES, Adaptive Spatial Averaging and Spatial Convolution. The three methods for making the covariance matrix Toeplitz will be compared and analyzed to other known adaptive beamformers to detect their strengths and weaknesses