Abstract
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.