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.

In this thesis, we investigate a sparse basis for ultrasound images, so that we can use sparse regularization in imaging. Actually, there are few previous researches explicitly demonstrating that medical ultrasound images can be sparsified for some dictionary. We consider various orthogonal transforms such as wavelet transforms, cosine transforms and wave atom transforms. Then, we perform those transforms on various ultrasound images and analyzes their sparsity. These ultrasound images include the images of two computer ultrasound phantoms and beamformed ultrasound images with good quality from real people. We looked at sparsity of the true pre-beamformed images, as well as beamformed images. We also consider constructing a specific ultrasound image dictionary using the K-SVD algorithm. We observed that, the pre-beamformed images hardly haVe no sparse basis, and the sparsity of beamformed images will only increase slightly if we use different 1D-DWT in each direction. We also found that the wide overdetermined dictionary generated by K-SVD significantly increases sparsity. After this, we simulate the ultrasound image reconstruction from the ultrasound RF measurements, and we analyze the effects of the different sparse spaces on the reconstruction performance. We observed that, the L1-regularization can work for ultrasound imaging better than L2-regularization, but the orthogonal transforms as well as the dictionary do not improve the reconstruction image quality much.