|M.Sc Student||Eldad Vizel|
|Subject||Sparse Representation and Blind Source Separation of MRI|
|Department||Department of Biomedical Engineering||Supervisor||Professor Emeritus Zeevi Yehoshua|
|Full Thesis text|
Blind-Source-Separation (BSS) of images is implemented in this thesis by combining the Sparse-Component-Analysis (SCA) with the geometrical approach. Automatic selection of sparse representation coeﬃcients and performance in noisy mixture systems are investigated and applied to Magnetic Resonance (MR) Images.
We introduce a method for automatic selection of the coefficients used for the sparse representation. We conjecture that across the image domain and along various signal dictionaries, local-extrema coeﬃcients are the most significant. These coeﬃcients are expected to demonstrate the highest SNR. We term this method Matched-Filtering-Coeﬃcient-Selection (MFCS). The performance of MFCS is demonstrated with several signal dictionaries, including incomplete, complete and redundant, with varying scale and up to 156 atoms long. The performance is shown to be at least as good as previous state-of-the-art, in both noiseless and noisy images.
We analyze the reasons for error in BSS, and draw a relation between the variance of sensor noise and the mixing matrix variance as a cause for error. We illustrate theoretical and empirical results, and compare the performance of diﬀerent BSS algorithms in noisy mixture systems.
We develop a model that adapts the BSS framework to Spin-Echo MR images, and consider the Proton Density (PD) and Water Fraction (WF) as being the sources of the mixtures. We apply the SCA to pairs of T1 and T2 images, and thereby estimate the inverse of the mixing matrix. The inverse of the mixing matrix is used, in turn, to recover the structure of the recovered PD and WF images. The PD images are compared to available and known PD images, with normalized-cross-correlation of 0.72 to 0.8. The WF image values are in accordance with expected values. We use the WF images to classify the tissues to CSF, Grey Matter and White Matter. The classification results are assessed and confirmed by an expert radiologist.