Efficient S-transform techniques for magnetic resonance imaging

The S-transform (ST) is a promising technique for magnetic resonance (MR) image texture analysis that has previously been successfully applied to the study of multiple sclerosis (MS) and brain cancer. Two of the major limitations of the ST are the computation time and the storage requirements. This thesis introduces two new techniques that reduce the complexity and redundancy of the ST, addressing these limitations.;Space-frequency transforms such as the ST can also be utilized for image filtering and denoising. A novel application of the ST is proposed to study lesion dynamics in MS. It is found that a texture measure derived from the cST can discriminate between the core of a hyperintense active lesion and its less hyperintense periphery.;A two-dimensional (2D) frequency-domain implementation of the discrete orthonormal S-transform (DOST) is also presented. The DOST addresses both the computational and storage requirements of the ST by removing redundancy from the ST and providing a rapid calculation of the space-frequency domain. Novel texture features are derived from the DOST and it is shown that these features are more powerful when classifying unknown texture patterns than a leading method using the discrete wavelet transform (DWT).;Finally, the cST, pST and the DOST are applied to a study of glioblastoma (GBM) texture. It is shown that the DOST is the most accurate texture analysis approach when blindly classifying tumors based on their methylation status. Interestingly, differences were only found when analyzing small region of interests (ROIs) within the tumors, not when analyzing the entire image and extracting spectra from the entire tumor.;A version of the ST that uses circularly symmetric windows, known as the circular S-transform (cST), is proposed and its properties are studied. It is shown that the cST produces results similar to the polar S-transform (pST) but requires less computation time.