## Evaluation of Self-calibrated Cartesian Sense Methods for Parallel MRI.One of most commonly used parallel imaging methods is Sensitivity Encoding (SENSE) developed by Preussman, et al., in 1999, based on which a series of algorithms have been developed over the decade. Most of the algorithms focused on the noise issues in reconstructed images, while others also involved the concerns in phase component of the complex MRI image. This Thesis implements five different SENSE algorithms and makes systematic comparisons among them, with evaluations given both visually and quantitatively. This work also addresses the reconstruction speed of each of the algorithms, which is an important feature for clinical MRI. The results of those comparisons then lead to the investigation into noise and aliasing artifacts, which are the two major problems in SENSE reconstruction. Through a series of experiments, this thesis discusses the various sources of noise and artifacts as well as the varying effects of these sources on the resulting images. This work shows that noise and aliasing artifacts are actually two different kinds of perturbations to reconstructed images from very different sources. Finally, one problem remaining in SENSE is that there is no standard method of quantitative assessment of aliasing artifacts in the final images, other than a general SNR value or the g-factor map. However, the SNR values can be heavily biased by the chosen of regions of interest and the g-factor map is a measurement of noise amplification of the noise across the image, both of which are not assessment specifically for aliasing artifacts. To address this issue, this thesis introduces a metric for aliasing artifacts in the reconstructed images for research purposes. |

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### Contents

INTRODUCTION | 1 |

Algorithms for SENSE Improvement | 14 |

SENSITIVITY MAPS | 48 |

TEST OF DIFFERENT ALGORITHMS ON REAL MRI DATA | 79 |

DEEPER INVESTIGATION INTO NOISE ALIASING | 131 |

CONCLUSIONS | 190 |

APPENDIX MATLAB FUNCTIONS | 197 |

### Common terms and phrases

16 Reference line 32 16 Reference additive noise aliased images aliasing artifacts aliasing index brain data set Butterworth filter calculated chapter core equation covariance matrix decorrelation errors in sensitivity experiments final reconstructed images full FOV images g-factor map Gaussian distributed Gaussian noise higher acceleration rate images and sensitivity images reconstructed k-space data least squares method low-pass filter magnitude maps after implementation maximum likelihood method noise degree Noise Deviation noise in aliased noise in k-space noise in sensitivity number of reference obtained P-values parallel imaging parallel MRI performance phantom datasets phase encoding direction phase refinement method phased array coil pixel pMRI polynomial fitting method quadratic phase shift Rayleigh distributed receiver channels reconstruction process Residual maps resulting images scan self-calibration method SENSE reconstruction sensitivity maps shown in figure signal SNR trends surface coils technique Tikhonov regularization method total least squares trend in reconstructed trends with varying varying reference lines vivo datasets