Magnetic Resonance Imaging in Inhomogeneous Magnetic Fields with Noisy Signal

In this study, an image reconstruction algorithm for a Magnetic Resonance Imaging (MRI) system with inhomogeneous magnetic fields is proposed. The proposed reconstruction algorithm uses spatial distributions of main magnetic field, Radio Frequency (RF) and gradient fields as inputs, together with the pulse sequence and the noisy Magnetic Resonance (MR) signal. To calculate the noise signal, noise model for MRI with homogeneous fields is extended for inhomogeneous magnetic fields. Using this embedded noise module, different levels of noise signals are generated and added to the MR signal. By using this signal, noise performance of the proposed reconstruction algorithm is evaluated. In order to do that, inputs must be defined. As the main magnetic field input, measured magnetic field outside of a 0.15 T Oxford magnet, which is inhomogeneous, is used. Spin echo pulse sequence with parameters selected for proton density weighted images is used to evaluate the performance of the algorithm. Without noise, relative reconstruction error of the algorithm is 8.5 %. As seen from the simulation results if the noise level increases due to decrease in number of averages or slice thickness, then the relative error increases. Results are obtained for different slice thickness and number of averages. In the worst case, SNR is 18.6 with a relative error of 23 %.