Research On Parallel MRI Reconstruction Algorithm Based On Partial K-space Data

In magnetic resonance imaging (MRI), the characteristic of spin motion of the atomic nucleus is the basic physical principle of the application and then the images about various organizations of human beings are obtained. Nowadays, MRI has become one of the most important non-invasive diagnostic tools in current clinical medicine. However, owing to the defect of slow imaging speed in MRI, the requirements of fast imaging such as functional brain imaging and cardiac dynamic imaging can not be satisfied. Therefore, the application of MRI is restricted to a large extent. Fortunately, parallel magnetic resonance imaging (PMRI) broke through the limitations of hardware condition and magnetic properties which restrain the improvement of imaging speed in conventional MRI. Parallel MRI applies the spatial position information of phased array coils instead of partial steps of phase encoding. Parallel MRI not only can reduce the imaging time, but also can keep the satisfied quality and high spatial resolution of reconstructed images. That is to say, parallel MRI plays an important role in promoting the development of MRI. However, the undersampling factor cannot be too big and there are problems such as morbid problem during the process of reconstruction in parallel MRI. Nevertheless, Partial fourier imaging can combine with parallel MRI easily and then achieve higher sampling speed. But also the combination of the two algorithms can alleviate the problem of the noise amplified effectively whish existed in parallel MRI. Therefore, the parallel MRI reconstruction algorithm based on partial fourier imaging is mainly studied in this thesis.Sum of squares (SOS) algorithm is regarded as the optimal method of image synthesis in the condition that the exact sensitivity of each phased array coils is unknown. However, SOS algorithm uses the equal weights to composite the reconstructed images of each phased array coils. In addition, SOS algorithm does not inhibit the external noise well. Thus, the final image exists signal bias and has low signal-to-noise ratio (SNR). Taken the defect of SOS algorithm into consideration, the weighted sum of squares (WSOS) algorithm based on the smoothing filter is put forward in this thesis. First, the smoothing filter is chosen for reconstructed images denoising of each phased array coils. And then the coils sensitivity is taken as the weight coefficients in the reconstruction formula. Finally, the effect of destroyed data to the final composite images is reduced effectively. Compared to SOS algorithm, the experiment results show that the algorithm proposed in this thesis can eliminate artifacts effectively and increase the SNR.In the conventional generalized auto-calibrating partially parallel acquisitions (GRAPPA) algorithm, the sampled data of K-space is used to obtain the weight coefficients by liner fitting. However, includes the measurements of noise and truncation error are included in the actual data that the phased array coils collected, so that there is a bias between the weight coefficients calculated according to the linear relationship and the real value. To solve the problem, the improved algorithm is proposed. Firstly, the adaptive error back propagation (BP) learning algorithm is used to train the weight coefficients. Secondly, the trained neural network and the sampled data are applied to estimate the data of K-space that is not sampled. As compared with the conventional GRAPPA algorithm, the simulations results prove that the value of artifact power (AP) and root mean squared error (RMSE) is decreased effectively in the novel algorithm presented in this thesis. Furthermore, the quality of reconstructed images is improved.