A Study On Parallel Magnetic Resonance Imaging Based On Three-dimensional Tight Frame

Parallel magnetic resonance imaging(p MRI)is a commonly used clinical diagnostic technique.Unlike imaging techniques such as computed tomography(CT)and X-ray,there is no ionizing radiation and no harm to humans.The p MRI system uses multiple coils to simultaneously receive MRI signals to obtain multi-coil k-space data about the target slice.The k-space data of each coil can be transformed into two-dimensional spatial domain image information by inverse Fourier transform.Then multi-coil images are merged into an image to represent the target slice information.The p MRI machines limited by the Nyquist sampling theorem require a long time to scan and collect data.Under the constraints of technology,human capacity and other factors,hardware acceleration has reached its bottleneck.At the current hardware acquisition rate,the p MRI system accelerates the scanning imaging by acquiring part of k-space data and reconstructs the target information from the collected data using the reconstruction algorithm.The goal of reconstruction algorithm is to reconstruct high-quality MRI images that meet the requirements of medical diagnosis at a low sampling rate.The pMRI reconstruction is a typical inverse problem,which improves the quality of the reconstructed image by constraining the target slice image,such as total variation,sparse representation technology of wavelet transform,etc.Without considering the correlation between coil images,these two-dimensional regularization techniques only aim at twodimensional target images and reconstruct images with artifact defects.In this dissertation,according to the merits of multi-coil data in the p MRI system,the correlation between coil images is analyzed by a three-dimensional tight frame system.The regularization models for p MRI reconstruction are constructed and solved by an iterative algorithm.The main contributions are as follows: 1)Multiple two-dimensional coil images are stacked to form a three-dimensional spatial image.The three-dimensional features are extracted by a threedimensional tight frame system.The correlation of three-dimensional image data is analyzed at multiple scales.The problem of p MRI reconstruction is regularized by sparsing the coefficients of correlated features.2)In uniform sampling mode,regularizations on GRAPPA by three-dimensional tight frame is proposed,which can effectively suppress aliasing artifacts and noise.3)The SPIRi T reconstruction model regularized by three-dimensional tight frame constraints is proposed to effectively reduce the problem of reconstruction artifacts under the random sampling model.Under the iterative framework of the alternating direction multiplier method(ADMM),two iterative algorithms,3D-GRAPPA and 3D-SPIRi T,are proposed to solve their corresponding models.The experimental results show that the proposed 3D-GRAPPA and 3D-SPIRi T algorithms can effectively suppress aliasing artifacts and noise,and improve imaging quality.