Reference-Guided Fast Magnetic Resonance Imaging And Field Inhomogeneity Correction

Magnetic resonance imaging (MRI) is a powerful imaging technique used in a variety of medical imaging applications. The main drawback of MRI is its relatively long acquisition times, which significantly affects the image quality and throughput. Thus, reconstruction from partially sampled k-space data is desired, as it allows for significantly acceleration in imaging speed. This paper addresses two problems with limited data using the prior information extracted from reference images which can be acquired with relative ease in most MRI applications.The first problem is MR image reconstruction from highly under-sampled k-space data. Compressive sensing (CS) methods exploit the sparsity of the images in some fixed or adaptive transform domain for accurate reconstructions. This paper has proposed a reference-guided union of subspaces image model. This model enables to use sparse sampling and prior information effectively to significantly improve the image speed. Specifically, this model is based on an image subspace spanned by three types of bases functions:reference weighted harmonic functions, selected sparse transform bases functions, and pixel/voxel indicator functions. These bases are efficient for representing different image features such as global and local contrast variations from the reference to the target image as well as localized novel image features. Under the proposed image model, three associated methods have been proposed.The first method exploits the sparsity of the local variations and novel features simultaneously in appropriately selected transform domains using a combined regularization formulation. The optimization problem can be solved iteratively using the operator splitting algorithm and the split Bregman algorithm. The second method take full advantage of the GS model to pursuit higher sparsity level in the residual signal by expending the GS model order at each iteration. The third method exploits the structural information within the proposed image subspaces using a group sparse regularization, and it is highly robust to the quality of the reference image by controlling the energy distribution of different bases. Adaptive grouping is also adopted here to achieve superior reconstruction performances. The proposed framework is demonstrated with experimental results that it is highly flexible and applicable to a number of MR imaging scenarios, and provides higher quality results than existing MRI reconstruction methods. Another novel method for compressive sensing MRI based on the design of reference-guided analysis transforms is also proposed in this paper. Most CS methods employ analytical sparsifying transforms to model the unknown image and constrain the solution space during reconstruction. Recently, nonparametric dictionary-based methods for CS-MRI reconstruction have shown significant improvements over the classical methods. In this paper, we present a new framework for analysis-based reconstruction, where the sparsifying transform is learnt from a reference image to capture the anatomical structure of unknown image, and is used to guide the reconstruction process. We demonstrate with experimental data the high performance of the proposed approach over traditional methods.The second problem is the correction of field inhomogeneity effects on limited k-space MRSI data. Magnetic field inhomogeneity is often problematic in MRI and magnetic resonance spectroscopic imaging (MRSI) experiments. In MRSI experiments, field inhomogeneity produces not only frequency shifts, but also lineshape distortions in the resulting spectra. These distortions complicate subsequent quantification of the MRSI dataset. In this paper, a new method is proposed to correct the field inhomogeneity effects on k-space MRSI data. The proposed method uses two types of constraints:a high resolution field map, as well as an anatomical reference. These two constraints are imposed using a penalized maximum-likelihood formulation, which helps correct frequency shift and line shape distortions. The proposed method has been validated using both simulation and in-vivo proton MRSI experiment data, yielding very encouraging results. The method was proved useful for correcting field inhomogeneity effects on k-space data, especially when k-space coverage is limited.