Partial K-space Sampling Rapid MR Reconstruction And Phase Unwrapping

Magnetic Resonance Imaging (MRI) is a non-invasive imaging modality. Unlike Computed Tomography (CT), MRI does not use ionizing radiation. In addition, MRI provides a large number of flexible contrast parameters. These provide excellent soft tissue contrast and spatial resolution. Therefore, MRI has been widely applied in clinics and maybe the most promising non-invasive diagnostic tool in medicine.However, the main drawback of MRI is the long data acquisition time. Reducing scan time can improve the imaging efficiency, make the patient feel more comfortable and mitigate the time-depending motion artifacts. Moreover, imaging speed is essential to many of the MRI applications such as cardio-vascular examination, acquiring functional information, real time temperature monitoring, dynamic imaging in interventional therapy etc. Therefore, seeking for methods to reduce the scan time is one of the important goals of the MRI development.Compressed sensing, a big idea in signal processing community, is an interesting new area of research which has gained enormous popularity due to its ability to reconstruct perfect images from a limited number of samples by making advantage of the sparse nature of the image in a proper transform domain. MR image data are often highly redundant, which can be exploited to reduce the amount of acquired data, and hence the scan time. Specifically, we can design a proper measurement matrix and collect data very sparsely in k-space, and then obtain a perfect MR image through nonlinear reconstruction algorithm. The rapid MR reconstruction based on CS theory is called CS-MRI in this paper hereafter.CS-MRI is still in its infancy. Many crucial issues remain unsettled. These include: optimizing sampling trajectories, expressions of the sparsity in various sequence images, developing improved sparse transforms that are incoherent to the sampling operator, studying reconstruction quality in terms of clinical significance, and improving the speed of reconstruction algorithm.In this paper we explore some basic elements of compressed sensing: Sparsity, Incoherency and Sparsity based reconstruction algorithm. Many image are inherently sparse. For example, angiograms are extremely sparse in the pixel representation. More complex medical images may not be sparse in the pixel representation, but they do exhibit transform sparsity, since they have a sparse representation in terms of a proper transform (such as spatial finite difference transform, wavelet transform etc.). Sparsity is a powerful constraint and is used as prior knowledge in most of the current CS-MRI models. Mathematically speaking, reconstruction image from significantly few data is an ill-conditioned problem. The theory of CS suggests random undersampling rather than equispaced undersampling. In the random undersampling case, the aliasing artifacts due to k-space undersampling is incoherent (noise like). By random undersampling, we can turn the ill-conditioned problem into a sparse signal denoising problem. To apply CS-MRI in clinical practice, a robust rapid reconstruction algorithm is indispensable. In our work, we focus on designing an efficient algorithm which can deal with large scale data.The model currently adopted in the CS-MRI includes two terms: a prior term and a data fidelity term. Since the prior term is not differential and the variables in fidelity term are not independent, the model can neither be solved through traditional gradient method nor has a closed form solution.An alternate model for partial k-space data reconstruction is that the gradient is sparse. Therefore, we can use the total variation as the prior in the reconstruction model. Candes et al. used this model to recover image and obtained perfect result. However, in their algorithm the selection of barrier parameter is non-adaptive. In other words, the information in the process of iteration was not used.The contributions in our MR reconstruction work mainly include:1) Based on several recent algorithms, we apply the proximal forward-backward splitting idea into the CS-MRI and propose an efficient algorithm based on fixed point iteration. Furthermore, we give the proof of the algorithm's convergency. The calculation are accelerated by avoiding any linear system solvers or matrix factorizations~we restrict ourselves to vector operations and matrix-vector multiplications. Experiments show that faithful MR images can be reconstructed efficiently through our algorithm and our algorithm is robust and convergent.2) We use the total variation of the reconstructed images in the process of iteration to adaptively define the barrier parameter. We apply this improved algorithm into partial k-space sampling rapid MR reconstruction and obtain perfect result.Generally speaking, the MR image is the magnitude image. Based on the intensity distribution and tissue contrast, an experienced doctor can diagnose exactly and make a proper therapy plan. However, phase is an another important information in the process of imaging. Phase images can be used to monitor temperature changes during hyperthermic ablation procedure, to carry out the water/fat separation work, to measure the flow velocity, to eliminate chemical shift artifacts, to produce SWI image etc.However, the observed phase data are wrapped principal values, which are restricted in a 2 n modulus, and they must be unwrapped to their true absolute phase values. Phase unwrapping is the process of recovering the absolute phase from the wrapped phase. Obviously, the new MRI applications based on phase information require exact and efficient phase unwrapping algorithm.Phase unwrapping approaches belong mainly to one of the following categories: integration-based method, minimum norm, model-based method and Bayesian regularization. The common of these methods is to estimate the wrapped gradient field. Bioucas-Dias and Valadao proposed a new energy minimization framework based on network flow theory in 2007. However, they did not tackle the noise in the phase image. Furthermore, the energy function in their framework is too specific to be minimized conveniently using the network flow theory.The main contributions in our phase unwrapping work are as following:1) We regard the phase unwrapping problem as a labeling problem in computer vision. The corresponding energy function can be conveniently minimized by an efficient network flow algorithm.2) To eliminate the residuals caused by noise, a new phase filtering method is proposed to reduce the noise in the phase data. 3) We propose a new fuzzy gradient field as quality map to guide the unwrapping process.The proposed method has been tested with experimental data, yielding better results than some of the state-of-the-art methods.