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Clinical magnetic resonance imaging (MRI) protocols typically include multiple acquisitions of the same region of interest under different contrast settings. This paper presents an efficient algorithm to jointly reconstruct a set of undersampled images with different contrasts. The proposed method has faster reconstruction time and better quality as measured by the normalized root-mean-square error (RMSE) compared to the existing methods consisting of multi-contrast Fast Composite Splitting Algorithm (FCSA-MT), Multiple measurement vectors FOCal Underdetermined System Solver (M-FOCUSS), and total variation regularized compressed sensing (SparseMRI). To efficiently solve the £2, 1-regularized optimization problem, our proposed algorithm adopts the Split Bregman (SB) technique to divide the problem into sub-problems. We efficiently compute a closed-form solution to each of the sub-problems by implementing a 3D spatial gradient operator as element-wise multiplication in k-space. As demonstrated by the in vivo results, the proposed algorithm (SB-L21) offers 2x, 32x, and 66x faster reconstruction with lower RMSE averaged across all contrasts and slices compared to FCSA-MT, M-FOCUSS, and SparseMRI, respectively.

Accelerating magnetic resonance imaging (MRI) by reducing the number of acquired k-space scan lines benefits conventional MRI significantly by decreasing the time subjects remain in the magnet. In this paper, we formulate a novel method for Joint estimation from Undersampled LinEs in Parallel MRI (JULEP) that simultaneously calibrates the GeneRalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) reconstruction kernel and reconstructs the full multi-channel k-space. We employ a joint sparsity signal model for the channel images in conjunction with observation models for both the acquired data and GRAPPA reconstructed k-space. We demonstrate using real MRI data that JULEP outperforms conventional GRAPPA reconstruction at high levels of undersampling, increasing the peak-signal-to-noise ratio by up to 10 dB., National Science Foundation (U.S.) (CAREER Grant 0643836), National Center for Research Resources (U.S.) (P41 RR014075), National Institutes of Health (U.S.) (NIH R01 EB007942), National Institutes of Health (U.S.) (NIH R01 EB006847), Siemens Corporation, National Science Foundation (U.S.). Graduate Research Fellowship Program

Both compressed sensing (CS) and parallel imaging effectively reconstruct magnetic resonance images from undersampled data. Combining both methods enables imaging with greater undersampling than accomplished previously. This paper investigates the choice of a suitable sampling pattern to accommodate both CS and parallel imaging. A combined method named SpRING is described and extended to handle random undersampling, and both GRAPPA and SpRING are evaluated for uniform and random undersampling using both simulated and real data. For the simulated data, when the undersampling factor is large, SpRING performs better with random undersampling. However, random undersampling is not as beneficial to SpRING for real data with approximate sparsity.

The combination of compressed sensing (CS) and parallel magnetic resonance (MR) imaging enables further scan acceleration via undersampling than previously feasible. While many of these methods incorporate similar styles of CS, there remains significant variation in the particular choice of function used to promote sparsity. Having developed SpRING, a framework for combining CS and GRAPPA, a parallel MR image reconstruction method, we view the choice of penalty function as a design choice rather than a defining feature of the algorithm. For both simulated and real data, we compare different sparsity penalty functions to the empirical distribution of the reference images. Then, we perform reconstructions on uniformly undersampled data using a variety of penalty functions to illustrate the impact appropriately choosing the penalty function has on the performance of SpRING. These experiments demonstrate the importance of choosing an appropriate penalty function and how such a choice may differ between simulated data and real data.

Magnetic resonance imaging (MRI) may be viewed as a two-stage experiment that yields a non-invasive spatial mapping of hydrogen nuclei in living subjects. Nuclear spins within a subject are first excited using a radio-frequency (RF) excitation pulse and proportions of excited spins are then detected using a resonant coil; images are then reconstructed from this data. Excitation pulses need to be tailored to a user's specific needs and in most applications need to be as short as possible, due to spin relaxation, tissue heating, signal-to-noise ratio (SNR), and data readout limitations. The design of short-duration excitation pulses is an important topic and the focus of our work. One may show that RF excitation pulse design, under certain conditions, involves choosing to deposit energy in a continuous, 3-D, Fourier-like domain ("excitation k-space") in order to form some desired excitation in the spatial domain. Energy may only be deposited along a 1-D contour, and there are limitations on where and how it may be placed; the most important fact is that excitation pulse duration directly corresponds to the length of the chosen contour and the rate it is traversed. The problem then is to find a sparse "trajectory" (and corresponding energy deposition) within this k-space such that a high-fidelity version of the desired excitation is formed in the spatial domain. We show how sparsity and simultaneous sparsity are applicable to 2-D and 3-D excitation pulse design and present a novel instance where simultaneous sparsity is desirable. We then discuss how to apply sparse approximation concepts to produce RF pulses. These "sparsity-enforced" designs, generated via convex relaxation techniques, significantly outperform conventional pulses: for fixed pulse duration, sparsity-enforced pulses always produce higher-fidelity excitations.