I. Introduction
Imaging speed is a major limitation of magnetic resonance (MR) imaging, especially in comparison to competing imaging modalities such as computed tomography (CT). MR allows much more flexible contrast-generation and does not expose patients to ionizing radiation, and hence does not increase risk of cancer. However, other imaging modalities are substantially more popular, as MR scans are slow, expensive, and in some cases less robust. Patient motion during long scans frequently causes image artifacts, and for uncooperative patients, like children, anesthesia is a frequent solution. Acquisition time in MRI can be reduced by faster scanning or by subsampling. Parallel imaging [1]–[3] is a well-established acceleration technique based on the spatial sensitivity of array receivers. Compressed sensing (CS) [4]–[6] is an emerging acceleration technique that is based on the compressibility of medical images. Attempts to combine the two have mostly focused on extensions of iterative SENSE [7] with SparseMRI [6]. In [8] Block et al., added total-variation to a SENSE reconstruction from radial sampling, Liang et al., in [9] showed improved acceleration by first performing CS on aliased images and then applying SENSE to unfold the aliasing, Otazo et al. used compressed sensing with SENSE to accelerate first-pass cardiac perfusion [10]. More recently [11], [12] have presented some improvements, again, using an extension of SENSE. The difficulty in estimating exact sensitivity maps in SENSE has created the need for autocalibrating techniques. One class of autocalibrating algorithms extends the SENSE model to joint estimation of the images and the sensitivity maps [13], [14]. Combination of these approaches with compressed sensing have also been proposed. Knoll et al. [15] proposed a combination with Uecker's nonlinear inversion and Huang et al. [16] proposed a self-feeding SENSE combined with compressed sensing.