Magnetic resonance imaging (MRI) is a noninvasive diagnostic tool that provides excellent soft-tissue contrast without the use of ionizing radiation. Compared to other clinical imaging modalities (e.g., computed tomography or ultrasound), however, the data acquisition process for MRI is inherently slow, which motivates undersampling; thus, there is a need for accurate, efficient reconstruction methods from undersampled data sets. In this article, we describe the use of plug-and-play (PnP) algorithms for MRI image recovery. We first describe the linearly approximated inverse problem encountered in MRI. Then, we review several PnP methods for which the unifying commonality is to iteratively call a denoising subroutine as one step of a larger optimization-inspired algorithm. Next, we describe how the result of the PnP method can be interpreted as a solution to an equilibrium equation, allowing convergence analysis from this perspective. Finally, we present illustrative examples of PnP methods applied to MRI image recovery.

Purpose: To improve image quality and reduce data requirements for spatial electron paramagnetic resonance imaging (EPRI) by developing a novel reconstruction approach using compressed sensing (CS).Methods: EPRI is posed as an optimization problem, which is solved using regularized least‐squares with sparsity promoting penalty terms, consisting of the l1 norms of the image itself and the total variation of the image. Pseudo‐random sampling was employed to facilitate recovery of the sparse signal. The reconstruction was compared with the traditional filtered back‐projection reconstruction for simulations, phantoms, isolated rat hearts, and mouse gastrointestinal (GI) tracts labeled with paramagnetic probes.Results: A combination of pseudo‐random sampling and CS was able to generate high‐fidelity EPR images at high acceleration rates. For three‐dimensional (3D) phantom imaging, CS‐based EPRI showed little visual degradation at nine‐fold acceleration. In rat heart datasets, CS‐based EPRI produced high quality images with eight‐fold acceleration. A high resolution mouse GI tract reconstruction demonstrated a visual improvement in spatial resolution and a doubling in signal‐to‐noise ratio (SNR).Conclusion: A novel 3D EPRI reconstruction using compressed sensing was developed and offers superior SNR and reduced artifacts from highly undersampled data. Magn Reson Med 72:893–901, 2014.

Measurement of blood oxygen saturation (O2 saturation) is of great importance for evaluation of patients with many cardiovascular diseases, but currently there are no established non-invasive methods to measure blood O2 saturation in the heart. While T2-based CMR oximetry methods have been previously described, these approaches rely on technique-specific calibration factors that may not generalize across patient populations and are impractical to obtain in individual patients. We present a solution that utilizes multiple T2 measurements made using different inter-echo pulse spacings. These data are jointly processed to estimate all unknown parameters, including O2 saturation, in the Luz-Meiboom (L-M) model. We evaluated the accuracy of the proposed method against invasive catheterization in a porcine hypoxemia model. Sufficient data diversity to estimate the various unknown parameters of the L-M model, including O2 saturation, was achieved by acquiring four T2 maps, each at a different τ 180 (12, 15, 20, and 25 ms). Venous and arterial blood T2 values from these maps, together with hematocrit and arterial O2 saturation, were jointly processed to derive estimates for venous O2 saturation and other nuisance parameters in the L-M model. The technique was validated by a progressive graded hypoxemia experiment in seven pigs. CMR estimates of O2 saturation in the right ventricle were compared against a reference O2 saturation obtained by invasive catheterization from the right atrium in each pig, at each hypoxemia stage. O2 saturation derived from the proposed technique was also compared against the previously described method of applying a global calibration factor (K) to the simplified L-M model. Venous O2 saturation results obtained using the proposed CMR oximetry method exhibited better agreement (y = 0.84× + 12.29, R2 = 0.89) with invasive blood gas analysis when compared to O2 saturation estimated by a global calibration method (y = 0.69× + 27.52, R2 = 0.73). We have demonstrated a novel, non-invasive method to estimate O2 saturation using quantitative T2 mapping. This technique may provide a valuable addition to the diagnostic utility of CMR in patients with congenital heart disease, heart failure, and pulmonary hypertension.