MRI with multiple receiver coils (parallel MRI) has been extensively used to achieve higher spatial and temporal resolution, suppress imaging artifacts, and reduced scan time. A number of techniques have been proposed to reconstruct images from reduced (undersampled) k-space datasets acquired by multiple coils. All the techniques require some type of calibration information to describe image encoding by spatially varying coil sensitivities. This information can be derived from supplementary calibration scans. However, this approach increases scan time and can be erroneous due to patient motion between calibration and imaging scans. Auto-calibrating techniques such as the commonly used GRAPPA, do not require calibration scans and estimate reconstruction coefficients directly from acquired k-space data. GRAPPA typically gives good quality results for low undersampling rates. However, strong noise amplification and non-resolved aliasing artifacts makes the technique less applicable in cases of high undersampling. In this work, we have proposed a novel auto-calibrating technique for image reconstruction from sensitivity encoded MRI data that overcomes limitations of the existing auto-calibrating techniques. In the proposed technique (GARSE), specifics of coil sensitivity representation in the image and k-space domains are utilized in the reconstruction in such a way that more trustworthy reconstruction coefficients can be identified resulting in improved image quality. GARSE reconstruction coefficients are spatially variable and adjusted according to local coil sensitivities characteristics, whereas GRAPPA reconstruction coefficients are spatially invariant and, therefore, sub-optimal. Results from MRI studies of phantoms and humans demonstrate substantial advantages of GARSE in comparison with GRAPPA, especially for high undersampling rates.
In magnetic resonance imaging (MRI), the theoretically achievable spatial resolution is characterized by the extent of k-space used for image reconstruction, which is inversely proportional to the pixel size. Therefore, spatial resolution increases with the extent of k-space sampled. Whereas the visible resolution is characterized by the object size at which the object of interest is visually separable from the background. Since noise in MRI data is "white" (uniformly distributed across the k-space), sampling more k-space results in adding more noise to the image. This can result in the decrease of the object visibility with increase in the spatial resolution. Hence, it is important to choose the right spatial resolution to view the object of interest. In this paper, we present a theoretical relationship between the visibility of vessel detail in magnetic resonance angiography (MRA) and also the probability of projection of vessels in the minimum intensity projection (MinIP) and maximum intensity projection (MIP) images as a function of spatial resolution. This theory lays a foundation for determining the extent of k-space that should be used for image reconstruction to visually identify a particular vessel/anatomic detail of interest. The theory is validated using imaging studies and it is demonstrated that the vessel information displayed in MRA as well as projection images can be maximized for a particular anatomic detail of interest by optimal choice of spatial resolution.
Parallel imaging techniques for MRI use differences in spatial sensitivity of multiple receiver coils to achieve additional encoding effect and significantly reduce data acquisition time. Recently, a projection onto convex sets (POCS) based method for reconstruction from sensitivity-encoded data (POCSENSE) has been proposed. The main advantage of the POCSENCE in comparison with other iterative reconstruction techniques is that it offers a straightforward and computationally efficient way to incorporate non-linear constraints into the reconstruction that can lead to improved image quality and/or reliable reconstruction for underdetermined problems. However, POCSENSE algorithm demonstrates slow convergence in cases of badly conditioned problems. In this work, we propose a novel method for image reconstruction from sensitivity encoded MRI data that overcomes the limitation of the original POCSENSE technique. In the proposed method, the convex combination of projections onto convex sets is used to obtain an updated estimate of the solution via relaxation. The new method converges very efficiently due to the use of an iteration-dependent relaxation parameter that may extend far beyond the theoretical limits of POCS. The developed method was validated with phantom and volunteer MRI data and was demonstrated to have a much higher convergence rate than that of the original POCSENSE technique.