The phase correlation method (PCM) is known to provide straightforward estimation of rigid translational motion between two images. It is often claimed that the original method is best suited to identify integer pixel displacements, which has prompted the development of numerous subpixel displacement identification methods. However, the fact that the phase correlation matrix is rank one for a noise-free rigid translation model is often overlooked. This property leads to the low complexity subspace identification technique presented here. The combination of non-integer pixel displacement identification without interpolation, robustness to noise, and limited computational complexity make this approach a very attractive extension of the PCM. In addition, this approach is shown to be complementary with other subpixel phase correlation based techniques.

Structured low-rank matrix models have previously been introduced to enable calibrationless MR image reconstruction from sub-Nyquist data, and such ideas have recently been extended to enable navigator-free echo-planar imaging (EPI) ghost correction. This paper presents a novel theoretical analysis which shows that, because of uniform subsampling, the structured low-rank matrix optimization problems for EPI data will always have either undesirable or non-unique solutions in the absence of additional constraints. This theory leads us to recommend and investigate problem formulations for navigator-free EPI that incorporate side information from either image-domain or k-space domain parallel imaging methods. The importance of using nonconvex low-rank matrix regularization is also identified. We demonstrate using phantom and in vivo data that the proposed methods are able to eliminate ghost artifacts for several navigator-free EPI acquisition schemes, obtaining better performance in comparison with the state-of-the-art methods across a range of different scenarios. Results are shown for both single-channel acquisition and highly accelerated multi-channel acquisition.

Purpose We seek improved image quality from accelerated EPI data, particularly at ultra-high field. Certain artifacts in EPI reconstructions can be attributed to nonlinear phase differences between data acquired using frequency encoding gradients of alternating polarity. These errors appear near regions of local susceptibility gradients, and typically cannot be corrected with conventional Nyquist ghost correction (NGC) methods. Methods We propose a new reconstruction method that integrates ghost correction into the parallel imaging data recovery process. This is achieved through a pair of GRAPPA kernels that operate directly on the measured EPI data. The proposed Dual-Polarity GRAPPA (DPG) method estimates missing k-space data while simultaneously correcting inherent EPI phase errors. Results Simulation results demonstrate that standard NGC is incapable of correcting higher-order phase errors, whereas the Dual-Polarity GRAPPA kernel approach successfully removes these errors. The presence of higher-order phase errors near regions of local susceptibility gradients is demonstrated with in vivo data. DPG reconstructions of in vivo 3T and 7T EPI data acquired near these regions show a marked improvement over conventional methods. Conclusion This new parallel imaging method for reconstructing accelerated EPI data shows better resilience to inherent EPI phase errors, resulting in higher image quality in regions where higher-order EPI phase errors commonly occur.

The characterization of the distribution of noise in the magnitude MR image is a very important problem within image processing algorithms. The Rician noise assumed in single-coil acquisitions has been the keystone for signal-to-noise ratio estimation, image filtering, or diffusion tensor estimation for years. With the advent of parallel protocols such as sensitivity encoding or Generalized Autocalibrated Partially Parallel Acquisitions that allow accelerated acquisitions, this noise model no longer holds. Since Generalized Autocalibrated Partially Parallel Acquisitions reconstructions yield the combination of the squared signals recovered at each receiving coil, noncentral Chi statistics have been previously proposed to model the distribution of noise. However, we prove in this article that this is a weak model due to several artifacts in the acquisition scheme, mainly the correlation existing between the signals obtained at each coil. Alternatively, we propose to model such correlations with a reduction in the number of degrees of freedom of the signal, which translates in an equivalent nonaccelerated system with a minor number of independent receiving coils and, consequently, a lower signal-to-noise ratio. With this model, a noncentral Chi distribution can be assumed for all pixels in the image, whose effective number of coils and effective variance of noise can be explicitly computed in a closed form from the Generalized Autocalibrated Partially Parallel Acquisitions interpolation coefficients. Extensive experiments over both synthetic and in vivo data sets have been performed to show the goodness of fit of out model.