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.

New MR acquisition techniques are enabling fast acquisition of data from an entire 3D volume. Parallel MR imaging methods can provide additional acceleration to the data acquisition rate. However, the large computational memory requirements associated with 3D imaging requires new efficient reconstruction techniques. This manuscript presents an efficient implementation of SPACE-RIP for the rapid reconstruction of sub-sampled 3D MR data. Uniform sub-sampling effectively decouples the SPACE-RIP linear system of equations into a number of smaller systems which can each be solved independently, thus requiring fewer computational resources. We present a particular phase-encode sampling pattern to capitalize on this effect which allows SPACE-RIP to be computationally competitive with SENSE in 3D imaging, while providing the added benefits of self-calibrated coil sensitivity maps and improved artifact suppression through irregular sub-sampling.

This paper presents an extension of the phase correlation image alignment method to N-dimensional data sets. By the Fourier shift theorem, the motion model for translational shifts between N-dimensional images can be represented as a rank-one tensor. Through use of a high-order singular value decomposition, the phase correlation between two N-dimensional data sets can be decomposed to independently identify translational displacements along each dimension with subpixel resolution. Using three-dimensional MRI data sets, we demonstrate the effectiveness of this approach relative to other N-dimensional image registration methods.

During development of new and experimental imaging techniques, one must compare with other well established methods to qualify the validity of the new methods. The use of diffusion tensor magnetic resonance imaging for the visualization of collateral nerve fibers in the spinal cord was recently proposed. To validate this new imaging method, the MR results need to be compared with histology tissue samples in which the nerve fibers are clarified through staining. We present here a method for the mostly-automatic merging of very high resolution "tiles" of the histology slides to construct a composite image of a tissue slice. This application is novel in that it uses a phase correlation registration techniques with sub-pixel resolution to construct the composite image. Registration error detection is achieved by comparing the sub-pixel registration result with a standard phase correlation estimate.

This method is an extension of the phase correlation method for image registration to multidimensional data sets. Through use of a high-order singular value decomposition, phase correlation can be used to identify translational displacements independently along each dimension with subpixel resolution. The validity of this approach is demonstrated using multiple 3D MRI data sets.

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.

Dynamic magnetic resonance imaging (MRI) refers to the acquisition of a sequence of MRI images to monitor temporal changes in tissue structure. We present a method for the estimation of dynamic MRI sequences based on two complimentary strategies: an adaptive framework for the estimation of the MRI images themselves, and an adaptive method to tailor the MRI system excitations for each data acquisition. We refer to this method as the doubly adaptive temporal update method (DATUM) for dynamic MRI. Analysis of the adaptive image estimate framework shows that calculating the optimal system excitations for each new image requires complete knowledge of the next image in the sequence. Since this is not realizable, we introduce a linear predictor to aid in determining appropriate excitations. Simulated examples using real MRI data are included to illustrate that the doubly adaptive strategy can provide estimates with lower steady state error than previously proposed methods and also the ability to recover from dramatic changes in the image sequence.

Motivated by work in the area of dynamic magnetic resonance imaging (MRI), we develop a new approach to the problem of reduced-order MRI acquisition. Efforts in this field have concentrated on the use of Fourier and singular value decomposition (SVD) methods to obtain low-order representations of an entire image plane. We augment this work to the case of imaging an arbitrarily-shaped region of interest (ROI) embedded within the full image. After developing a natural error metric for this problem, we show that determining the minimal order required to meet a prescribed error level is in general intractable, but can be solved under certain assumptions. We then develop an optimization approach to the related problem of minimizing the error for a given order. Finally, we demonstrate the utility of this approach and its advantages over existing Fourier and SVD methods on a number of MRI images.