POCS-ICE can inherently and reliably correct motion-induced phase errors in navigator-free multishot DWI, and it is easier to determine the stopping criterion without manual interventions. The improved spatial resolution and image resolvability are beneficial to study of brain microstructures and physiological features for neuroscience.

In non-Cartesian SENSE reconstruction based on the conjugate gradient (CG) iteration method, the iteration very often exhibits a "semi-convergence" behavior, which can be characterized as initial convergence toward the exact solution and later divergence. This phenomenon causes difficulties in automatic implementation of this reconstruction strategy. In this study, the convergence behavior of the iterative SENSE reconstruction is analyzed based on the mathematical principle of the CG method. It is revealed that the semi-convergence behavior is caused by the ill-conditioning of the underlying generalized encoding matrix (GEM) and the intrinsic regularization effect of CG iteration. From the perspective of regularization, each iteration vector is a regularized solution and the number of iterations plays the role of the regularization parameter. Therefore, the iteration count controls the compromise between the SNR and the residual aliasing artifact. Based on this theory, suggestions with respect to the stopping rule for well-behaved reconstructions are provided. Parallel imaging techniques have shown potential to revolutionize the field of fast MRI in recent years (1-11). By using sensitivity information from an RF coil array to perform some of the spatial encoding that is traditionally accomplished by magnetic field gradient, parallel imaging allows reduction of phase encoding steps and consequently decreases the scan time. Several practical parallel imaging reconstruction strategies have been proposed, including the k-space based simultaneous acquisition of spatial harmonics (SMASH) (2-5), the generalized auto-calibrating partially parallel acquisitions (GRAPPA) (6), and the image-domain based sensitivity encoding (SENSE) approach (7).In general, the essence of parallel imaging reconstruction is to solve a linear system of equations (LSE) representing the encoding scheme, or more specifically, to inverse the generalized encoding matrix (GEM) produced by magnetic gradient modulation and coil sensitivity modulation (8). For image acquisitions of appreciable matrix size, the dimension of GEM is rather large, and straightforward inversion is numerically prohibitive. For the case of sampling along a regular Cartesian k-space grid, a Fourier transform may be separated out from the inversion process as a distinct step, and the GEM then attains a block diagonal structure and its processing can be significantly simplified. Specifically, in SENSE, each block corresponds to a set of aliased pixels, and the inversion becomes a block-by-block (pixel-by-pixel) inversion. However, for non-Cartesian k-space trajectories, such as spiral or radial schemes, such transformations of the GEM are no longer applicable because the k-space samples are not uniformly distributed and fast Fourier transform (FFT) cannot be applied in a straightforward manner. In these cases, the inversion of GEM is much more complicated and timeconsuming. One efficient way is to perform reconstruction iteratively, as proposed by Pruessmann and Kannengie␤er (...

ABSTRACT:The conjugate-gradient (CG)-based non-Cartesian SENSE reconstruction usually exhibits unstable convergence behavior due to the ill conditioning of the generalized encoding matrix (GEM). To overcome this difficulty, an improved iterative SENSE approach is presented. During a so-called Lanczos iteration process, which is equally efficient as CG, the inversion of GEM can be gradually approximated by calculating inversions of a series of small tridiagonal matrices. In this fashion, inner regularization can be incorporated into the reconstruction without touching the iteration process. The degree of regularization can be determined based on the eigenvalue information provided by the Lanczos process. With inner regularization adaptively applied for every iteration vector, the convergence behavior of iterative SENSE can be significantly improved and noise amplification can be avoided. The feasibility of this novel iterative SENSE technique is demonstrated by radial and spiral MRI experiments.