Calibrationless parallel imaging reconstruction based on structured low-rank matrix completion

Abstract

Purpose A calibrationless parallel imaging reconstruction method, termed simultaneous auto-calibrating and k-space estimation (SAKE), is presented. It is a data-driven, coil-by-coil reconstruction method that does not require a separate calibration step for estimating coil sensitivity information. Methods In SAKE, an under-sampled multi-channel dataset is structured into a single data matrix. Then the reconstruction is formulated as a structured low-rank matrix completion problem. An iterative solution that implements a projection-onto-sets algorithm with singular value thresholding is described. Results Reconstruction results are demonstrated for retrospectively and prospectively under-sampled, multi-channel Cartesian data having no calibration signals. Additionally, non-Cartesian data reconstruction is presented. Finally, improved image quality is demonstrated by combining SAKE with wavelet-based compressed sensing. Conclusion As estimation of coil sensitivity information is not needed, the proposed method could potentially benefit MR applications where acquiring accurate calibration data is limiting or not possible at all.

A General Framework for Compressed Sensing and Parallel MRI Using Annihilating Filter Based Low-Rank Hankel Matrix

“…In both approaches, an accurate estimation of coil sensitivity maps or GRAPPA kernel is essential to fully exploit the coil sensitivity diversity. In order to overcome these difficulties, calibration-less parallel imaging methods have been extensively investigated, among which SAKE (simultaneous autocalibrating and k-space estimation) [16] represents one of the first steps. In SAKE, the missing k-space elements are reconstructed by imposing the data consistency and the structural maintenance constraints of the block Hankel structure matrix.…”

“…In compressed sensing MRI, the reconstruction image grid is always fixed; therefore, cardinal spline model that has knot locations on a fixed grid is more appropriate. Therefore, the results in (16) implies that the required number of samples are proportional to the sparsity level up to log 2 (n) factor. Considering that the standard compressed sensing analysis showed that the required number of Fourier samples in the l 1 minimization approach is proportional to the sparsity level up to log q (n) factor for some integer q [1], [2], the result in (16) is comparable to the standard CS-MRI approach.…”

“…The data from 4 receiver coils were used. For comparison, we used the identical data and sampling masks for SAKE with ESPIRiT [16], [43]. Note that GRAPPA [13] requires ACS lines, so with the additional 50 samples along ACS, the effective downsampling ratio was 3.1, which is not good as the four time acceleration in other algorithms.…”

“…The k-t space samples including four lines around zero frequency were retrospectively obtained at the reduction factor of eight according to a Gaussian distribution. For comparison, k-t FOCUSS [7], C-LORAKS [17], and SAKE [16] was used. In case of C-LORAKS (single coil) and SAKE (multi coil), these algorithms were applied to k-t domain for dynamic reconstruction.…”

Singular spectrum-based matrix completion for time series recovery and prediction

“…Due to the intuitive sampling, the MC framework has been considered for a variety of signal recovery problems including collaborative spectrum sensing [19], sensor localization [20,21], and image reconstruction problems [22,23] among others. MC has been recently explored as a sampling scheme for WSNs [24][25][26][27].…”