Parallel imaging reconstruction for arbitrary trajectories using k‐space sparse matrices (kSPA)

Abstract

Although the concept of receiving MR signal using multiple coils simultaneously has been known for over two decades, the technique has only recently become clinically available as a result of the development of several effective parallel imaging reconstruction algorithms. Despite the success of these algorithms, it remains a challenge in many applications to rapidly and reliably reconstruct an image from partially-acquired general non-Cartesian k-space data. Such applications include, for example, three-dimensional (3D) imaging, functional MRI (fMRI), perfusion-weighted imaging, and diffusion tensor imaging (DTI), in which a large number of images have to be reconstructed. In this work, a systematic k-space-based reconstruction algorithm based on k-space sparse matrices (kSPA) is introduced. This algorithm formulates the image reconstruction problem as a system of sparse linear equations in k-space. The inversion of this system of equations is achieved by computing a sparse approximate inverse matrix. The algorithm is demonstrated using both simulated and in vivo data, and the resulting image quality is comparable to that of the iterative sensitivity encoding (SENSE) algorithm. The kSPA algorithm is noniterative and the computed sparse approximate inverse can be applied repetitively to reconstruct all subsequent images. This algorithm, therefore, is particularly suitable for the aforementioned applications.

SPIRiT: Iterative self‐consistent parallel imaging reconstruction from arbitrary k‐space

“…These methods differ by the way the sensitivity information is used. Methods like SMASH (3), SENSE (4,5), SPACE-RIP (6), PARS (7) and kSPA (8) explicitly require the coil sensitivities to be known. In practice, it is very difficult to measure the coil sensitivities with high accuracy.…”

Advances in real-time magnetic resonance imaging of the vocal tract for speech science and technology research

“…To this end, a thin-plate spline-based intensity correction procedure [45] is applied, to obtain an estimate of the combined coil sensitivity map, which is constant for all images contained in the sequence. Thus, corrected maximally flat magnitude images can be obtained [39].…”

Improved l1-SPIRiT using 3D walsh transform-based sparsity basis

“…To reduce scan duration, two different types of techniques are often used. The first one is the multiple-coil based parallel MR imaging (pMRI) schemes, which have been actively investigated over the recent years using a variety of methods [1][2][3][4][5][6][7][8][9][10][11][12]. Some of these pMRI methods require the coil sensitivities to be known explicitly, while others reconstruct images with an implicit usage of the coil sensitivity information, through an auto-calibration process.…”