Prospective Snr Optimization in K-t-based Sensitivity-encoded Dynamic Imaging Using a Fast Geometric Algorithm

Introduction MR data acquisition and image reconstruction are typically formulated using Fourier transform (FT) theory, i.e., the classical k-space relationship. However, in dynamic MR imaging (e.g., 2D Cartesian sampling) it takes a few milliseconds from collecting one k-space phase-encode (PE) line to the next, i.e., sampling in the PE direction is time-sequential and not instantaneous [1]. Hence, a more accurate model for MR data acquisition is the so called “k-t-space perspective” (k=spatial frequency, t=time) [1,2]. Most well known k-t-based schemes use k-t sampling patterns that are restricted to a lattice (generalized sheared grid) [1-3]. Based on sampling theory, k-t sampling on a lattice will result in aliasing of the object’s spectrum in the reciprocal domain, referred to as dual k-t domain [4-6] or the x-f-space (x=PE direction, f=temporal frequency) [3]. The replication pattern is on the corresponding point-spread function (PSF) which is the FT of the sampling lattice [2,4]. The acceleration in k-t-based techniques results from multifold undersampling that the k-t lattice provides relative to the Nyquist rate. In UNFOLD [3] and PARADIGM [4], the k-t lattice is designed so that there is no overlap of the support region in x-f-space. On the contrary, in UNFOLD-based parallel imaging (e.g., TSENSE), k-t SENSE, and PARADISE [5-6], there is overlap in x-f-space which can potentially be undone using sensitivity encoding (SE) and prior information (signal model). The prior information is in form of statistics for k-t SENSE, cross-shaped x-f support model (Fig 1a) for UNFOLD [3], and multi-banded patient-adaptive x-f support model (Fig 1b) for PARADISE [4-6]. Optimizing the reconstruction SNR in this context has been previously introduced and its significance has been demonstrated in-silico for PARADISE [5]. A similar study has been conducted for k-t SENSE [7]. We focus on nongated cardiac MR techniques that use x-f support models and SE, namely, PARADISE [5-6] or UNFOLD-based parallel imaging. We propose a novel algorithm for designing the SNR-optimal k-t sampling pattern and study its performance invivo. The proposed algorithm is geometric, i.e., it is based on geometry of overlap patterns in x-f space and does not require any knowledge of coil sensitivity profiles.