A subspace approach to high-resolution spectroscopic imaging

Abstract

Purpose: To accelerate spectroscopic imaging using sparse sampling of (k,t)-space and subspace (or low-rank) modeling to enable high-resolution metabolic imaging with good signal-to-noise ratio.

Methods: The proposed method, called SPectroscopic Imaging by exploiting spatiospectral CorrElation, exploits a unique property known as partial separability of spectroscopic signals. This property indicates that high-dimensional spectroscopic signals reside in a very low-dimensional subspace and enables special data acquisition and image reconstruction strategies to be used to obtain high-resolution spatiospectral distributions with good signal-to-noise ratio. More specifically, a hybrid chemical shift imaging/echo-planar spectroscopic imaging pulse sequence is proposed for sparse sampling of (k,t)-space, and a low-rank model-based algorithm is proposed for subspace estimation and image reconstruction from sparse data with the capability to incorporate prior information and field inhomogeneity correction.

Results: The performance of the proposed method has been evaluated using both computer simulations and phantom studies, which produced very encouraging results. For two-dimensional spectroscopic imaging experiments on a metabolite phantom, a factor of 10 acceleration was achieved with a minimal loss in signal-to-noise ratio compared to the long chemical shift imaging experiments and with a significant gain in signal-to-noise ratio compared to the accelerated echo-planar spectroscopic imaging experiments.

Conclusion: The proposed method, SPectroscopic Imaging by exploiting spatiospectral CorrElation, is able to significantly accelerate spectroscopic imaging experiments, making high-resolution metabolic imaging possible.

Keywords: chemical shift imaging; echo-planar spectroscopic imaging; low-rank model; partial separability; spectroscopic imaging; subspace modeling.

Figure 1

An example of SPICE (k, t)-space sampling for 2D spectroscopic imaging (with k_x pointing into the page): (a) (k, t)-space sampling for data in for subspace estimation. covers only a limited region of central k-space (based on SNR consideration), and sample the free precession period (T_A;1) fully (to capture the spectral information); (b) (k, t)-space sampling for data in for determination of the spatial coefficients. Note that a set of FIDs with different echo shifts (Δt₁, Δt₂, … Δt_q) is collected, each of which traverses entire k-space (also see Fig. 2) but with limited spectral encoding (T_A;2 < T_A;1).

Figure 2

A prototypical hybrid CSI/EPSI sequence for SPICE: (a) the CSI component used to collect the data in with limited k-space coverage but full spectral encoding, and (b) an EPSI-like component used to acquire the data in with extended k-space coverage but limited spectral encoding. Note that there is only one k_y reversal in each TR due to SNR consideration, although more k_y reversals can be included in principle. Note also that the proposed EPSI component supports bipolar acquisition but requires additional correction if data acquired on both positive and negative Gx are used.

Figure 3

Simulation results: (a) the gold standard, (b) CSI reconstruction from 16 × 16 spatial encodings, (c) EPSI reconstruction from 128 × 128 spatial encodings averaged twice, and (d) SPICE reconstruction from 8 × 8 CSI encodings in , 48 echo-shifts in averaged four times and L = 8. The left column shows the spatial distributions of a frequency component at 345 Hz and the right column shows the spectra corresponding to the voxel identified by the red dot for each case.

Figure 4

Experimental results from a water-oil phantom: (a) field inhomogeneity corrected CP reconstruction from an EPSI data with 128 × 128 spatial encodings, and (b) SPICE reconstruction with eight conventional EPSI encodings in (two temporal interleaves), 48 echo shifts in (a total of 64 excitations) and L = 16. Note that the reconstructions are almost comparable but the data acquisition time for the SPICE experiment is only 1/4 of that for the EPSI experiment.

Figure 5

Experimental results from a metabolite phantom shown in (a) with spectroscopic imaging data acquired in the presence of B₀ inhomogeneity shown in (b): (c) CSI reconstruction from 60 × 60 spatial encodings, (d) CSI reconstruction from 19 × 19 spatial encodings, (e) EPSI reconstruction from 100 × 100 spatial encodings with two averages, and (f) SPICE reconstruction with 12 × 12 CSI encodings in , 45 echo shifts in with five averages, and L = 12. The left column shows the spatial distributions of NAA and the right column shows the spectra from the voxel identified by the red dot in (a). Field inhomogeneity correction was included for all the cases as described in the text. The results in (d)–(f) correspond to a factor of 10 reduction in data acquisition time (6 min) compared to the high-resolution CSI acquisition in (c).

Figure 6

Experimental results from the metabolite phantom in Fig. 5a: (a) the high-resolution CSI reconstruction in Fig. 5c and SPICE reconstructions with 12 × 12 CSI encodings in , L = 12 and different numbers of echo shifts in : (b) 45 echo shifts, (c) 80 echo shifts, and (d) the entire EPSI data set.

Figure 7

Two alternative (k, t)-space sampling trajectories that can be used to generate : (a) EPSI trajectories, and (b) spiral EPSI trajectories. Note that in (a), the echo spacing is not constrained by the spectral Nyquist criterion as in traditional EPSI schemes. In both cases, different colors represent trajectories for different excitations.