Recently, several novel methods that exploit spatiospectral priors have been developed to address the dimensionality, sensitivity and nuisance signal challenges of MR spectroscopic imaging, and enabled significantly improved combinations of speed, resolution, SNR and organ coverage. This talk will review the new low-dimensional models, special acquisition and reconstruction strategies underlying these exciting developments, as well as potential neuroscience and clinical applications of these new techniques. Current limitations and future research opportunities will also be discussed.
MRSI allows the mapping of spatially-resolved metabolic information and has been long recognized as a potentially powerful molecular imaging modality. But the in vivo applications of MRSI have been hindered by the fundamental challenges of high dimensionality, due to the additional spectral dimensions in the imaging problem, and inherently low SNR, due to the very low concentrations of the molecules of interest [1,2]. Mathematically, the imaging problem can be defined as recovering a high-dimensional spatiospectral function $$$\rho(r,f)$$$ from measurements in a corresponding (k,t)-space represented by
$$s(k,t)=\int_{V}\int_{\Omega}\rho(r,f)e^{-i2\pi ft}e^{-i2\pi\delta f(r)t}e^{-i2\pi kr}dfdr + n(k,t)\quad\quad [1]$$
where $$$V$$$ and $$$\Omega$$$ are the imaging volume and spectral bandwidth of interest, respectively, $$$\delta f(r)$$$ captures the $$$B_0$$$ field inhomogeneity, $$$s(k,t)$$$ contains the spatiospectral encodings and $$$n(k,t)$$$ the measurement noise. The conventional Fourier reconstruction treats individual discretized voxels and spectral points as independent unknowns and uses the inverse Fourier transform for reconstruction from limited (k,t)-space samples (for SNR consideration), i.e.,
$$\hat{\rho}(r,f)=\sum_{m=1}^M\sum_{q=1}^Qs(k_m,t_q)e^{i2\pi k_mr}e^{i2\pi t_qf}. \qquad [2]$$
Such an encoding and decoding paradigm requires an exponentially growing number of high-SNR measurements as the desired spatiospectral resolution for $$$\hat{\rho}(r,f)$$$ increases, which strongly limits its in vivo applications.
A number of methods have been developed to address the limitations of Fourier reconstruction. Earlier methods typically used very strong spatial or spectral priors that were too constrained for practical experimental data and offered limited improvement in the combination of speed, resolution and SNR [3-8]. Recently, new approaches have been proposed to exploit the spatiospectral/spatiotemporal correlation in the high-dimensional function of interest for fast, high-resolution MRSI [9-13]. The key to the success of these methods is to effectively reduce the dimensionality of the imaging problem. One particular example is to represent $$$\rho(r,f)$$$ using the partial separability model [14-16]
$$\rho(r,f)=\sum_{l=1}^Lc_l(r)\phi_l(f)\qquad\qquad [3]$$
where $$$\{\phi_l(f)\}$$$ is a set of spectral basis functions with $$$\{c_l(r)\}$$$ being the corresponding spatial coefficients. This model can be motivated by the fact that the image object only has a small number of tissue types each of which has a unique spectral signature or each voxel spectrum contains a finite number of spectral components, whose spectral variations can be well approximated by a linear combination of only a few $$$\{\phi_l(f)\}$$$ (i.e., L is a small number). This low-dimensional model implies that the high-dimensional $$$\rho(r,f)$$$ resides in a low-dimensional subspace which has a significantly reduced number of degrees-of-freedom, making better tradeoffs for speed, resolution and SNR possible. With the model in Eq. [3], special acquisition and reconstruction can be designed to determine $$$\{\phi_l(f)\}$$$ and $$$\{c_l(r)\}$$$ separately. More specifically, the estimation of $$$\{\phi_l\}$$$ requires data with high spectral resolution but not necessarily high spatial resolution. With $$$\{\phi_l\}$$$ determined, the estimation of $$$\{c_l\}$$$ requires data with extended k-space coverage to achieve the desired spatial resolution but not necessarily high spectral resolution. Special low-rank constrained optimization can be applied to solve the reconstruction problem from noisy data with capability to incorporate additional regularization terms.
Extension of the subspace model in Eq. [3] to union-of-subspaces models and higher-order low-rank tensor models have been developed [17,18]. Other spatiospectral models that take advantage of spatial constraints obtained from high-resolution anatomical images and spatiospectral sparsity have also been described [19,20], and can be integrated with the subspace models to further improve the performance of in vivo MRSI.
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