Introduction

Proton MRSI (¹H-MRSI) provides unique spatially resolved molecular information for various physiological and pathological studies ^1-2. A long-standing challenge for practical applications of ¹H-MRSI is the strong water/lipids signals. These nuisance signals, sometimes overwhelming, prevent meaningful analysis of the metabolite signals if not effectively suppressed or removed. Both acquisition and postprocessing methods have been proposed to address this challenge ^3-7. The union-of-subspaces (UoSS) model has demonstrated strong capability in nuisance signal removal (NSRM) from ¹H-MRSI data by integrating spatial and spectral constraints on water/lipids ^8-9. Nevertheless, substantial residual nuisance may still be present after UoSS NSRM, especially when the initial water/lipid signals are stronger (e.g., in short-TE and/or unsuppressed acquisitions) and/or in the regions with severe B₀ inhomogeneity or imprecise spatial support information. We proposed here a strategy to further reduce these residual nuisance signals for improved MRSI data quality by synergizing sparsity constraints and data-adapted learned subspaces through the low-rank plus sparse modeling framework¹⁰.

Theory

Low-Rank+Sparse (L+S) model for NSRM

The choice of L+S model was motivated by repeated observations that residual nuisance signals after UoSS processing typically appear as spatially sparse features (e.g., locally bright regions) with distinct residual water/lipid peaks and the low-rank property of the metabolite component ^8-9. However, a direct application of the L+S model does not offer effective signal separation separation as (1) the low-rank component will compete with the sparse components in capturing nuisance components and (2) the sparse component may absorb metabolite signals leading to over removal. Therefore, we propose the following explicit low-rank+sparse formulation to address these issues:

$$C_{r,meta},S_{nu}=argmin\parallel d_{t} - \Omega F B(DC_{r,meta}\phi_{t}+S_{nu})\parallel_{2}^{2}+\alpha\parallel W(F_{t}(S_{nu})) \parallel_{1} (1)$$
where $$$C_{r,meta}\phi_{t}$$$ and $$$S_{nu}$$$ denotes the metabolite and nuisance components, respectively, with $$$C_{r,meta}$$$ and $$$\phi_{t}$$$ being low-rank matrices for the spatial coefficients and temporal basis, $$$d_{t}$$$ is (k,t)-space data, $$$\Omega$$$ an encoding operator, $$$F$$$ refers to 3D Fouerier transform, $$$B$$$ models B₀ inhomogeneity induced phases, and $$$ D$$$ is a brain mask enforcing a spatial prior for metabolites.$$$W$$$ represents db4 wavelet tranform and $$$F_{t}$$$ refers to Fourier transform along t-dimension . The combination of $$$D$$$ and $$$\phi_{t}$$$ serves to protect the metabolite from being absorbed into $$$S_{nu}$$$ and also make $$$S_{nu}$$$ target the nuisance more specifically. The resulting optimization is solved using a fast iterative soft thresholding method¹².

Estimation of the metabolite basis
Accurate estimation of metabolite basis $$$\phi_{t}$$$ plays an important role in our L+S model. One way to get the basis is applying frequency selective HSVD to the data itself or high-SNR calibration data, which is sensitive to noise and lineshape distortion. We propose to use a learned subspace approach¹¹ (Fig.1). Specifically, we prelearned a metabolite subspace from previous training data then project residual signals onto the learned subspace. A parametric fitting with lineshape adaptation was then applied to the projection data to extract metabolite components and filter out residual nuisance projection. The fitted data was used to regenerate an adapted basis $$$\phi_{t}$$$.

Results

In vivo data were collected using a fast MRSI sequence¹³ on a Prisma 3T scanner (IRB approved) to evaluate the performance of our L+S method in further reducing the residual nuisance from UoSS NSRM. Fig.2 shows the NSRM results for one dataset produced w/wo the proposed L+S method. Compared to the original UOSS method, the L+S method further separated the residual nuisance signals into the sparse component (not shown here) and produced lower residuals. The L+S model with adapted basis further improved the removal performance. Fig.3 shows some representative spectra for different methods. Our L+S method further suppressed the residual water peaks at the voxels where UoSS did not perform well (voxels A&B) and produced similar spectra where UoSS performed well (voxel C), demonstrating the metabolite signal protection capability.

The NSRM results for another volunteer are shown in Fig.4. The L+S method with either options of metabolite basis could further suppress the residual nuisance inside the brain and outside the brain. Note that reduction of strong residual nuisance outside the brain is still helpful as it can affect advanced processing such as low-rank filtering steps. Fig.5 shows reconstructed metabolite maps and localized spectra from data produced with only UoSS NSRM and UoSS plus our L+S NSRM. Improved spatiospectral data quality is apparent with improved NSRM offered by the proposed method.

Conclusion

We propose a low-rank plus sparse model to improve nuisance signal removal for ¹H-MRSI data. A learned metabolite subspace adapted to the subject-specific experimental data is included to facilitate the separation of the sparse nuisance and low-rank metabolite components. We demonstrated that the proposed method can further remove nuisance signals after a state-of-the-art UoSS removal while protecting the metabolite signals, which lead to better metabolite spatiospectral reconstruction. We expect the proposed method to make 1H-MRSI more robust.

Acknowledgements

No acknowledgement found.

References

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