  Objective: Magnetic Resonance Spectroscopy (MRS) is an important technique
for biomedical detection. However, it is challenging to accurately quantify
metabolites with proton MRS due to serious overlaps of metabolite signals,
imperfections because of non-ideal acquisition conditions, and interference
with strong background signals mainly from macromolecules. The most popular
method, LCModel, adopts complicated non-linear least square to quantify
metabolites and addresses these problems by designing empirical priors such as
basis-sets, imperfection factors. However, when the signal-to-noise ratio of
MRS signal is low, the solution may have large deviation. Methods: Linear Least
Squares (LLS) is integrated with deep learning to reduce the complexity of
solving this overall quantification. First, a neural network is designed to
explicitly predict the imperfection factors and the overall signal from
macromolecules. Then, metabolite quantification is solved analytically with the
introduced LLS. In our Quantification Network (QNet), LLS takes part in the
backpropagation of network training, which allows the feedback of the
quantification error into metabolite spectrum estimation. This scheme greatly
improves the generalization to metabolite concentrations unseen for training
compared to the end-to-end deep learning method. Results: Experiments show that
compared with LCModel, the proposed QNet, has smaller quantification errors for
simulated data, and presents more stable quantification for 20 healthy in vivo
data at a wide range of signal-to-noise ratio. QNet also outperforms other
end-to-end deep learning methods. Conclusion: This study provides an
intelligent, reliable and robust MRS quantification. Significance: QNet is the
first LLS quantification aided by deep learning.
