We present an algorithm for blindly recovering constituent source spectra from magnetic resonance (MR) chemical shift imaging (CSI) of the human brain. The algorithm, which we call constrained nonnegative matrix factorization (cNMF), does not enforce independence or sparsity, instead only requiring the source and mixing matrices to be nonnegative. It is based on the nonnegative matrix factorization (NMF) algorithm, extending it to include a constraint on the positivity of the amplitudes of the recovered spectra. This constraint enables recovery of physically meaningful spectra even in the presence of noise that causes a significant number of the observation amplitudes to be negative. We demonstrate and characterize the algorithm's performance using 31P volumetric brain data, comparing the results with two different blind source separation methods: Bayesian spectral decomposition (BSD) and nonnegative sparse coding (NNSC). We then incorporate the cNMF algorithm into a hierarchical decomposition framework, showing that it can be used to recover tissue-specific spectra given a processing hierarchy that proceeds coarse-to-fine. We demonstrate the hierarchical procedure on 1H brain data and conclude that the computational efficiency of the algorithm makes it well-suited for use in diagnostic work-up.
Abstract. Particle sensing technology has shown great potential for
monitoring particulate matter (PM) with very few temporal and spatial
restrictions because of its low cost, compact size, and easy operation.
However, the performance of low-cost sensors for PM monitoring in ambient
conditions has not been thoroughly evaluated. Monitoring results by low-cost
sensors are often questionable. In this study, a low-cost fine particle
monitor (Plantower PMS 5003) was colocated with a reference instrument,
the Synchronized Hybrid Ambient Real-time Particulate (SHARP) monitor, at the
Calgary Varsity air monitoring station from December 2018 to April 2019. The
study evaluated the performance of this low-cost PM sensor in ambient
conditions and calibrated its readings using simple linear regression (SLR),
multiple linear regression (MLR), and two more powerful machine-learning
algorithms using random search techniques for the best model architectures.
The two machine-learning algorithms are XGBoost and a feedforward neural
network (NN). Field evaluation showed that the Pearson correlation (r) between the
low-cost sensor and the SHARP instrument was 0.78. The Fligner and Killeen (F–K)
test indicated a statistically significant difference between the variances
of the PM2.5 values by the low-cost sensor and the SHARP
instrument. Large overestimations by the low-cost sensor before calibration
were observed in the field and were believed to be caused by the variation
of ambient relative humidity. The root mean square error (RMSE) was 9.93
when comparing the low-cost sensor with the SHARP instrument. The
calibration by the feedforward NN had the smallest RMSE of 3.91 in the test
dataset compared to the calibrations by SLR (4.91), MLR (4.65), and XGBoost
(4.19). After calibrations, the F–K test using the test dataset showed that
the variances of the PM2.5 values by the NN, XGBoost, and the
reference method were not statistically significantly different. From this
study, we conclude that a feedforward NN is a promising method to address the
poor performance of low-cost sensors for PM2.5 monitoring. In
addition, the random search method for hyperparameters was demonstrated to
be an efficient approach for selecting the best model structure.
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