Chemical exchange saturation transfer (CEST) MRI at 3 T suffers from low specificity due to overlapping CEST effects from multiple metabolites, while higher field strengths (B0) allow for better separation of Z-spectral \"peaks,\" aiding signal interpretation and quantification. However, data acquisition at higher B0 is restricted by equipment access, field inhomogeneity and safety issues. Herein, we aim to synthesize higher-B0 Z-spectra from readily available data acquired with 3 T clinical scanners using a deep learning framework. Trained with simulation data using models based on Bloch-McConnell equations, this framework comprised two deep neural networks (DNNs) and a singular value decomposition (SVD) module. The first DNN identified B0 shifts in Z-spectra and aligned them to correct frequencies. After B0 correction, the lower-B0 Z-spectra were streamlined to the second DNN, casting into the key feature representations of higher-B0 Z-spectra, obtained through SVD truncation. Finally, the complete higher-B0 Z-spectra were recovered from inverse SVD, given the low-rank property of Z-spectra. This study constructed and validated two models, a phosphocreatine (PCr) model and a pseudo-in-vivo one. Each experimental dataset, including PCr phantoms, egg white phantoms, and in vivo rat brains, was sequentially acquired on a 3 T human and a 9.4 T animal scanner. Results demonstrated that the synthetic 9.4 T Z-spectra were almost identical to the experimental ground truth, showing low RMSE (0.11% ± 0.0013% for seven PCr tubes, 1.8% ± 0.2% for three egg white tubes, and 0.79% ± 0.54% for three rat slices) and high R2 (>0.99). The synthesized amide and NOE contrast maps, calculated using the Lorentzian difference, were also well matched with the experiments. Additionally, the synthesis model exhibited robustness to B0 inhomogeneities, noise, and other acquisition imperfections. In conclusion, the proposed framework enables synthesis of higher-B0 Z-spectra from lower-B0 ones, which may facilitate CEST MRI quantification and applications.

The prestige target selectivity and imaging depth of optical-resolution photoacoustic microscope (OR-PAM) have gained attentions to enable advanced intra-cellular visualizations. However, the broad-band nature of photoacoustic signals is prone to noise and artifacts caused by the inefficient light-to-pressure translation, resulting in poor image quality. The present study foresees application of singular value decomposition (SVD) to effectively extract the photoacoustic signals from these noise and artifacts. Although spatiotemporal SVD succeeded in ultrasound flow signal extraction, the conventional multi frame model is not suitable for data acquired with scanning OR-PAM due to the burden of accessing multiple frames. To utilize SVD on the OR-PAM, this study began with exploring SVD applied on multiple A-lines of photoacoustic signal instead of frames. Upon explorations, an obstacle of uncertain presence of unwanted singular vectors was observed. To tackle this, a data-driven weighting matrix was designed to extract relevant singular vectors based on the analyses of temporal-spatial singular vectors. Evaluation on the extraction capability by the SVD with the weighting matrix showed a superior signal quality with efficient computation against past studies. In summary, this study contributes to the field by providing exploration of SVD applied on A-line signals as well as its practical utilization to distinguish and recover photoacoustic signals from noise and artifact components.

Imaging the spatial distribution of low concentrations of metal is a growing problem of interest with applications in medical and material sciences. X-ray fluorescence emission tomography (XFET) is an emerging metal mapping imaging modality with potential sensitivity improvements and practical advantages over other methods. However, XFET detector placement must first be optimized to ensure accurate metal density quantification and adequate spatial resolution. In this work, we first use singular value decomposition of the imaging model and eigendecomposition of the object-specific Fisher information matrix to study how detector arrangement affects spatial resolution and feature preservation. We then perform joint image reconstructions of a numerical gold phantom. For this phantom, we show that two parallel detectors provide metal quantification with similar accuracy to four detectors, despite the resulting anisotropic spatial resolution in the attenuation map estimate. Two orthogonal detectors provide improved spatial resolution along one axis, but underestimate the metal concentration in distant regions. Therefore, this work demonstrates the minor effect of using fewer, but strategically placed, detectors in the case where detector placement is restricted. This work is a critical investigation into the limitations and capabilities of XFET prior to its translation to preclinical and benchtop uses.

We propose an artificial intelligence approach based on deep neural networks to tackle a canonical 2D scalar inverse source problem. The learned singular value decomposition (L-SVD) based on hybrid autoencoding is considered. We compare the reconstruction performance of L-SVD to the Truncated SVD (TSVD) regularized inversion, which is a canonical regularization scheme, to solve an ill-posed linear inverse problem. Numerical tests referring to far-field acquisitions show that L-SVD provides, with proper training on a well-organized dataset, superior performance in terms of reconstruction errors as compared to TSVD, allowing for the retrieval of faster spatial variations of the source. Indeed, L-SVD accommodates a priori information on the set of relevant unknown current distributions. Different from TSVD, which performs linear processing on a linear problem, L-SVD operates non-linearly on the data. A numerical analysis also underlines how the performance of the L-SVD degrades when the unknown source does not match the training dataset.

A method based on Gabor spectral mode transmissibility functions (GSMTFs) is proposed to detect local damage in a cantilevered structure under nonstationary ambient excitations. Gabor transformation and singular value decomposition are used to reduce the influences of other vibration modes on Gabor spectral mode transmissibility functions and process nonstationary structural responses, respectively. A new state characteristic based on the fundamental structure frequency is formulated on the basis of the GSMTFs, eventually leading to the development of a new damage indicator. The probability density functions of the damage indicator for healthy and damaged states can be estimated from the measured data, and the receiver operating characteristic (ROC) curve derived from these probability distributions and the corresponding area under the ROC curve (AUC) are used to determine the damage location. A six-degree-of-freedom system and a typical transmission tower are numerically studied, and the results show that the proposed method can estimate the structural damage location under nonstationary random loads. The proposed method is further validated with a planar frame in the laboratory, which exhibits multiple damage elements via random force hammer excitations. The results show that the AUC values computed for certain parts of the structure containing the damaged elements are greater than those for other parts of the structure, indicating the effectiveness of the proposed method. Moreover, the proposed method is compared with the dot product difference (DPD) index, and the results from the laboratory planar frame demonstrate that the proposed method can better identify damage.

Bridges may undergo structural vibration responses when exposed to seismic waves. An analysis of structural vibration characteristics is essential for evaluating the safety and stability of a bridge. In this paper, a signal time-frequency feature extraction method (NTFT-ESVD) integrating standard time-frequency transformation, singular value decomposition, and information entropy is proposed to analyze the vibration characteristics of structures under seismic excitation. First, the experiment simulates the response signal of the structure when exposed to seismic waves. The results of the time-frequency analysis indicate a maximum relative error of only 1% in frequency detection, and the maximum relative errors in amplitude and time parameters are 5.9% and 6%, respectively. These simulation results demonstrate the reliability of the NTFT-ESVD method in extracting the time-frequency characteristics of the signal and its suitability for analyzing the seismic response of the structure. Then, a real seismic wave event of the Su-Tong Yangtze River Bridge during the Hengchun earthquake in Taiwan (2006) is analyzed. The results show that the seismic waves only have a short-term impact on the bridge, with the maximum amplitude of the vibration response no greater than 1 cm, and the maximum vibration frequency no greater than 0.2 Hz in the three-dimensional direction, indicating that the earthquake in Hengchun will not have any serious impact on the stability and security of the Su-Tong Yangtze River Bridge. Additionally, the reliability of determining the arrival time of seismic waves by extracting the time-frequency information from structural vibration response signals is validated by comparing it with results from seismic stations (SSE/WHN/QZN) at similar epicenter distances published by the USGS. The results of the case study show that the combination of dynamic GNSS monitoring technology and time-frequency analysis can be used to analyze the impact of seismic waves on the bridge, which is of great help to the manager in assessing structural seismic damage.

The matrix profile serves as a fundamental tool to provide insights into similar patterns within time series. Existing matrix profile algorithms have been primarily developed for the normalized Euclidean distance, which may not be a proper distance measure in many settings. The methodology work of this paper was motivated by statistical analysis of beat-to-beat interval (BBI) data collected from smartwatches to monitor e-cigarette users\' heart rate change patterns for which the original Euclidean distance ( L 2 $$ {L}_2 $$ -norm) would be a more suitable choice. Yet, incorporating the Euclidean distance into existing matrix profile algorithms turned out to be computationally challenging, especially when the time series is long with extended query sequences. We propose a novel methodology to efficiently compute matrix profile for long time series data based on the Euclidean distance. This methodology involves four key steps including (1) projection of the time series onto eigenspace; (2) enhancing singular value decomposition (SVD) computation; (3) early abandon strategy; and (4) determining lower bounds based on the first left singular vector. Simulation studies based on BBI data from the motivating example have demonstrated remarkable reductions in computational time, ranging from one-fourth to one-twentieth of the time required by the conventional method. Unlike the conventional method of which the performance deteriorates sharply as the time series length or the query sequence length increases, the proposed method consistently performs well across a wide range of the time series length or the query sequence length.

There is a large surface-groundwater exchange downstream of wastewater treatment plants (WWTPs), and antibiotics upstream may influence sites downstream of rivers. Thus, samples from 9 effluent-receiving urban rivers (ERURs) and 12 groundwater sites were collected in Shijiazhuang City in December 2020 and April 2021. For ERURs, 8 out of 13 target quinolone antibiotics (QNs) were detected, and the total concentration of QNs in December and April were 100.6-4,398 ng/L and 8.02-2,476 ng/L, respectively. For groundwater, all target QNs were detected, and the total QNs concentration was 1.09-23.03 ng/L for December and 4.54-170.3 ng/L for April. The distribution of QNs was dissimilar between ERURs and groundwater. Most QN concentrations were weakly correlated with land use types in the system. The results of a positive matrix factorization model (PMF) indicated four potential sources of QNs in both ERURs and groundwater, and WWTP effluents were the main source of QNs. From December to April, the contribution of WWTP effluents and agricultural emissions increased, while livestock activities decreased. Singular value decomposition (SVD) results showed that the spatial variation of most QNs was mainly contributed by sites downstream (7.09%-88.86%) of ERURs. Then, a new method that combined the results of SVD and PMF was developed for a specific-source-site risk quotient (SRQ), and the SRQ for QNs was at high level, especially for the sites downstream of WWTPs. Regarding temporal variation, the SRQ for WWTP effluents, aquaculture, and agricultural emissions increased. Therefore, in order to control the antibiotic pollution, more attention should be paid to WWTP effluents, aquaculture, and agricultural emission sources for the benefit of sites downstream of WWTPs.

Gearboxes operate in challenging environments, which leads to a heightened incidence of failures, and ambient noise further compromises the accuracy of fault diagnosis. To address this issue, we introduce a fault diagnosis method that employs singular value decomposition (SVD) and graph Fourier transform (GFT). Singular values, commonly employed in feature extraction and fault diagnosis, effectively encapsulate various fault states of mechanical equipment. However, prior methods neglect the inter-relationships among singular values, resulting in the loss of subtle fault information concealed within. To precisely and effectively extract subtle fault information from gear vibration signals, this study incorporates graph signal processing (GSP) technology. Following SVD of the original vibration signal, the method constructs a graph signal using singular values as inputs, enabling the capture of topological relationships among these values and the extraction of concealed fault information. Subsequently, the graph signal undergoes a transformation via GFT, facilitating the extraction of fault features from the graph spectral domain. Ultimately, by assessing the Mahalanobis distance between training and testing samples, distinct defect states are discerned and diagnosed. Experimental results on bearing and gear faults demonstrate that the proposed method exhibits enhanced robustness to noise, enabling accurate and effective diagnosis of gearbox faults in environments with substantial noise.

We propose and demonstrate a single-pixel imaging method based on deep learning network enhanced singular value decomposition. The theoretical framework and the experimental implementation are elaborated and compared with the conventional methods based on Hadamard patterns or deep convolutional autoencoder network. Simulation and experimental results show that the proposed approach is capable of reconstructing images with better quality especially under a low sampling ratio down to 3.12%, or with fewer measurements or shorter acquisition time if the image quality is given. We further demonstrate that it has better anti-noise performance by introducing noises in the SPI systems, and we show that it has better generalizability by applying the systems to targets outside the training dataset. We expect that the developed method will find potential applications based on single-pixel imaging beyond the visible regime.