Tensor data have been widely used in many fields,e.g.,modern biomedical imaging,chemometrics,and economics,but often suffer from some common issues as in high dimensional statistics.How to find their low-dimensional l...Tensor data have been widely used in many fields,e.g.,modern biomedical imaging,chemometrics,and economics,but often suffer from some common issues as in high dimensional statistics.How to find their low-dimensional latent structure has been of great interest for statisticians.To this end,we develop two efficient tensor sufficient dimension reduction methods based on the sliced average variance estimation(SAVE)to estimate the corresponding dimension reduction subspaces.The first one,entitled tensor sliced average variance estimation(TSAVE),works well when the response is discrete or takes finite values,but is not■consistent for continuous response;the second one,named bias-correction tensor sliced average variance estimation(CTSAVE),is a de-biased version of the TSAVE method.The asymptotic properties of both methods are derived under mild conditions.Simulations and real data examples are also provided to show the superiority of the efficiency of the developed methods.展开更多
The quality of a multichannel audio signal may be reduced by missing data, which must be recovered before use. The data sets of multichannel audio can be quite large and have more than two axes of variation, such as c...The quality of a multichannel audio signal may be reduced by missing data, which must be recovered before use. The data sets of multichannel audio can be quite large and have more than two axes of variation, such as channel, frame, and feature. To recover missing audio data, we propose a low-rank tensor completion method that is a high-order generalization of matrix completion. First, a multichannel audio signal with missing data is modeled by a three-order tensor. Next, tensor completion is formulated as a convex optimization problem by defining the trace norm of the tensor, and then an augmented Lagrange multiplier method is used for solving the constrained optimization problem. Finally, the missing data is replaced by alternating iteration with a tensor computation. Experiments were conducted to evaluate the effectiveness on data of a 5.1-channel audio signal. The results show that the proposed method outperforms state-of-the-art methods. Moreover, subjective listening tests with MUSHRA(Multiple Stimuli with Hidden Reference and Anchor) indicate that better audio effects were obtained by tensor completion.展开更多
Computation of impedance tensor elements is one of the important steps in magnetotelluric data processing. Conventionally, the impedance tensor is defined as a 2 x 2 matrix with Zxx, Zxy, Zyx, and Zyy as elements. In ...Computation of impedance tensor elements is one of the important steps in magnetotelluric data processing. Conventionally, the impedance tensor is defined as a 2 x 2 matrix with Zxx, Zxy, Zyx, and Zyy as elements. In the present study, the six-element impedance tensor is computed with a 2 × 3 matrix using Zxx, Zxy, Zyx, Zyy, Zxz, and Zyz. The properties of the impedance tensor elements have been analyzed for these above two types. The methodology has been tested with five component magnetotelluric data from the Kutch sedimentary basin, Gujarat, India. From the computation of apparent resistivity computation and phase we observed that there is small difference between the four and six impedance elements of Zxy and Zyx for most of the frequency band. However for longer period data, more than 100 sec, an increase in the apparent resistivity and decrease in the phase is observed. We also note that the tipper magnitude is nearly zero for most of the periods, but gradually shows an increasing trend for longer periods （〉100 see）. The Kutch sedimentary basin geoeleetric section shows near horizontal layers at shallow depths and anomalous high conductivity heterogeneous layers at deeper depths may be responsible for the large Hz component at longer periods. This indicates that the vertical component of the magnetic field, Hz, does play an important role in the estimation of electric field parameters in the region with large 2D/3D structures.展开更多
Moment tensor inversion was carried out for small and moderate earthquakes with near-source broadband data recorded by a temporal small-aperture network consisting of three component accelerographs. Accelerograms were...Moment tensor inversion was carried out for small and moderate earthquakes with near-source broadband data recorded by a temporal small-aperture network consisting of three component accelerographs. Accelerograms were integrated twice to produce displacement seismograms and filtered by a Butterworth band-pass filter. Green's functions were calculated for a homogeneous semi-infinite elastic medium in the inversion. Direct P,S and converted SP phases were identified for the inversion with reference to the synthetic seismograms. Through the moment tensor inversion it is demonstrated that with very simple structure model and selected phases, one is able to retrieve the source mechanism and the seismic moment for small events, andthe source mechanism for moderate events. It is also demonstrated that the technique described in this studyis convenient for the determination of source mechanismal and stress state in dealing with numbers of small andmoderate earthquakes without detailed knowledge about the structure. As an application of the present technique, moment tensors of 15 aftershocks of the Ms 6. 1 earthquake occurred on April 18, 1985 in Luquan,Yunnan Province, China were retrieved. The inversion results show that these events can be reasonably modeled by a predominant double couple. It can be found from the distribution of principal stress axes and the average moment tensor that the pressure axis in this area lies horizontally in the NNW direction, which is consistent with the results obtained from previous studies. It implies that the occurrence of the Luquan earthquake sequence is tectonically related to the relative collision motion between the Indian and Eurasian Plates.展开更多
Edge detection is a commonly requested task in the interpretation of potential field data. Different methods have different results for varied depths and shapes of geological bodies. In this paper,we propose using the...Edge detection is a commonly requested task in the interpretation of potential field data. Different methods have different results for varied depths and shapes of geological bodies. In this paper,we propose using the combination of structure tensor and tilt angle to detect the edges of the sources,which can display the edges of shallow and deep bodies simultaneously. Through tests on synthetic potential field data,it is obvious that the proposed edge detection methods can display the sources edges more clearly and precisely,compared with other commonly used methods. The application on real potential field data shows similar result,obtaining the edges of layers and faults clearly. In addition,another advantage of the new method is its insensitivity to noise.展开更多
基金supported by the National Natural Science Foundation of China(Grant NO.12301377,11971208,92358303)the National Social Science Foundation of China(Grant NO.21&ZD152)+4 种基金the Outstanding Youth Fund Project of the Science and Technology Department of Jiangxi Province(Grant No.20224ACB211003)Jiangxi Provincial National Natural Science Foundation(Grant NO.20232BAB211014)the Science and technology research project of the Education Department of Jiangxi Province(Grant No.GJJ210535)the opening funding of Key Laboratory of Data Science in Finance and Economicsthe innovation team funding of Digital Economy and Industrial Development,Jiangxi University of Finance and Economics。
文摘Tensor data have been widely used in many fields,e.g.,modern biomedical imaging,chemometrics,and economics,but often suffer from some common issues as in high dimensional statistics.How to find their low-dimensional latent structure has been of great interest for statisticians.To this end,we develop two efficient tensor sufficient dimension reduction methods based on the sliced average variance estimation(SAVE)to estimate the corresponding dimension reduction subspaces.The first one,entitled tensor sliced average variance estimation(TSAVE),works well when the response is discrete or takes finite values,but is not■consistent for continuous response;the second one,named bias-correction tensor sliced average variance estimation(CTSAVE),is a de-biased version of the TSAVE method.The asymptotic properties of both methods are derived under mild conditions.Simulations and real data examples are also provided to show the superiority of the efficiency of the developed methods.
基金partially supported by the National Natural Science Foundation of China under Grants No. 61571044, No.61620106002, No.61473041, No.11590772, No.61640012Inner Mongolia Natural Science Foundation under Grants No. 2017MS(LH)0602
文摘The quality of a multichannel audio signal may be reduced by missing data, which must be recovered before use. The data sets of multichannel audio can be quite large and have more than two axes of variation, such as channel, frame, and feature. To recover missing audio data, we propose a low-rank tensor completion method that is a high-order generalization of matrix completion. First, a multichannel audio signal with missing data is modeled by a three-order tensor. Next, tensor completion is formulated as a convex optimization problem by defining the trace norm of the tensor, and then an augmented Lagrange multiplier method is used for solving the constrained optimization problem. Finally, the missing data is replaced by alternating iteration with a tensor computation. Experiments were conducted to evaluate the effectiveness on data of a 5.1-channel audio signal. The results show that the proposed method outperforms state-of-the-art methods. Moreover, subjective listening tests with MUSHRA(Multiple Stimuli with Hidden Reference and Anchor) indicate that better audio effects were obtained by tensor completion.
文摘Computation of impedance tensor elements is one of the important steps in magnetotelluric data processing. Conventionally, the impedance tensor is defined as a 2 x 2 matrix with Zxx, Zxy, Zyx, and Zyy as elements. In the present study, the six-element impedance tensor is computed with a 2 × 3 matrix using Zxx, Zxy, Zyx, Zyy, Zxz, and Zyz. The properties of the impedance tensor elements have been analyzed for these above two types. The methodology has been tested with five component magnetotelluric data from the Kutch sedimentary basin, Gujarat, India. From the computation of apparent resistivity computation and phase we observed that there is small difference between the four and six impedance elements of Zxy and Zyx for most of the frequency band. However for longer period data, more than 100 sec, an increase in the apparent resistivity and decrease in the phase is observed. We also note that the tipper magnitude is nearly zero for most of the periods, but gradually shows an increasing trend for longer periods （〉100 see）. The Kutch sedimentary basin geoeleetric section shows near horizontal layers at shallow depths and anomalous high conductivity heterogeneous layers at deeper depths may be responsible for the large Hz component at longer periods. This indicates that the vertical component of the magnetic field, Hz, does play an important role in the estimation of electric field parameters in the region with large 2D/3D structures.
文摘Moment tensor inversion was carried out for small and moderate earthquakes with near-source broadband data recorded by a temporal small-aperture network consisting of three component accelerographs. Accelerograms were integrated twice to produce displacement seismograms and filtered by a Butterworth band-pass filter. Green's functions were calculated for a homogeneous semi-infinite elastic medium in the inversion. Direct P,S and converted SP phases were identified for the inversion with reference to the synthetic seismograms. Through the moment tensor inversion it is demonstrated that with very simple structure model and selected phases, one is able to retrieve the source mechanism and the seismic moment for small events, andthe source mechanism for moderate events. It is also demonstrated that the technique described in this studyis convenient for the determination of source mechanismal and stress state in dealing with numbers of small andmoderate earthquakes without detailed knowledge about the structure. As an application of the present technique, moment tensors of 15 aftershocks of the Ms 6. 1 earthquake occurred on April 18, 1985 in Luquan,Yunnan Province, China were retrieved. The inversion results show that these events can be reasonably modeled by a predominant double couple. It can be found from the distribution of principal stress axes and the average moment tensor that the pressure axis in this area lies horizontally in the NNW direction, which is consistent with the results obtained from previous studies. It implies that the occurrence of the Luquan earthquake sequence is tectonically related to the relative collision motion between the Indian and Eurasian Plates.
基金Supported by projects of National Key Research and Development Plan(Nos.2017YFC0601606,2017YFC0602203)National Science and Technology Major Project(No.2016ZX05027-002-03)+1 种基金National Natural Science Foundation of China(Nos.41604098,41404089)State Key Program of National Natural Science of China(No.41430322)
文摘Edge detection is a commonly requested task in the interpretation of potential field data. Different methods have different results for varied depths and shapes of geological bodies. In this paper,we propose using the combination of structure tensor and tilt angle to detect the edges of the sources,which can display the edges of shallow and deep bodies simultaneously. Through tests on synthetic potential field data,it is obvious that the proposed edge detection methods can display the sources edges more clearly and precisely,compared with other commonly used methods. The application on real potential field data shows similar result,obtaining the edges of layers and faults clearly. In addition,another advantage of the new method is its insensitivity to noise.
