Pub Date : 2017-12-01DOI: 10.1109/CAMSAP.2017.8313209
M. Mardani, E. Gong, Joseph Y. Cheng, J. Pauly, L. Xing
Recovering images from highly undersampled measurements has a wide range of applications across imaging sciences. State-of-the-art analytics however are not aware of the image perceptual quality, and demand iterative algorithms that incur significant computational overhead. To sidestep these hurdles, this paper brings forth a novel compressive imaging framework using deep neural networks that approximates a low-dimensional manifold of images using generative adversarial networks. To ensure the images are consistent with the measurements a recurrent GAN (RGAN) architecture is deployed that consists of multiple alternative blocks of generator networks and affine projection, which is then followed by a discriminator network to score the perceptual quality of the generated images. A deep residual network with skip connections is used for the generator, while the discriminator is a multilayer perceptron. Experiments performed with real-world contrast enhanced MRI data corroborate the diagnostic quality of the retrieved images relative to state-of-the-art CS schemes. In addition, it achieves about two-orders of magnitude faster reconstruction.
{"title":"Recurrent generative adversarial neural networks for compressive imaging","authors":"M. Mardani, E. Gong, Joseph Y. Cheng, J. Pauly, L. Xing","doi":"10.1109/CAMSAP.2017.8313209","DOIUrl":"https://doi.org/10.1109/CAMSAP.2017.8313209","url":null,"abstract":"Recovering images from highly undersampled measurements has a wide range of applications across imaging sciences. State-of-the-art analytics however are not aware of the image perceptual quality, and demand iterative algorithms that incur significant computational overhead. To sidestep these hurdles, this paper brings forth a novel compressive imaging framework using deep neural networks that approximates a low-dimensional manifold of images using generative adversarial networks. To ensure the images are consistent with the measurements a recurrent GAN (RGAN) architecture is deployed that consists of multiple alternative blocks of generator networks and affine projection, which is then followed by a discriminator network to score the perceptual quality of the generated images. A deep residual network with skip connections is used for the generator, while the discriminator is a multilayer perceptron. Experiments performed with real-world contrast enhanced MRI data corroborate the diagnostic quality of the retrieved images relative to state-of-the-art CS schemes. In addition, it achieves about two-orders of magnitude faster reconstruction.","PeriodicalId":315977,"journal":{"name":"2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124939960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-12-01DOI: 10.1109/CAMSAP.2017.8313122
Jorge Bacca, Héctor Vargas, H. Arguello
Recent hyperspectral imaging systems are constructed on the idea of compressive sensing for efficient acquisition. However, the traditional reconstruction model in compressive hyperspectral imaging has a high computational complexity. In this work, compressive hyperspectral imaging and unmixing are combined for hyperspectral reconstruction in a low-complexity scheme. The compressed hyperspectral measurements are acquired with a single pixel spectrometer. The reconstruction model is represented in a space of lower dimension named linear mixture model. Hyperspectral reconstruction is then formulated as a nonnegative matrix factorization problem with respect to the endmembers and abundances, bypassing high-complexity tasks involving the hyperspectral data cube itself. The nonnegative matrix factorization problem is solved by combining an alternating least-squares based estimation strategy with the alternating direction method of multipliers. The estimated performance of the proposed scheme is illustrated in experiments conducted on a simulated acquisition in real data outperforming in 3dB the state-of-the-art reconstruction algorithms.
{"title":"A constrained formulation for compressive spectral image reconstruction using linear mixture models","authors":"Jorge Bacca, Héctor Vargas, H. Arguello","doi":"10.1109/CAMSAP.2017.8313122","DOIUrl":"https://doi.org/10.1109/CAMSAP.2017.8313122","url":null,"abstract":"Recent hyperspectral imaging systems are constructed on the idea of compressive sensing for efficient acquisition. However, the traditional reconstruction model in compressive hyperspectral imaging has a high computational complexity. In this work, compressive hyperspectral imaging and unmixing are combined for hyperspectral reconstruction in a low-complexity scheme. The compressed hyperspectral measurements are acquired with a single pixel spectrometer. The reconstruction model is represented in a space of lower dimension named linear mixture model. Hyperspectral reconstruction is then formulated as a nonnegative matrix factorization problem with respect to the endmembers and abundances, bypassing high-complexity tasks involving the hyperspectral data cube itself. The nonnegative matrix factorization problem is solved by combining an alternating least-squares based estimation strategy with the alternating direction method of multipliers. The estimated performance of the proposed scheme is illustrated in experiments conducted on a simulated acquisition in real data outperforming in 3dB the state-of-the-art reconstruction algorithms.","PeriodicalId":315977,"journal":{"name":"2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114283716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-12-01DOI: 10.1109/CAMSAP.2017.8313191
A. Koochakzadeh, P. Pal
Decomposition of tensors into summation of rank one components, known as Canonical Polyadic (CP) decomposition, has long been studied in the literature. Although the CP-rank of tensors can far exceed their dimensions (in which case they are called overcomplete tensors), there are only a handful of algorithms which consider CP-decomposition of such overcomplete tensors, and most of the CP-decomposition algorithms proposed in literature deal with simpler cases where the rank is of the same order as the dimensions of the tensor. In this paper, we consider symmetric tensors of arbitrary even order whose eigenvalues are assumed to be positive. We show that for a 2dth order tensor with dimension N, under some mild conditions, the problem of CP-decomposition is equivalent to solving a system of quadratic equations, even when the rank is as large as O(Nd). We will develop two different algorithms (one convex, and one nonconvex) to solve this system of quadratic equations. Our simulations show that successful recovery of eigenvectors is possible even if the rank is much larger than the dimension of the tensor.1
{"title":"On canonical polyadic decomposition of overcomplete tensors of arbitrary even order","authors":"A. Koochakzadeh, P. Pal","doi":"10.1109/CAMSAP.2017.8313191","DOIUrl":"https://doi.org/10.1109/CAMSAP.2017.8313191","url":null,"abstract":"Decomposition of tensors into summation of rank one components, known as Canonical Polyadic (CP) decomposition, has long been studied in the literature. Although the CP-rank of tensors can far exceed their dimensions (in which case they are called overcomplete tensors), there are only a handful of algorithms which consider CP-decomposition of such overcomplete tensors, and most of the CP-decomposition algorithms proposed in literature deal with simpler cases where the rank is of the same order as the dimensions of the tensor. In this paper, we consider symmetric tensors of arbitrary even order whose eigenvalues are assumed to be positive. We show that for a 2dth order tensor with dimension N, under some mild conditions, the problem of CP-decomposition is equivalent to solving a system of quadratic equations, even when the rank is as large as O(Nd). We will develop two different algorithms (one convex, and one nonconvex) to solve this system of quadratic equations. Our simulations show that successful recovery of eigenvectors is possible even if the rank is much larger than the dimension of the tensor.1","PeriodicalId":315977,"journal":{"name":"2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131496883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-12-01DOI: 10.1109/CAMSAP.2017.8313206
Xu Han, L. Albera, A. Kachenoura, H. Shu, L. Senhadji
In this paper, we propose a new rank-(L, L, 1) Block Term Decomposition (BTD) method. Contrarily to classical techniques, the proposed method estimates also the number of terms and the rank-(L, L, 1) of each term from an overestimated initialization of them. This is achieved by using Group Sparsity of the Loading (GSL) matrices. Numerical experiments with noisy tensors show the good behavior of GSL-BTD and its robustness with respect to the presence of noise in comparison with classical methods. Experiments on epileptic signals confirm its efficiency in practical contexts.
{"title":"Block term decomposition with rank estimation using group sparsity","authors":"Xu Han, L. Albera, A. Kachenoura, H. Shu, L. Senhadji","doi":"10.1109/CAMSAP.2017.8313206","DOIUrl":"https://doi.org/10.1109/CAMSAP.2017.8313206","url":null,"abstract":"In this paper, we propose a new rank-(L, L, 1) Block Term Decomposition (BTD) method. Contrarily to classical techniques, the proposed method estimates also the number of terms and the rank-(L, L, 1) of each term from an overestimated initialization of them. This is achieved by using Group Sparsity of the Loading (GSL) matrices. Numerical experiments with noisy tensors show the good behavior of GSL-BTD and its robustness with respect to the presence of noise in comparison with classical methods. Experiments on epileptic signals confirm its efficiency in practical contexts.","PeriodicalId":315977,"journal":{"name":"2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127805112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-12-01DOI: 10.1109/CAMSAP.2017.8313183
M. Kowalski, P. Willett
This paper provides an analysis of several scenarios of target tracking state estimation when additionally estimating the biases of the measuring sensors in the state. Line of Sight (LOS) sensors are used with noisy data and angle biases that are unknown to the estimator. The addition of new state components can potentially be a drawback to the estimator and this is addressed by comparing the accuracy of estimation with 2, 3, and 4 sensors. Of particular interest to us is whether “more” is worth it: More sensors? Is bias estimation even worth doing? The answers are a qualified “yes” and a definite “sometimes.”.
{"title":"Simultaneous target state and sensor bias estimation: Is more better?","authors":"M. Kowalski, P. Willett","doi":"10.1109/CAMSAP.2017.8313183","DOIUrl":"https://doi.org/10.1109/CAMSAP.2017.8313183","url":null,"abstract":"This paper provides an analysis of several scenarios of target tracking state estimation when additionally estimating the biases of the measuring sensors in the state. Line of Sight (LOS) sensors are used with noisy data and angle biases that are unknown to the estimator. The addition of new state components can potentially be a drawback to the estimator and this is addressed by comparing the accuracy of estimation with 2, 3, and 4 sensors. Of particular interest to us is whether “more” is worth it: More sensors? Is bias estimation even worth doing? The answers are a qualified “yes” and a definite “sometimes.”.","PeriodicalId":315977,"journal":{"name":"2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128094044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-12-01DOI: 10.1109/CAMSAP.2017.8313185
Han Yan, S. Chaudhari, D. Cabric
Millimeter-wave (mmWave) systems require a large number of antennas at both base station (BS) and user equipment (UE) for a desirable link budget. Due to time varying channel under UE mobility, up-to-date channel state information (CSI) is important to obtain the beamforming gain. The overhead cost of frequent channel estimation becomes a bottleneck to achieve high throughput. In this paper, we propose the first mmWave frequency selective channel tracking technique for hybrid analog and digital beamforming architecture. During tracking, this technique exploits mmWave channel sparsity and uses only one training symbol to update the CSI. Our simulation study utilizes a dynamic channel simulator that builds on top of recently proposed geometric stochastic approach from mmMAGIC project at 28 GHz. Assuming 10m/s moving speed and 200 deg/s rotation speed at UE, the proposed algorithm maintains the 80% of the spectral efficiency as compared to static environment over a time window of 100 ms. The proposed tracking algorithm reduces the overhead by 3 times as compared to existing channel estimation technique.
{"title":"Wideband channel tracking for mmWave MIMO system with hybrid beamforming architecture: (Invited Paper)","authors":"Han Yan, S. Chaudhari, D. Cabric","doi":"10.1109/CAMSAP.2017.8313185","DOIUrl":"https://doi.org/10.1109/CAMSAP.2017.8313185","url":null,"abstract":"Millimeter-wave (mmWave) systems require a large number of antennas at both base station (BS) and user equipment (UE) for a desirable link budget. Due to time varying channel under UE mobility, up-to-date channel state information (CSI) is important to obtain the beamforming gain. The overhead cost of frequent channel estimation becomes a bottleneck to achieve high throughput. In this paper, we propose the first mmWave frequency selective channel tracking technique for hybrid analog and digital beamforming architecture. During tracking, this technique exploits mmWave channel sparsity and uses only one training symbol to update the CSI. Our simulation study utilizes a dynamic channel simulator that builds on top of recently proposed geometric stochastic approach from mmMAGIC project at 28 GHz. Assuming 10m/s moving speed and 200 deg/s rotation speed at UE, the proposed algorithm maintains the 80% of the spectral efficiency as compared to static environment over a time window of 100 ms. The proposed tracking algorithm reduces the overhead by 3 times as compared to existing channel estimation technique.","PeriodicalId":315977,"journal":{"name":"2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)","volume":"105 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134630196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-12-01DOI: 10.1109/CAMSAP.2017.8313157
Javier Rodríguez-Fernández, N. G. Prelcic, R. Heath
Obtaining accurate channel state information is crucial to configure the antenna arrays and the digital precoders and combiners in hybrid millimeter wave (mmWave) MIMO architectures. Most of prior work on channel estimation with hybrid MIMO architectures relies on the use of finite-resolution dictionaries to estimate angles of arrival (AoA) and angles of departure (AoD). When the AoAs or AoDs do not fall within the quantization grids used to generate these dictionaries, there is an unavoidable grid error in the estimation of the channel. In this paper, we propose a mixed compressed sensing-maximum likelihood algorithm that uses continuous dictionaries to estimate the channel. The quantization error due to using finite resolution dictionaries can be neglected with this approach, enhancing estimation performance without resorting to very large dictionaries. Simulation results show how the new algorithm outperforms approaches based on finite resolution dictionaries previously proposed for the estimation of mmWave channels.
{"title":"A compressive sensing-maximum likelihood approach for off-grid wideband channel estimation at mmWave","authors":"Javier Rodríguez-Fernández, N. G. Prelcic, R. Heath","doi":"10.1109/CAMSAP.2017.8313157","DOIUrl":"https://doi.org/10.1109/CAMSAP.2017.8313157","url":null,"abstract":"Obtaining accurate channel state information is crucial to configure the antenna arrays and the digital precoders and combiners in hybrid millimeter wave (mmWave) MIMO architectures. Most of prior work on channel estimation with hybrid MIMO architectures relies on the use of finite-resolution dictionaries to estimate angles of arrival (AoA) and angles of departure (AoD). When the AoAs or AoDs do not fall within the quantization grids used to generate these dictionaries, there is an unavoidable grid error in the estimation of the channel. In this paper, we propose a mixed compressed sensing-maximum likelihood algorithm that uses continuous dictionaries to estimate the channel. The quantization error due to using finite resolution dictionaries can be neglected with this approach, enhancing estimation performance without resorting to very large dictionaries. Simulation results show how the new algorithm outperforms approaches based on finite resolution dictionaries previously proposed for the estimation of mmWave channels.","PeriodicalId":315977,"journal":{"name":"2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)","volume":"447 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116230388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-12-01DOI: 10.1109/CAMSAP.2017.8313214
P. Dreesen, K. Tiels, Mariya Ishteva, J. Schoukens
The use of black-box models is wide-spread in signal processing and system identification applications. However, often such models possess a large number of parameters, and obfuscate their inner workings, as there are cross-connections between all inputs and all outputs (and possibly all internal states) of the model. Although black-box models have proven their success and wide applicability, there is a need to shed a light on what goes on inside the model. We have developed a tensor-based method that aims at pinpointing the nonlinearities of a given nonlinear model into a small number of univariate nonlinear mappings, with the advantageous side-effect of reducing the parametric complexity. In this contribution we will discuss how the method is conceived, and how it can be applied to the task of finding structure in blackbox models. We have found that the tensor-based decoupling method is able to reconstruct up to high accuracy a given blackbox nonlinear model, while reducing the parametric complexity and revealing some of the inner operation of the model. Due to their universal use, we will focus the presentation on the use of nonlinear state-space models, but the method is also suitable for other model structures. We validate the method on a case study in nonlinear system identification.
{"title":"Nonlinear system identification: Finding structure in nonlinear black-box models","authors":"P. Dreesen, K. Tiels, Mariya Ishteva, J. Schoukens","doi":"10.1109/CAMSAP.2017.8313214","DOIUrl":"https://doi.org/10.1109/CAMSAP.2017.8313214","url":null,"abstract":"The use of black-box models is wide-spread in signal processing and system identification applications. However, often such models possess a large number of parameters, and obfuscate their inner workings, as there are cross-connections between all inputs and all outputs (and possibly all internal states) of the model. Although black-box models have proven their success and wide applicability, there is a need to shed a light on what goes on inside the model. We have developed a tensor-based method that aims at pinpointing the nonlinearities of a given nonlinear model into a small number of univariate nonlinear mappings, with the advantageous side-effect of reducing the parametric complexity. In this contribution we will discuss how the method is conceived, and how it can be applied to the task of finding structure in blackbox models. We have found that the tensor-based decoupling method is able to reconstruct up to high accuracy a given blackbox nonlinear model, while reducing the parametric complexity and revealing some of the inner operation of the model. Due to their universal use, we will focus the presentation on the use of nonlinear state-space models, but the method is also suitable for other model structures. We validate the method on a case study in nonlinear system identification.","PeriodicalId":315977,"journal":{"name":"2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122602034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-12-01DOI: 10.1109/CAMSAP.2017.8313193
Kristina Naskovska, S. Lau, Amr Aboughazala, M. Haardt, J. Haueisen
Simultaneously recorded magnetoencephalography (MEG) and electroencephalography (EEG) signals can benefit from a joint analysis based on coupled Canonical Polyadic (CP) tensor decompositions. The coupled CP decomposition jointly decomposes tensors that have at least one factor matrix in common. The Coupled — Semi-Algebraic framework for approximate CP decomposition via SImultaneous matrix diagonalization framework (C-SECSI) efficiently estimates the factor matrices with adjustable complexity-accuracy trade-offs. Our objective is to decompose simultaneously recorded MEG and EEG signals above intact skull and above two conducting skull defects using C-SECSI in order to determine how such a tissue anomaly of the head is reflected in the tensor rank. The source of the MEG and EEG signals is a miniaturized electric dipole that is implanted into a rabbit's brain. The dipole is shifted along a line under the skull defects, and measurements are taken at regularly spaced points. The coupled SECSI analysis is conducted for MEG and EEG measurement series and ranks 1–3. This coupled decomposition produces meaningful components representing the three characteristic signal topographies for source positions under defect 1 and the positions on either side of defect 1. The rank estimation with respect to the complexity-accuracy trade-off of rank 3 reflects the three characteristic cases well and matches the dimensions spanned by the data set. The intact skull MEG signals show a higher complexity (rank 3) than the corresponding EEG signals (rank 1). The C-SECSI framework is a very promising method for blind signal separation in multidimensional data with coupled modalities, such as simultaneous MEG-EEG.
{"title":"Joint MEG-EEG signal decomposition using the coupled SECSI framework: Validation on a controlled experiment","authors":"Kristina Naskovska, S. Lau, Amr Aboughazala, M. Haardt, J. Haueisen","doi":"10.1109/CAMSAP.2017.8313193","DOIUrl":"https://doi.org/10.1109/CAMSAP.2017.8313193","url":null,"abstract":"Simultaneously recorded magnetoencephalography (MEG) and electroencephalography (EEG) signals can benefit from a joint analysis based on coupled Canonical Polyadic (CP) tensor decompositions. The coupled CP decomposition jointly decomposes tensors that have at least one factor matrix in common. The Coupled — Semi-Algebraic framework for approximate CP decomposition via SImultaneous matrix diagonalization framework (C-SECSI) efficiently estimates the factor matrices with adjustable complexity-accuracy trade-offs. Our objective is to decompose simultaneously recorded MEG and EEG signals above intact skull and above two conducting skull defects using C-SECSI in order to determine how such a tissue anomaly of the head is reflected in the tensor rank. The source of the MEG and EEG signals is a miniaturized electric dipole that is implanted into a rabbit's brain. The dipole is shifted along a line under the skull defects, and measurements are taken at regularly spaced points. The coupled SECSI analysis is conducted for MEG and EEG measurement series and ranks 1–3. This coupled decomposition produces meaningful components representing the three characteristic signal topographies for source positions under defect 1 and the positions on either side of defect 1. The rank estimation with respect to the complexity-accuracy trade-off of rank 3 reflects the three characteristic cases well and matches the dimensions spanned by the data set. The intact skull MEG signals show a higher complexity (rank 3) than the corresponding EEG signals (rank 1). The C-SECSI framework is a very promising method for blind signal separation in multidimensional data with coupled modalities, such as simultaneous MEG-EEG.","PeriodicalId":315977,"journal":{"name":"2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123989074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-12-01DOI: 10.1109/CAMSAP.2017.8313082
P. Tichavský, A. Phan, A. Cichocki
Analysis of multidimensional arrays, usually called tensors, often becomes difficult in cases when the tensor rank (a minimum number of rank-one components) exceeds all the tensor dimensions. Traditional methods of canonical polyadic decomposition of such tensors, namely the alternating least squares, can be used, but a presence of a large number of false local minima can make the problem hard. Usually, multiple random initializations are advised in such cases, but the question is how many such random initializations are sufficient to get a good chance of finding the right solution. It appears that the number of the initializations can be very large. We propose a novel approach to the problem. The given tensor is augmented by some unknown parameters to the shape that admits ordinary tensor diagonalization, i.e., transforming the augmented tensor into an exact or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices. Three possible constraints are proposed to make the optimization problem well defined. The method can be modified for an under-determined block-term decomposition.
{"title":"Under-Determined tensor diagonalization for decomposition of difficult tensors","authors":"P. Tichavský, A. Phan, A. Cichocki","doi":"10.1109/CAMSAP.2017.8313082","DOIUrl":"https://doi.org/10.1109/CAMSAP.2017.8313082","url":null,"abstract":"Analysis of multidimensional arrays, usually called tensors, often becomes difficult in cases when the tensor rank (a minimum number of rank-one components) exceeds all the tensor dimensions. Traditional methods of canonical polyadic decomposition of such tensors, namely the alternating least squares, can be used, but a presence of a large number of false local minima can make the problem hard. Usually, multiple random initializations are advised in such cases, but the question is how many such random initializations are sufficient to get a good chance of finding the right solution. It appears that the number of the initializations can be very large. We propose a novel approach to the problem. The given tensor is augmented by some unknown parameters to the shape that admits ordinary tensor diagonalization, i.e., transforming the augmented tensor into an exact or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices. Three possible constraints are proposed to make the optimization problem well defined. The method can be modified for an under-determined block-term decomposition.","PeriodicalId":315977,"journal":{"name":"2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126192850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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