Tracking online low-rank approximations of higher-order incomplete streaming tensors.

In this paper, we propose two new provable algorithms for tracking online low-rank approximations of high-order streaming tensors with missing data. The first algorithm, dubbed adaptive Tucker decomposition (ATD), minimizes a weighted recursive least-squares cost function to obtain the tensor factors and the core tensor in an efficient way, thanks to an alternating minimization framework and a randomized sketching technique. Under the canonical polyadic (CP) model, the second algorithm, called ACP, is developed as a variant of ATD when the core tensor is imposed to be identity. Both algorithms are low-complexity tensor trackers that have fast convergence and low memory storage requirements. A unified convergence analysis is presented for ATD and ACP to justify their performance. Experiments indicate that the two proposed algorithms are capable of streaming tensor decomposition with competitive performance with respect to estimation accuracy and runtime on both synthetic and real data.

Magnetic-Field-Based Indoor Positioning Using Temporal Convolutional Networks.

Traditional magnetic-field positioning methods collect magnetic-field information from each spatial point to construct a magnetic-field fingerprint database. During the positioning phase, real-time magnetic-field measurements are matched to a magnetic-field map to predict the user's location. However, this approach requires a significant amount of time to traverse the entire magnetic-field fingerprint database and does not effectively leverage the magnetic-field sequence's unique patterns to improve the accuracy and robustness of the positioning system. In recent years, the application of deep learning for the indoor positioning of magnetic fields has grown rapidly, especially by using the magnetic-field sequence as a time series and a trained long short-term memory (LSTM) model to predict the position, directly avoiding the time-consuming matching process. However, the training of LSTM is time-consuming, and the degradation problem occurs as the stack of layers increases. This article proposes a temporal convolutional network (TCN)-based magnetic-field positioning system that extracts magnetic-field sequence features by preprocessing them with coordinate transformation, smoothing filtering, and first-order differencing. The proposed method is seamlessly applicable to heterogeneous smartphones. The trained TCN models are compared with the LSTM and gated recurrent unit (GRU) models, showing the high accuracy and robustness of the proposed algorithm.

Analysis of Magnetic Field Measurements for Indoor Positioning.

Infrastructure-free magnetic fields are ubiquitous and have attracted tremendous interest in magnetic field-based indoor positioning. However, magnetic field-based indoor positioning applications face challenges such as low discernibility, heterogeneous devices, and interference from ferromagnetic materials. This paper first analyzes the statistical characteristics of magnetic field (MF) measurements from heterogeneous smartphones. It demonstrates that, in the absence of disturbances, the MF measurements in indoor environments follow a Gaussian distribution with temporal stability and spatial discernibility. It shows the fluctuations in magnetic field intensity caused by the rotation of a smartphone around the Z-axis. Secondly, it suggests that the RLOWESS method can be used to eliminate magnetic field anomalies, using magnetometer calibration to ensure consistent MF measurements in heterogeneous smartphones. Thirdly, it tests the magnetic field positioning performance of homogeneous and heterogeneous devices using different machine learning methods. Finally, it summarizes the feasibility/limitations of using only MF measurement for indoor positioning.

Estimation error bound for GRAPPA diffusion-weighted MRI.

In recent years, diffusion weight magnetic resonance imaging (DW-MRI) has become one of the most important MRI imaging modalities. The importance of the DW-MRI grew thanks to the combination of parallel magnetic resonance imaging (pMRI) techniques with the echo-planar imaging (EPI), which minimize scan time and lead to reduced distortion, allowing the DW-MRI to become a routine clinical exam. Additionally, this has brought various new parameters that influence image quality and biomarkers used in DW-MRI. This work aims to investigate the effects of these parameters on the estimation quality, by using the Cramér-Rao bound tool, which gives analytical expressions of the lower limit on the estimation error variance of different DW-MRI variables when using the pMRI technique. In particular, these bounds will be used to study and optimize the impact of different factors of generalized autocalibrating partially parallel acquisition (GRAPPA) technique and system parameters on the estimation quality of the desired clinical metrics. Moreover, the obtained results of this study can be exploited and adapted in all human body DW-MRI clinical routines, further improving disease diagnosis, and tractography studies.

Multi-channel EEG epileptic spike detection by a new method of tensor decomposition.

OBJECTIVE: Epilepsy is one of the most common brain disorders. For epilepsy diagnosis or treatment, the neurologist needs to observe epileptic spikes from electroencephalography (EEG) data. Since multi-channel EEG records can be naturally represented by multi-way tensors, it is of interest to see whether tensor decomposition is able to analyze EEG epileptic spikes. APPROACH: In this paper, we first proposed the problem of simultaneous multilinear low-rank approximation of tensors (SMLRAT) and proved that SMLRAT can obtain local optimum solutions by using two well-known tensor decomposition algorithms (HOSVD and Tucker-ALS). Second, we presented a new system for automatic epileptic spike detection based on SMLRAT. MAIN RESULTS: We propose to formulate the problem of feature extraction from a set of EEG segments, represented by tensors, as the SMLRAT problem. Efficient EEG features were obtained, based on estimating the 'eigenspikes' derived from nonnegative GSMLRAT. We compared the proposed tensor analysis method with other common tensor methods in analyzing EEG signal and compared the proposed feature extraction method with the state-of-the-art methods. Experimental results indicated that our proposed method is able to detect epileptic spikes with high accuracy. SIGNIFICANCE: Our method, for the first time, makes a step forward for automatic detection EEG epileptic spikes based on tensor decomposition. The method can provide a practical solution to distinguish epileptic spikes from artifacts in real-life EEG datasets.

A new detection method for EMG activity monitoring.

This paper introduces a new approach for electromyography (EMG) activity monitoring based on an improved version of the adaptive linear energy detector (ALED), a widely used technique in voice activity detection. More precisely, we propose a modified ALED technique (named M-ALED) to improve the method's robustness with respect to noise. To achieve this objective, M-ALED relies on the Teager-Kaiser operator for signal pre-conditioning to increase the SNR and uses the order statistics to gain robustness against the signal's impulsiveness. We propose again to exploit the order statistics for the initial signal baseline estimation to deal with the cases where such information is unavailable. Finally, since M-ALED detects the signal's activity at the frame level, we propose in a second stage to refine this detection (at the sample level) by using a constant false alarm rate (CFAR) approach leading to the fine M-ALED (FM-ALED) solution. The performance of FM-ALED is assessed via real and synthetic EMG signal recordings and the obtained results highlight its effectiveness as compared with the state-of-the-art methods (it reduces the mean error probability by a factor close to 2).

Analytical performance bounds for multi-tensor diffusion-MRI.

PURPOSE: To examine the effects of MR acquisition parameters on brain white matter fiber orientation estimation and parameter of clinical interest in crossing fiber areas based on the Multi-Tensor Model (MTM). MATERIAL AND METHODS: We compute the Cramér-Rao Bound (CRB) for the MTM and the parameter of clinical interest such as the Fractional Anisotropy (FA) and the dominant fiber orientations, assuming that the diffusion MRI data are recorded by a multi-coil, multi-shell acquisition system. Considering the sum-of-squares method for the reconstructed magnitude image, we introduce an approximate closed-form formula for Fisher Information Matrix that has the simplicity and easy interpretation advantages. In addition, we propose to generalize the FA and the mean diffusivity to the multi-tensor model. RESULTS: We show the application of the CRB to reduce the scan time while preserving a good estimation precision. We provide results showing how the increase of the number of acquisition coils compensates the decrease of the number of diffusion gradient directions. We analyze the impact of the b-value and the Signal-to-Noise Ratio (SNR). The analysis shows that the estimation error variance decreases with a quadratic rate with the SNR, and that the optimum b-values are not unique but depend on the target parameter, the context, and eventually the target cost function. CONCLUSION: In this study we highlight the importance of choosing the appropriate acquisition parameters especially when dealing with crossing fiber areas. We also provide a methodology for the optimal tuning of these parameters using the CRB.

A new look to multichannel blind image deconvolution.

The aim of this paper is to propose a new look to MBID, examine some known approaches, and provide a new MC method for restoring blurred and noisy images. First, the direct image restoration problem is briefly revisited. Then a new method based on inverse filtering for perfect image restoration in the noiseless case is proposed. The noisy case is addressed by introducing a regularization term into the objective function in order to avoid noise amplification. Second, the filter identification problem is considered in the MC context. A new robust solution to estimate the degradation matrix filter is then derived and used in conjunction with a total variation approach to restore the original image. Simulation results and performance evaluations using recent image quality metrics are provided to assess the effectiveness of the proposed methods.

Cross Psi(B)-energy operator-based signal detection.

In this paper, two methods for signal detection and time-delay estimation based on the cross Psi(B)-energy operator are proposed. These methods are well suited for mono-component AM-FM signals. The Psi(B) energy operator measures how much one signal is present in another one. The peak of the Psi(B) operator corresponds to the maximum of interaction between the two signals. Compared to the cross-correlation function, the Psi(B) operator includes temporal information and relative changes of the signal which are reflected in its first and second derivatives. The discrete version of the continuous-time form of the Psi(B) operator, which is used in its implementation, is presented. The methods are illustrated on synthetic and real signals and the results compared to those of the matched filter and the cross correlation. The real signals correspond to impulse responses of buried objects obtained by active sonar in iso-speed single path environments.