Flexible Multi-layer Sparse Approximations of Matrices and Applications

The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the complexity of applying linear operators in high dimension by approximately factorizing the corresponding matrix into few sparse factors. The approach relies on recent advances in non-convex optimization. It is first explained and analyzed in details and then demonstrated experimentally on various problems including dictionary learning for image denoising, and the approximation of large matrices arising in inverse problems

Fast Approximation of EEG Forward Problem and Application to Tissue Conductivity Estimation

Bioelectric source analysis in the human brain from scalp electroencephalography (EEG) signals is sensitive to the conductivity of the different head tissues. Conductivity values are subject dependent, so non-invasive methods for conductivity estimation are necessary to fine tune the EEG models. To do so, the EEG forward problem solution (so-called lead field matrix) must be computed for a large number of conductivity configurations. Computing one lead field requires a matrix inversion which is computationally intensive for realistic head models. Thus, the required time for computing a large number of lead fields can become impractical. In this work, we propose to approximate the lead field matrix for a set of conductivity configurations, using the exact solution only for a small set of basis points in the conductivity space. Our approach accelerates the computing time, while controlling the approximation error. Our method is tested for brain and skull conductivity estimation , with simulated and measured EEG data, corresponding to evoked somato-sensory potentials. This test demonstrates that the used approximation does not introduce any bias and runs significantly faster than if exact lead field were to be computed.Comment: Copyright (c) 2019 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]

Time-Frequency Mixed-Norm Estimates: Sparse M/EEG imaging with non-stationary source activations

International audienceMagnetoencephalography (MEG) and electroencephalography (EEG) allow functional brain imaging with high temporal resolution. While solving the inverse problem independently at every time point can give an image of the active brain at every millisecond, such a procedure does not capitalize on the temporal dynamics of the signal. Linear inverse methods (Minimum-norm, dSPM, sLORETA, beamformers) typically assume that the signal is stationary: regularization parameter and data covariance are independent of time and the time varying signal-to-noise ratio (SNR). Other recently proposed non-linear inverse solvers promoting focal activations estimate the sources in both space and time while also assuming stationary sources during a time interval. However such an hypothesis only holds for short time intervals. To overcome this limitation, we propose time-frequency mixed-norm estimates (TF-MxNE), which use time-frequency analysis to regularize the ill-posed inverse problem. This method makes use of structured sparse priors defined in the time-frequency domain, offering more accurate estimates by capturing the non-stationary and transient nature of brain signals. State-of-the-art convex optimization procedures based on proximal operators are employed, allowing the derivation of a fast estimation algorithm. The accuracy of the TF-MxNE is compared to recently proposed inverse solvers with help of simulations and by analyzing publicly available MEG datasets

Real-Time MEG Source Localization Using Regional Clustering

With its millisecond temporal resolution, Magnetoencephalography (MEG) is well suited for real-time monitoring of brain activity. Real-time feedback allows the adaption of the experiment to the subject’s reaction and increases time efficiency by shortening acquisition and off-line analysis. Two formidable challenges exist in real-time analysis: the low signal-to-noise ratio (SNR) and the limited time available for computations. Since the low SNR reduces the number of distinguishable sources, we propose an approach which downsizes the source space based on a cortical atlas and allows to discern the sources in the presence of noise. Each cortical region is represented by a small set of dipoles, which is obtained by a clustering algorithm. Using this approach, we adapted dynamic statistical parametric mapping for real-time source localization. In terms of point spread and crosstalk between regions the proposed clustering technique performs better than selecting spatially evenly distributed dipoles. We conducted real-time source localization on MEG data from an auditory experiment. The results demonstrate that the proposed real-time method localizes sources reliably in the superior temporal gyrus. We conclude that real-time source estimation based on MEG is a feasible, useful addition to the standard on-line processing methods, and enables feedback based on neural activity during the measurements.Deutsche Forschungsgemeinschaft (grant Ba 4858/1-1)National Institutes of Health (U.S.) (grants 5R01EB009048 and 2P41EB015896)Universitätsschule Jena (J21)German Academic Exchange Servic