Compressive Wave Computation

This paper considers large-scale simulations of wave propagation phenomena. We argue that it is possible to accurately compute a wavefield by decomposing it onto a largely incomplete set of eigenfunctions of the Helmholtz operator, chosen at random, and that this provides a natural way of parallelizing wave simulations for memory-intensive applications. This paper shows that L1-Helmholtz recovery makes sense for wave computation, and identifies a regime in which it is provably effective: the one-dimensional wave equation with coefficients of small bounded variation. Under suitable assumptions we show that the number of eigenfunctions needed to evolve a sparse wavefield defined on N points, accurately with very high probability, is bounded by C log(N) log(log(N)), where C is related to the desired accuracy and can be made to grow at a much slower rate than N when the solution is sparse. The PDE estimates that underlie this result are new to the authors' knowledge and may be of independent mathematical interest; they include an L1 estimate for the wave equation, an estimate of extension of eigenfunctions, and a bound for eigenvalue gaps in Sturm-Liouville problems. Numerical examples are presented in one spatial dimension and show that as few as 10 percents of all eigenfunctions can suffice for accurate results. Finally, we argue that the compressive viewpoint suggests a competitive parallel algorithm for an adjoint-state inversion method in reflection seismology.Comment: 45 pages, 4 figure

Integrated Analysis of EEG and fMRI Using Sparsity of Spatial Maps

International audienceIntegration of electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) is an open problem, which has motivated many researches. The most important challenge in EEG-fMRI integration is the unknown relationship between these two modalities. In this paper, we extract the same features (spatial map of neural activity) from both modality. Therefore, the proposed integration method does not need any assumption about the relationship of EEG and fMRI. We present a source localization method from scalp EEG signal using jointly fMRI analysis results as prior spatial information and source separation for providing temporal courses of sources of interest. The performance of the proposed method is evaluated quantitatively along with multiple sparse priors method and sparse Bayesian learning with the fMRI results as prior information. Localization bias and source distribution index are used to measure the performance of different localization approaches with or without a variety of fMRI-EEG mismatches on simulated realistic data. The method is also applied to experimental data of face perception of 16 subjects. Simulation results show that the proposed method is significantly stable against the noise with low localization bias. Although the existence of an extra region in the fMRI data enlarges localization bias, the proposed method outperforms the other methods. Conversely, a missed region in the fMRI data does not affect the localization bias of the common sources in the EEG-fMRI data. Results on experimental data are congruent with previous studies and produce clusters in the fusiform and occipital face areas (FFA and OFA, respectively). Moreover, it shows high stability in source localization against variations in different subjects

Video modeling via implicit motion representations

Video modeling refers to the development of analytical representations for explaining the intensity distribution in video signals. Based on the analytical representation, we can develop algorithms for accomplishing particular video-related tasks. Therefore video modeling provides us a foundation to bridge video data and related-tasks. Although there are many video models proposed in the past decades, the rise of new applications calls for more efficient and accurate video modeling approaches.;Most existing video modeling approaches are based on explicit motion representations, where motion information is explicitly expressed by correspondence-based representations (i.e., motion velocity or displacement). Although it is conceptually simple, the limitations of those representations and the suboptimum of motion estimation techniques can degrade such video modeling approaches, especially for handling complex motion or non-ideal observation video data. In this thesis, we propose to investigate video modeling without explicit motion representation. Motion information is implicitly embedded into the spatio-temporal dependency among pixels or patches instead of being explicitly described by motion vectors.;Firstly, we propose a parametric model based on a spatio-temporal adaptive localized learning (STALL). We formulate video modeling as a linear regression problem, in which motion information is embedded within the regression coefficients. The coefficients are adaptively learned within a local space-time window based on LMMSE criterion. Incorporating a spatio-temporal resampling and a Bayesian fusion scheme, we can enhance the modeling capability of STALL on more general videos. Under the framework of STALL, we can develop video processing algorithms for a variety of applications by adjusting model parameters (i.e., the size and topology of model support and training window). We apply STALL on three video processing problems. The simulation results show that motion information can be efficiently exploited by our implicit motion representation and the resampling and fusion do help to enhance the modeling capability of STALL.;Secondly, we propose a nonparametric video modeling approach, which is not dependent on explicit motion estimation. Assuming the video sequence is composed of many overlapping space-time patches, we propose to embed motion-related information into the relationships among video patches and develop a generic sparsity-based prior for typical video sequences. First, we extend block matching to more general kNN-based patch clustering, which provides an implicit and distributed representation for motion information. We propose to enforce the sparsity constraint on a higher-dimensional data array signal, which is generated by packing the patches in the similar patch set. Then we solve the inference problem by updating the kNN array and the wanted signal iteratively. Finally, we present a Bayesian fusion approach to fuse multiple-hypothesis inferences. Simulation results in video error concealment, denoising, and deartifacting are reported to demonstrate its modeling capability.;Finally, we summarize the proposed two video modeling approaches. We also point out the perspectives of implicit motion representations in applications ranging from low to high level problems

Neuromorphic Computing with Resistive Switching Devices.

Resistive switches, commonly referred to as resistive memory (RRAM) devices and modeled as memristors, are an emerging nanoscale technology that can revolutionize data storage and computing approaches. Enabled by the advancement of nanoscale semiconductor fabrication and detailed understanding of the physical and chemical processes occurring at the atomic scale, resistive switches offer high speed, low-power, and extremely dense nonvolatile data storage. Further, the analog capabilities of resistive switching devices enables neuromorphic computing approaches which can achieve massively parallel computation with a power and area budget that is orders of magnitude lower than today’s conventional, digital approaches. This dissertation presents the investigation of tungsten oxide based resistive switching devices for use in neuromorphic computing applications. Device structure, fabrication, and integration are described and physical models are developed to describe the behavior of the devices. These models are used to develop array-scale simulations in support of neuromorphic computing approaches. Several signal processing algorithms are adapted for acceleration using arrays of resistive switches. Both simulation and experimental results are reported. Finally, guiding principles and proposals for future work are discussed.PhDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/116743/1/sheridp_1.pd

Algorithms for Neural Prosthetic Applications

abstract: In the last 15 years, there has been a significant increase in the number of motor neural prostheses used for restoring limb function lost due to neurological disorders or accidents. The aim of this technology is to enable patients to control a motor prosthesis using their residual neural pathways (central or peripheral). Recent studies in non-human primates and humans have shown the possibility of controlling a prosthesis for accomplishing varied tasks such as self-feeding, typing, reaching, grasping, and performing fine dexterous movements. A neural decoding system comprises mainly of three components: (i) sensors to record neural signals, (ii) an algorithm to map neural recordings to upper limb kinematics and (iii) a prosthetic arm actuated by control signals generated by the algorithm. Machine learning algorithms that map input neural activity to the output kinematics (like finger trajectory) form the core of the neural decoding system. The choice of the algorithm is thus, mainly imposed by the neural signal of interest and the output parameter being decoded. The various parts of a neural decoding system are neural data, feature extraction, feature selection, and machine learning algorithm. There have been significant advances in the field of neural prosthetic applications. But there are challenges for translating a neural prosthesis from a laboratory setting to a clinical environment. To achieve a fully functional prosthetic device with maximum user compliance and acceptance, these factors need to be addressed and taken into consideration. Three challenges in developing robust neural decoding systems were addressed by exploring neural variability in the peripheral nervous system for dexterous finger movements, feature selection methods based on clinically relevant metrics and a novel method for decoding dexterous finger movements based on ensemble methods.Dissertation/ThesisDoctoral Dissertation Bioengineering 201