Identifying almost invariant sets in stochastic dynamical systems

We consider the approximation of fluctuation induced almost invariant sets arising from stochastic dynamical systems. The dynamical evolution of densities is derived from the stochastic Frobenius– Perron operator. Given a stochastic kernel with a known distribution, approximate almost invariant sets are found by translating the problem into an eigenvalue problem derived from reversible Markov processes. Analytic and computational examples of the methods are used to illustrate the technique, and are shown to reveal the probability transport between almost invariant sets in nonlinear stochastic systems. Both small and large noise cases are considered. © 2008 American Institute of Physics

Time-varying parametric modelling and time-dependent spectral characterisation with applications to EEG signals using multi-wavelets

A new time-varying autoregressive (TVAR) modelling approach is proposed for nonstationary signal processing and analysis, with application to EEG data modelling and power spectral estimation. In the new parametric modelling framework, the time-dependent coefficients of the TVAR model are represented using a novel multi-wavelet decomposition scheme. The time-varying modelling problem is then reduced to regression selection and parameter estimation, which can be effectively resolved by using a forward orthogonal regression algorithm. Two examples, one for an artificial signal and another for an EEG signal, are given to show the effectiveness and applicability of the new TVAR modelling method

FaultSSL: Seismic Fault Detection via Semi-supervised learning

The prevailing methodology in data-driven fault detection leverages synthetic data for training neural networks. However, it grapples with challenges when it comes to generalization in surveys exhibiting complex structures. To enhance the generalization of models trained on limited synthetic datasets to a broader range of real-world data, we introduce FaultSSL, a semi-supervised fault detection framework. This method is based on the classical mean teacher structure, with its supervised part employs synthetic data and a few 2D labels. The unsupervised component relying on two meticulously devised proxy tasks, allowing it to incorporate vast unlabeled field data into the training process. The two proxy tasks are PaNning Consistency (PNC) and PaTching Consistency (PTC). PNC emphasizes the feature consistency of the overlapping regions between two adjacent views in predicting the model. This allows for the extension of 2D slice labels to the global seismic volume. PTC emphasizes the spatially consistent nature of faults. It ensures that the predictions for the seismic, whether made on the entire volume or on individual patches, exhibit coherence without any noticeable artifacts at the patch boundaries. While the two proxy tasks serve different objectives, they uniformly contribute to the enhancement of performance. Experiments showcase the exceptional performance of FaultSSL. In surveys where other mainstream methods fail to deliver, we present reliable, continuous, and clear detection results. FaultSSL breaks the shackles of synthetic data, unveiling a promising route for incorporating copious amounts of field data into training and fostering model generalization across a broader spectrum of surveys.Comment: This work has been submitted to journal for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Method and System for Object Recognition Search

A method for object recognition using shape and color features of the object to be recognized. An adaptive architecture is used to recognize and adapt the shape and color features for moving objects to enable object recognition

Analysis of hyper-spectral data derived from an imaging Fourier transform: A statistical perspective

Fourier transform spectrometers (FTS) using optical sensors are increasingly being used in various branches of science. Typically, a FTS generates a three-dimensional data cube with two spatial dimensions and one frequency/wavelength dimension. The number of frequency dimensions in such data cubes is generally very large, often in the hundreds, making data analytical procedures extremely complex. In the present report, the problem is viewed from a statistical perspective. A set of procedures based on the high degree of inter-channel correlation structure often present in such hyper-spectral data, has been identified and applied to an example data set of dimension 100 x 128 x 128 comprising 128 spectral bands. It is shown that in this case, the special eigen-structure of the correlation matrix has allowed the authors to extract just a few linear combinations of the channels (the significant principal vectors) that effectively contain almost all of the spectral information contained in the data set analyzed. This in turn, enables them to segment the objects in the given spatial frame using, in a parsimonious yet highly effective way, most of the information contained in the data set

Digital Signal Processing Research Program

Contains table of contents for Section 2, an introduction and reports on fourteen research projects.U.S. Navy - Office of Naval Research Grant N00014-91-J-1628Defense Advanced Research Projects Agency/U.S. Navy - Office of Naval Research Grant N00014-89-J-1489MIT - Woods Hole Oceanographic Institution Joint ProgramLockheed Sanders, Inc./U.S. Navy Office of Naval Research Contract N00014-91-C-0125U.S. Air Force - Office of Scientific Research Grant AFOSR-91-0034U.S. Navy - Office of Naval Research Grant N00014-91-J-1628AT&T Laboratories Doctoral Support ProgramNational Science Foundation Fellowshi