Nonlinear denoising of transient signals with application to event related potentials

We present a new wavelet based method for the denoising of {\it event related potentials} ERPs), employing techniques recently developed for the paradigm of deterministic chaotic systems. The denoising scheme has been constructed to be appropriate for short and transient time sequences using circular state space embedding. Its effectiveness was successfully tested on simulated signals as well as on ERPs recorded from within a human brain. The method enables the study of individual ERPs against strong ongoing brain electrical activity.Comment: 16 pages, Postscript, 6 figures, Physica D in pres

A Distributed Tracking Algorithm for Reconstruction of Graph Signals

The rapid development of signal processing on graphs provides a new perspective for processing large-scale data associated with irregular domains. In many practical applications, it is necessary to handle massive data sets through complex networks, in which most nodes have limited computing power. Designing efficient distributed algorithms is critical for this task. This paper focuses on the distributed reconstruction of a time-varying bandlimited graph signal based on observations sampled at a subset of selected nodes. A distributed least square reconstruction (DLSR) algorithm is proposed to recover the unknown signal iteratively, by allowing neighboring nodes to communicate with one another and make fast updates. DLSR uses a decay scheme to annihilate the out-of-band energy occurring in the reconstruction process, which is inevitably caused by the transmission delay in distributed systems. Proof of convergence and error bounds for DLSR are provided in this paper, suggesting that the algorithm is able to track time-varying graph signals and perfectly reconstruct time-invariant signals. The DLSR algorithm is numerically experimented with synthetic data and real-world sensor network data, which verifies its ability in tracking slowly time-varying graph signals.Comment: 30 pages, 9 figures, 2 tables, journal pape

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

Image fusion techniqes for remote sensing applications

Image fusion refers to the acquisition, processing and synergistic combination of information provided by various sensors or by the same sensor in many measuring contexts. The aim of this survey paper is to describe three typical applications of data fusion in remote sensing. The first study case considers the problem of the Synthetic Aperture Radar (SAR) Interferometry, where a pair of antennas are used to obtain an elevation map of the observed scene; the second one refers to the fusion of multisensor and multitemporal (Landsat Thematic Mapper and SAR) images of the same site acquired at different times, by using neural networks; the third one presents a processor to fuse multifrequency, multipolarization and mutiresolution SAR images, based on wavelet transform and multiscale Kalman filter. Each study case presents also results achieved by the proposed techniques applied to real data

Parameter Estimation from Time-Series Data with Correlated Errors: A Wavelet-Based Method and its Application to Transit Light Curves

We consider the problem of fitting a parametric model to time-series data that are afflicted by correlated noise. The noise is represented by a sum of two stationary Gaussian processes: one that is uncorrelated in time, and another that has a power spectral density varying as $1/f^\gamma$. We present an accurate and fast [O(N)] algorithm for parameter estimation based on computing the likelihood in a wavelet basis. The method is illustrated and tested using simulated time-series photometry of exoplanetary transits, with particular attention to estimating the midtransit time. We compare our method to two other methods that have been used in the literature, the time-averaging method and the residual-permutation method. For noise processes that obey our assumptions, the algorithm presented here gives more accurate results for midtransit times and truer estimates of their uncertainties.Comment: Accepted in ApJ. Illustrative code may be found at http://www.mit.edu/~carterja/code/ . 17 page

An Adaptive Semi-Parametric and Context-Based Approach to Unsupervised Change Detection in Multitemporal Remote-Sensing Images

In this paper, a novel automatic approach to the unsupervised identification of changes in multitemporal remote-sensing images is proposed. This approach, unlike classical ones, is based on the formulation of the unsupervised change-detection problem in terms of the Bayesian decision theory. In this context, an adaptive semi-parametric technique for the unsupervised estimation of the statistical terms associated with the gray levels of changed and unchanged pixels in a difference image is presented. Such a technique exploits the effectivenesses of two theoretically well-founded estimation procedures: the reduced Parzen estimate (RPE) procedure and the expectation-maximization (EM) algorithm. Then, thanks to the resulting estimates and to a Markov Random Field (MRF) approach used to model the spatial-contextual information contained in the multitemporal images considered, a change detection map is generated. The adaptive semi-parametric nature of the proposed technique allows its application to different kinds of remote-sensing images. Experimental results, obtained on two sets of multitemporal remote-sensing images acquired by two different sensors, confirm the validity of the proposed approach