Dynamic Denoising of Tracking Sequences

©2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/TIP.2008.920795In this paper, we describe an approach to the problem of simultaneously enhancing image sequences and tracking the objects of interest represented by the latter. The enhancement part of the algorithm is based on Bayesian wavelet denoising, which has been chosen due to its exceptional ability to incorporate diverse a priori information into the process of image recovery. In particular, we demonstrate that, in dynamic settings, useful statistical priors can come both from some reasonable assumptions on the properties of the image to be enhanced as well as from the images that have already been observed before the current scene. Using such priors forms the main contribution of the present paper which is the proposal of the dynamic denoising as a tool for simultaneously enhancing and tracking image sequences.Within the proposed framework, the previous observations of a dynamic scene are employed to enhance its present observation. The mechanism that allows the fusion of the information within successive image frames is Bayesian estimation, while transferring the useful information between the images is governed by a Kalman filter that is used for both prediction and estimation of the dynamics of tracked objects. Therefore, in this methodology, the processes of target tracking and image enhancement "collaborate" in an interlacing manner, rather than being applied separately. The dynamic denoising is demonstrated on several examples of SAR imagery. The results demonstrated in this paper indicate a number of advantages of the proposed dynamic denoising over "static" approaches, in which the tracking images are enhanced independently of each other

Learning Linear Dynamical Systems via Spectral Filtering

We present an efficient and practical algorithm for the online prediction of discrete-time linear dynamical systems with a symmetric transition matrix. We circumvent the non-convex optimization problem using improper learning: carefully overparameterize the class of LDSs by a polylogarithmic factor, in exchange for convexity of the loss functions. From this arises a polynomial-time algorithm with a near-optimal regret guarantee, with an analogous sample complexity bound for agnostic learning. Our algorithm is based on a novel filtering technique, which may be of independent interest: we convolve the time series with the eigenvectors of a certain Hankel matrix.Comment: Published as a conference paper at NIPS 201