Source localization by matched-field processing (MFP) generally involves solving a number of computationally intensive partial differential equations. This paper introduces a technique that mitigates this computational workload by "compressing" these computations. Drawing on key concepts from the recently developed field of compressed sensing, it shows how a low-dimensional proxy for the Green's function can be constructed by backpropagating a small set of random receiver vectors. Then the source can be located by performing a number of "short" correlations between this proxy and the projection of the recorded acoustic data in the compressed space. Numerical experiments in a Pekeris ocean waveguide are presented that demonstrate that this compressed version of MFP is as effective as traditional MFP even when the compression is significant. The results are particularly promising in the broadband regime where using as few as two random backpropagations per frequency performs almost as well as the traditional broadband MFP but with the added benefit of generic applicability. That is, the computationally intensive backpropagations may be computed offline independently from the received signals, and may be reused to locate any source within the search grid area.
Localization, estimating the positions and orientations of a set of cameras, is a critical first step in camera-based sensor network applications such as geometric estimation, scene reconstruction, and motion tracking. We propose a new distributed localization algorithm for networks of cameras with sparse overlapping view structure that is energy efficient and copes well with networking dynamics. The distributed nature of the localization computations can result in order-ofmagnitude savings in communication energy over centralized approaches. I. INTRODUCTION Increasingly powerful microprocessors, along with recent advances in micro-sensor technology, wireless communications, and power efficiency, provide new opportunities to sense, compute, and discover via wireless sensor networks. A sensor network consists of a collection of nodes placed or scattered throughout an environment of interest. Each node consists of a power supply, set of sensors, data processor, and a wireless communication system. In this paper, we focus on networks of digital cameras. As CCD and CMOS image/video cameras become smaller, less expensive, and more power efficient, camera networks will become increasingly practical and widespread. Example camera network applications include most of the key tasks from computer vision, including low-dimensional correspondence searches, mosaicking through image rectification, view morphing, image-based navigation, and scene geometry extraction. Due to the high-dimensionality of image and video data, it is paramount in a camera network to distribute as much processing as possible locally within the network. A critical first step in any camera network deployment is localization; the camera nodes must determine their positions and orientations in three-dimensional (3-D) space. Most current sensor network localization techniques use acoustic delays and radio frequency (RF) intensities to create a set of pairwise distances in order to localize [1]. In contrast, little work has been done on distributed algorithms for camera localization via the images acquired at each node. In this paper, we develop the Distributed Alternating Localization-Triangulation algorithm (DALT), an iterative, distributed algorithm for camera network localization. This
We consider the general problem of matching a subspace to a signal in R N that has been observed indirectly (compressed) through a random projection. We are interested in the case where the collection of K-dimensional subspaces is continuously parameterized, i.e. naturally indexed by an interval from the real line, or more generally a region of R D . Our main results show that if the dimension of the random projection is on the order of K times a geometrical constant that describes the complexity of the collection, then the match obtained from the compressed observation is nearly as good as one obtained from a full observation of the signal. We give multiple concrete examples of collections of subspaces for which this geometrical constant can be estimated, and discuss the relevance of the results to the general problems of template matching and source localization.where ∆ is a quantity that captures the geometrical complexity of the collection of subspaces {S θ }.As described in detail in Section 2, it is related to the covering number of {S θ } under the standard metric for subspaces, the operator norm of the difference of projectors d(θ 1 , θ 2 ) = P θ 1 − P θ 2 . In all of our motivating applications, we will have ∆ = small constant + log(K). This means that we can control the approximation gap in (3) by making M slightly larger than K (and potentially significantly smaller than N ). The result (4) holds "with high probability" for an arbitrary (but fixed) h 0 , where the randomness comes from the matrix Φ.As this requires solving a least-squares problem of dimension K, it will only be practical to search over all of Θ when D (the dimension of the θ ∈ Θ) is small (1 or 2). This is indeed the case in the applications we discuss in the next section.
Multipath interference is an ubiquitous phenomenon in modern communication systems. The conventional way to compensate for this effect is to equalize the channel by estimating its impulse response by transmitting a set of training symbols. The primary drawback to this type of approach is that it can be unreliable if the channel is changing rapidly. In this paper, we show that randomly encoding the signal can protect it against channel uncertainty when the channel is sparse. Before transmission, the signal is mapped into a slightly longer codeword using a random matrix. From the received signal, we are able to simultaneously estimate the channel and recover the transmitted signal. We discuss two schemes for the recovery. Both of them exploit the sparsity of the underlying channel. We show that if the channel impulse response is sufficiently sparse, the transmitted signal can be recovered reliably.
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