In compressive sensing, a small collection of linear projections of a sparse signal contains enough information to permit signal recovery. Distributed compressive sensing extends this framework by defining ensemble sparsity models, allowing a correlated ensemble of sparse signals to be jointly recovered from a collection of separately acquired compressive measurements. In this paper, we introduce a framework for modeling sparse signal ensembles that quantifies the intra- and intersignal dependences within and among the signals. This framework is based on a novel bipartite graph representation that links the sparse signal coefficients with the measurements obtained for each signal. Using our framework, we provide fundamental bounds on the number of noiseless measurements that each sensor must collect to ensure that the signals are jointly recoverable.

Compressive sensing is an emerging field based on the rev elation that a small group of non-adaptive linear projections of a compressible signal contains enough information for reconstruction and processing. In this paper, we propose algorithms and hardware to support a new theory of compressive imaging. Our approach is based on a new digital image/video camera that directly acquires random projections of the signal without first collecting the pixels/voxels. Our camera architecture employs a digital micromirror array to perform optical calculations of linear projections of an image onto pseudorandom binary patterns. Its hallmarks include the ability to obtain an image with a single detection element while measuring the image/video fewer times than the number of pixels this can significantly reduce the computation required for video acquisition/encoding. Because our system relies on a single photon detector, it can also be adapted to image at wavelengths that are currently impossible with conventional CCD and CMOS imagers. We are currently testing a proto type design for the camera and include experimental results.

Sudocodes are a new scheme for lossless compressive sampling and reconstruction of sparse signals. Consider a sparse signal x isin RopfNcontaining only K Lt N non-zero values. Sudo-encoding computes the codeword via the linear matrix-vector multiplication y = Phix, with K < M Lt N. We propose a non-adaptive construction of a sparse Phi comprising only the values 0 and 1; hence the computation of y involves only sums of subsets of the elements of x. An accompanying sudodecoding strategy efficiently recovers x given y. Sudocodes require only M = O(Klog(N)) measurements for exact reconstruction with worst-case computational complexity O(Klog(K) log(N)). Sudocodes can be used as erasure codes for real-valued data and have potential applications in peer-to-peer networks and distributed data storage systems. They are also easily extended to signals that are sparse in arbitrary bases

Though several wavelet-based compression solutions for wireless sensor network measurements have been proposed, no such technique has yet appreciated the need to couple a wavelet transform tolerant of irregularly sampled data with the data transport protocol governing communications in the network. As power is at a premium in sensor nodes, such a technique is necessary to reduce costly communication overhead. To this end, we present an irregular wavelet transform capable of adapting to an arbitrary, multiscale network routing hierarchy. Inspired by the Haar wavelet in the regular setting, our wavelet basis forms a tight frame adapted to the structure of the network. We demonstrate results highlighting the approximation capabilities of such a transform and the clear reduction in communication cost when transmitting a compressed snapshot of the network to an outside user.

Compressed sensing is an emerging field based on the revelation that a small group of linear projections of a sparse signal contains enough information for reconstruc- tion. In this paper we introduce a new theory for distributed compressed sensing (DCS) that enables new distributed coding algorithms for multi-signal ensembles that exploit both intra- and inter-signal correlation structures. The DCS theory rests on a new concept that we term the joint sparsity of a signal ensemble. We study three simple models for jointly sparse signals, propose algorithms for joint recov- ery of multiple signals from incoherent projections, and characterize theoretically and empirically the number of measurements per sensor required for accurate re- construction. In some sense DCS is a framework for distributed compression of sources with memory, which has remained a challenging problem in information theory for some time. DCS is immediately applicable to a range of problems in sensor networks and arrays.

Network traffic exhibits drastically different statistics, ranging from nearly Gaussian marginals and Long range dependence at very large time scales to highly non-Gaussian marginals and multi fractal scaling on small scales. This behavior can be explained by forming two components of the traffic according to the speed of connections, one component absorbing most traffic and being mostly Gaussian, the other constituting virtually all the small scale bursts. Towards a better understanding of this phenomenon, we propose a novel tree-based model which is flexible enough to accommodate Gaussian as well as bursty behavior on different scales in a parsimonious way.