Shriram Sarvotham

A new compressive imaging camera architecture using optical-domain compression

Compressive Sensing is an emerging field based on the revelation that a small number of linear projections of a compressible signal contain enough information for reconstruction and processing. It has many promising implications and enables the design of new kinds of Compressive Imaging systems and cameras. In this paper, we develop a new camera architecture that 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 sampling the image fewer times than the number of pixels. Other attractive properties include its universality, robustness, scalability, progressivity, and computational asymmetry. The most intriguing feature of the system is that, since it relies on a single photon detector, it can be adapted to image at wavelengths that are currently impossible with conventional CCD and CMOS imagers.

Distributed Compressed Sensing of Jointly Sparse Signals

Compressed sensing is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for recon- struction. In this paper we expand our theory for distributed compressed sensing (DCS) that enables new distributed cod- ing algorithms for multi-signal ensembles that exploit both intra- and inter-signal correlation structures. The DCS the- ory rests on a new concept that we term the joint sparsity of a signal ensemble. We present a second new model for jointly sparse signals that allows for joint recovery of multi- ple signals from incoherent projections through simultane- ous greedy pursuit algorithms. We also characterize theo- retically and empirically the number of measurements per sensor required for accurate reconstruction.

Bayesian Compressive Sensing Via Belief Propagation

Compressive sensing (CS) is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable, sub-Nyquist signal acquisition. When a statistical characterization of the signal is available, Bayesian inference can complement conventional CS methods based on linear programming or greedy algorithms. We perform asymptotically optimal Bayesian inference using belief propagation (BP) decoding, which represents the CS encoding matrix as a graphical model. Fast computation is obtained by reducing the size of the graphical model with sparse encoding matrices. To decode a length-N signal containing K large coefficients, our CS-BP decoding algorithm uses O(K log(N)) measurements and O(N log2(N)) computation. Finally, although we focus on a two-state mixture Gaussian model, CS-BP is easily adapted to other signal models.

An Architecture for Compressive Imaging

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.

Connection-level analysis and modeling of network traffic

Most network traffic analysis and modeling studies lump all connections together into a single flow. Such aggregate traffic typically exhibits long-range-dependent (LRD) correlations and non-Gaussian marginal distributions. Importantly, in a typical aggregate traffic model, traffic bursts arise from many connections being active simultaneously. In this paper, we develop a new framework for analyzing and modeling network traffic that moves beyond aggregation by incorporating connection-level information. A careful study of many traffic traces acquired in different networking situations reveals (in opposition to the aggregate modeling ideal) that traffic bursts typically arise from just a few high-volume connections that dominate all others. We term such dominating connections alpha traffic. Alpha traffic is caused by large file transmissions over high bandwidth links and is extremely bursty (non-Gaussian). Stripping the alpha traffic from an aggregate trace leaves a beta traffic residual that is Gaussian, LRD, and shares the same fractal scaling exponent as the aggregate traffic. Beta traffic is caused by both small and large file transmissions over low bandwidth links. In our alpha/beta traffic model, the heterogeneity of the network resources give rise to burstiness and heavy-tailed connection durations give rise to LRD. Queuing experiments suggest that the alpha component dictates the tail queue behavior for large queue sizes, whereas the beta component controls the tail queue behavior for small queue sizes.

Sudocodes ߝ Fast Measurement and Reconstruction of Sparse Signals

Sudocodes are a new scheme for lossless compressive sampling and reconstruction of sparse signals. Consider a sparse signal x isin RopfN containing 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

Measurement Bounds for Sparse Signal Ensembles via Graphical Models

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.

DNA Array Decoding from Nonlinear Measurements by Belief Propagation

We propose a signal recovery method using Belief Propagation (BP) for nonlinear Compressed Sensing (CS) and demonstrate its utility in DNA array decoding. In a CS DNA microarray, the array spots identify DNA sequences that are shared between multiple organisms, thereby reducing the number of spots required. The sparsity in DNA sequence commonality between different organisms translates to conditions that render Belief Propagation (BP) efficient for signal reconstruction. However, an excessively high concentration of target DNA molecules has a nonlinear effect on the measurements ¿ it causes saturation in the measurement intensities at the array spots. We use a modified BP to estimate the target signal coefficients since it is flexible to handle the nonlinearity unlike l1 decoding or other greedy algorithms and show that the original signal coefficients can be recovered from saturated measurements of their linear combinations.

Network and user driven alpha-beta on-off source model for network traffic

We shed light on the effect of network resources and user behavior on network traffic through a physically motivated model. The classical on-off model successfully captures the long-range, second-order correlations of traffic, allowing us to conclude that transport protocol mechanisms have little influence at time scales beyond the round trip time. However, the on-off model fails to capture the short-range spikiness of traffic, where protocols and congestion control mechanisms have greater influence. Based on observations at the connection-level we conclude that small rate sessions can be characterized by independent duration and rate, while large rate sessions have independent file size and rate. In other words, user patience is the limiting factor of small bandwidth connections, while users with large bandwidth freely choose their files. We incorporate these insights into an improved two-component on-off model--which we call the alpha-beta on-off model-comprising an aggressive alpha component (high rate, large transfer) and passive beta component (residual). We analyze the performance of our alpha-beta on-off model and use it to better understand the causes of burstiness and long-range dependence in network traffic. Our analysis yields new insights on Internet traffic dynamics, the effectiveness of congestion control, the performance of potential future network architectures, and the key parameters required for realistic traffic synthesis.

A multiscale data representation for distributed sensor networks

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.