Sparse Signal Recovery under Poisson Statistics

We are motivated by problems that arise in a number of applications such as Online Marketing and explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random variable whose mean is a sparse linear superposition of known patterns. Unlike many conventional problems observations here are not identically distributed since they are associated with different sensing modalities. We analyze the performance of a Maximum Likelihood (ML) decoder, which for our Poisson setting involves a non-linear optimization but yet is computationally tractable. We derive fundamental sample complexity bounds for sparse recovery when the measurements are contaminated with Poisson noise. In contrast to the least-squares linear regression setting with Gaussian noise, we observe that in addition to sparsity, the scale of the parameters also fundamentally impacts sample complexity. We introduce a novel notion of Restricted Likelihood Perturbation (RLP), to jointly account for scale and sparsity. We derive sample complexity bounds for $\ell_1$ regularized ML estimators in terms of RLP and further specialize these results for deterministic and random sensing matrix designs.Comment: 13 pages, 11 figures, 2 tables, submitted to IEEE Transactions on Signal Processin

SNAP: Stateful Network-Wide Abstractions for Packet Processing

Early programming languages for software-defined networking (SDN) were built on top of the simple match-action paradigm offered by OpenFlow 1.0. However, emerging hardware and software switches offer much more sophisticated support for persistent state in the data plane, without involving a central controller. Nevertheless, managing stateful, distributed systems efficiently and correctly is known to be one of the most challenging programming problems. To simplify this new SDN problem, we introduce SNAP. SNAP offers a simpler "centralized" stateful programming model, by allowing programmers to develop programs on top of one big switch rather than many. These programs may contain reads and writes to global, persistent arrays, and as a result, programmers can implement a broad range of applications, from stateful firewalls to fine-grained traffic monitoring. The SNAP compiler relieves programmers of having to worry about how to distribute, place, and optimize access to these stateful arrays by doing it all for them. More specifically, the compiler discovers read/write dependencies between arrays and translates one-big-switch programs into an efficient internal representation based on a novel variant of binary decision diagrams. This internal representation is used to construct a mixed-integer linear program, which jointly optimizes the placement of state and the routing of traffic across the underlying physical topology. We have implemented a prototype compiler and applied it to about 20 SNAP programs over various topologies to demonstrate our techniques' scalability

Signal Flow Graph Approach to Efficient DST I-IV Algorithms

In this paper, fast and efficient discrete sine transformation (DST) algorithms are presented based on the factorization of sparse, scaled orthogonal, rotation, rotation-reflection, and butterfly matrices. These algorithms are completely recursive and solely based on DST I-IV. The presented algorithms have low arithmetic cost compared to the known fast DST algorithms. Furthermore, the language of signal flow graph representation of digital structures is used to describe these efficient and recursive DST algorithms having $(n-1)$ points signal flow graph for DST-I and $n$ points signal flow graphs for DST II-IV