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The best algorithm for a computational problem generally depends on the "relevant inputs," a concept that depends on the application domain and often defies formal articulation. While there is a large literature on empirical approaches to selecting the best algorithm for a given application domain, there has been surprisingly little theoretical analysis of… (More)

High triangle density -- the graph property stating that a constant fraction of two-hop paths belong to a triangle -- is a common signature of social networks. This paper studies triangle-dense graphs from a structural perspective. We prove constructively that significant portions of a triangle-dense graph are contained in a disjoint union of dense, radius… (More)

We initiate the study of sparse recovery problems under the Earth-Mover Distance (EMD). Specifically, we design a distribution over m × n matrices A, for m « n, such that for any x, given Ax, we can recover a k-sparse approximation to x under the EMD distance. We also provide an empirical evaluation of the method that show, in some scenarios,… (More)

We propose a framework for compressive sensing of images with local geometric features. Specifically, let x ∈ R<sup>N</sup> be an N-pixel image, where each pixel p has value x<sub>p</sub>. The image is acquired by computing the <i>measurement vector</i> Ax, where A is an m x N measurement matrix for some m l N. The goal is then to design the matrix… (More)

We propose a framework for compressive sensing of images with local distinguishable objects, such as stars, and apply it to solve a problem in celestial navigation. Specifically, let x ∈ R N be an N-pixel image, consisting of a small number of local distinguishable objects plus noise. Our goal is to design an m × N measurement matrix A with m N , such that… (More)

We study the problem of reconstructing a mixture of Markov chains from the trajectories generated by random walks through the state space. Under mild non-degeneracy conditions, we show that we can uniquely reconstruct the underlying chains by only considering trajectories of length three, which represent triples of states. Our algorithm is spectral in… (More)

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract We propose a framework for compressive sensing of images with local geometric features. Specifically, let x ∈ R N be an N-pixel image, where each pixel p has value x p. The image is acquired by computing the measurement vector Ax,… (More)

- Rishi Vijay Gupta, Yaron Rachlin, Christopher J. Torman
- 2011

We propose a framework for compressive sensing of images with local distinguishable objects, such as stars, and apply it to solve a problem in celestial navigation. Specifically, let x E RN be an N-pixel image, consisting of a small number of local distinguishable objects plus noise. Our goal is to design an m x N measurement matrix A with m < N, such that… (More)

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