Chinese remaindering with errors
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Algorithms for facility location problems with outliers
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Beyond Moore's Law: The Interconnect Era
Computing in Science and Engineering
Finding Frequent Items in Data Streams
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
New Sky Pattern Recognition Algorithm
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part I
Compressive Sensing by Random Convolution
SIAM Journal on Imaging Sciences
Sequential sparse matching pursuit
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Lower bounds for sparse recovery
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
IEEE Transactions on Information Theory
Compressive sensing using locality-preserving matrices
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We propose a framework for compressive sensing of images with local geometric features. Specifically, let x ∈ RN be an N-pixel image, where each pixel p has value xp. The image is acquired by computing the measurement vector Ax, where A is an m x N measurement matrix for some m l N. The goal is then to design the matrix A and recovery algorithm which, given Ax, returns an approximation to x. In this paper we investigate this problem for the case where x consists of a small number (k) of "local geometric objects" (e.g., stars in an image of a sky), plus noise. We construct a matrix A and recovery algorithm with the following features: (i) the number of measurements m is O(k logk N), which undercuts currently known schemes that achieve m=O(k log (N/k)) (ii) the matrix A is ultra-sparse, which is important for hardware considerations (iii) the recovery algorithm is fast and runs in time sub-linear in N. We also present a comprehensive study of an application of our algorithm to a problem in satellite navigation.