Compressive sensing with local geometric features
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Indyk_Compressive sensing.pdf
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Author(s)
Gupta, Rishi V.
Indyk, Piotr
Price, Eric C.
Rachlin, Yaron
Date Issued
June 2011
Journal
Proceedings of the 27th Annual ACM Symposium on Computational Geometry (SoCG '11)
Publisher
Association for Computing Machinery (ACM)
Citation
Rishi Gupta, Piotr Indyk, Eric Price, and Yaron Rachlin. 2011. Compressive sensing with local geometric features. In Proceedings of the 27th annual ACM symposium on Computational geometry (SoCG '11). ACM, New York, NY, USA, 87-96.
Version
Author's final manuscript
Abstract
We propose a framework for compressive sensing of images with local geometric features. Specifically, let x ∈ R[superscript N] be an N-pixel image, where each pixel p has value x[subscript p]. 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 log[subscript k] 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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1145/1998196.1998211
