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COMPGEOM
2011
ACM

Compressive sensing with local geometric features

9 years 1 months ago
Compressive sensing with local geometric features
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 × N measurement matrix for some m 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 ...
Rishi Gupta, Piotr Indyk, Eric Price, Yaron Rachli
Added 25 Aug 2011
Updated 25 Aug 2011
Type Journal
Year 2011
Where COMPGEOM
Authors Rishi Gupta, Piotr Indyk, Eric Price, Yaron Rachlin
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