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Proceedings Paper

The smashed filter for compressive classification and target recognition
Author(s): Mark A. Davenport; Marco F. Duarte; Michael B. Wakin; Jason N. Laska; Dharmpal Takhar; Kevin F. Kelly; Richard G. Baraniuk
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Paper Abstract

The theory of compressive sensing (CS) enables the reconstruction of a sparse or compressible image or signal from a small set of linear, non-adaptive (even random) projections. However, in many applications, including object and target recognition, we are ultimately interested in making a decision about an image rather than computing a reconstruction. We propose here a framework for compressive classification that operates directly on the compressive measurements without first reconstructing the image. We dub the resulting dimensionally reduced matched filter the smashed filter. The first part of the theory maps traditional maximum likelihood hypothesis testing into the compressive domain; we find that the number of measurements required for a given classification performance level does not depend on the sparsity or compressibility of the images but only on the noise level. The second part of the theory applies the generalized maximum likelihood method to deal with unknown transformations such as the translation, scale, or viewing angle of a target object. We exploit the fact the set of transformed images forms a low-dimensional, nonlinear manifold in the high-dimensional image space. We find that the number of measurements required for a given classification performance level grows linearly in the dimensionality of the manifold but only logarithmically in the number of pixels/samples and image classes. Using both simulations and measurements from a new single-pixel compressive camera, we demonstrate the effectiveness of the smashed filter for target classification using very few measurements.

Paper Details

Date Published: 28 February 2007
PDF: 12 pages
Proc. SPIE 6498, Computational Imaging V, 64980H (28 February 2007); doi: 10.1117/12.714460
Show Author Affiliations
Mark A. Davenport, Rice Univ. (United States)
Marco F. Duarte, Rice Univ. (United States)
Michael B. Wakin, California Institute of Technology (United States)
Jason N. Laska, Rice Univ. (United States)
Dharmpal Takhar, Rice Univ. (United States)
Kevin F. Kelly, Rice Univ. (United States)
Richard G. Baraniuk, Rice Univ. (United States)

Published in SPIE Proceedings Vol. 6498:
Computational Imaging V
Charles A. Bouman; Eric L. Miller; Ilya Pollak, Editor(s)

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