Compressed sensing shape estimation of star-shaped objects in Fourier imaging

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Recent theory of compressed sensing informs us that near-exact recovery of an unknown sparse signal is possible from a very limited number of Fourier samples by solving a convex L-1 optimization problem. The main contribution of the present letter is a compressed sensing-based novel nonparametric shape estimation framework and a computational algorithm for binary star shape objects, whose radius functions belong to the space of bounded-variation functions. Specifically, in contrast with standard compressed sensing, the present approach involves directly reconstructing the-shape boundary under sparsity constraint. This is done by converting the standard pixel-based reconstruction approach into estimation of a nonparametric shape boundary on a wavelet basis. This results in an L-1 minimization under a nonlinear constraint, which makes the optimization problem nonconvex. We solve the problem by successive linearization and application of one-dimensional L-1 minimization, which significantly reduces the number of sampling requirements as well as the computational burden. Fourier imaging simulation results demonstrate that high quality reconstruction can be quickly obtained from a very limited number of samples. Furthermore, the algorithm outperforms the standard compressed sensing reconstruction approach using the total variation norm.
Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Issue Date
2007-10
Language
English
Article Type
Article
Citation

IEEE SIGNAL PROCESSING LETTERS, v.14, pp.750 - 753

ISSN
1070-9908
DOI
10.1109/LSP.2007.898342
URI
http://hdl.handle.net/10203/91040
Appears in Collection
AI-Journal Papers(저널논문)
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