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Copyright by SIAM. Unauthorized reproduction of this article is prohibited. SIAM J. IMAGING SCIENCES c 2012 Society for Industrial and Applied Mathematics
 

Summary: Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.
SIAM J. IMAGING SCIENCES c 2012 Society for Industrial and Applied Mathematics
Vol. 5, No. 1, pp. 57­89
Adaptive Compressed Image Sensing Using Dictionaries
Amir Averbuch, Shai Dekel, and Shay Deutsch§
Abstract. In recent years, the theory of compressed sensing has emerged as an alternative for the Shannon
sampling theorem, suggesting that compressible signals can be reconstructed from far fewer samples
than required by the Shannon sampling theorem. In fact the theory advocates that nonadaptive,
"random" functionals are in some sense optimal for this task. However, in practice, compressed sens-
ing is very difficult to implement for large data sets, particularly because the recovery algorithms
require significant computational resources. In this work, we present a new alternative method for
simultaneous image acquisition and compression called adaptive compressed sampling. We exploit
wavelet tree structures found in natural images to replace the "universal" acquisition of incoherent
measurements with a direct and fast method for adaptive wavelet tree acquisition. The main ad-
vantages of this direct approach are that no complex recovery algorithm is in fact needed and that
it allows more control over the compressed image quality, in particular, the sharpness of edges. Our
experimental results show, by way of software simulations, that our adaptive algorithms perform
better than existing nonadaptive methods in terms of image quality and speed.
Key words. compressed sensing, adaptive approximation, nonlinear approximation, wavelet trees
AMS subject classifications. 65T60, 65Y10, 68U10

  

Source: Averbuch, Amir - School of Computer Science, Tel Aviv University

 

Collections: Computer Technologies and Information Sciences