TY - JOUR

T1 - Adaptive compressed image sensing using dictionaries

AU - Averbuch, Amir

AU - Dekel, Shai

AU - Deutsch, Shay

PY - 2012

Y1 - 2012

N2 - 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 sensing 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 advantages 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.

AB - 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 sensing 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 advantages 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.

KW - Adaptive approximation

KW - Compressed sensing

KW - Nonlinear approximation

KW - Wavelet trees

UR - http://www.scopus.com/inward/record.url?scp=84856699425&partnerID=8YFLogxK

U2 - 10.1137/110820579

DO - 10.1137/110820579

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AN - SCOPUS:84856699425

SN - 1936-4954

VL - 5

SP - 57

EP - 89

JO - SIAM Journal on Imaging Sciences

JF - SIAM Journal on Imaging Sciences

IS - 1

ER -