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Hybrid Compressive Sampling via a New Total Variation TVL1

  • Xianbiao Shu
  • Narendra Ahuja
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6316)

Abstract

Compressive sampling (CS) is aimed at acquiring a signal or image from data which is deemed insufficient by Nyquist/Shannon sampling theorem. Its main idea is to recover a signal from limited measurements by exploring the prior knowledge that the signal is sparse or compressible in some domain. In this paper, we propose a CS approach using a new total-variation measure TVL1, or equivalently TV\(_{\ell_1}\), which enforces the sparsity and the directional continuity in the gradient domain. Our TV\(_{\ell_1}\) based CS is characterized by the following attributes. First, by minimizing the ℓ1-norm of partial gradients, it can achieve greater accuracy than the widely-used TV\(_{\ell_1\ell_2}\) based CS. Second, it, named hybrid CS, combines low-resolution sampling (LRS) and random sampling (RS), which is motivated by our induction that these two sampling methods are complementary. Finally, our theoretical and experimental results demonstrate that our hybrid CS using TV\(_{\ell_1}\) yields sharper and more accurate images.

Keywords

Gradient Magnitude Compressive Sampling Hybrid Sampling Diagonal Edge Partial Gradient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Xianbiao Shu
    • 1
  • Narendra Ahuja
    • 1
  1. 1.University of Illinois at Urbana-ChampaignUrbanaUSA

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