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Adaptive Regularization in Convex Composite Optimization for Variational Imaging Problems

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Pattern Recognition (GCPR 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10496))

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Abstract

We propose an adaptive regularization scheme in a variational framework where a convex composite energy functional is optimized. We consider a number of imaging problems including segmentation and motion estimation, which are considered as optimal solutions of the energy functionals that mainly consist of data fidelity, regularization and a control parameter for their trade-off. We presents an algorithm to determine the relative weight between data fidelity and regularization based on the residual that measures how well the observation fits the model. Our adaptive regularization scheme is designed to locally control the regularization at each pixel based on the assumption that the diversity of the residual of a given imaging model spatially varies. The energy optimization is presented in the alternating direction method of multipliers (ADMM) framework where the adaptive regularization is iteratively applied along with mathematical analysis of the proposed algorithm. We demonstrate the robustness and effectiveness of our adaptive regularization through experimental results presenting that the qualitative and quantitative evaluation results of each imaging task are superior to the results with a constant regularization scheme. The desired properties, robustness and effectiveness, of the regularization parameter selection in a variational framework for imaging problems are achieved by merely replacing the static regularization parameter with our adaptive one.

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Notes

  1. 1.

    The ground truth boundary is not uniquely provided in the Berkeley dataset and we have chosen the one suited for our bi-partitioning segmentation model.

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Acknowledgement

This work was supported by NRF-2014R1A2A1A11051941 and NRF-2017R1A2B4006023.

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Authors and Affiliations

  1. Computer Science Department, Chung-Ang University, Seoul, Korea

    Byung-Woo Hong & Ja-Keoung Koo

  2. Institute for Computational and Applied Mathematics, University of Münster, Münster, Germany

    Hendrik Dirks & Martin Burger

Authors
  1. Byung-Woo Hong
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  2. Ja-Keoung Koo
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  3. Hendrik Dirks
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  4. Martin Burger
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Correspondence to Byung-Woo Hong .

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Editors and Affiliations

  1. University of Basel, Basel, Switzerland

    Volker Roth

  2. University of Basel, Basel, Switzerland

    Thomas Vetter

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Hong, BW., Koo, JK., Dirks, H., Burger, M. (2017). Adaptive Regularization in Convex Composite Optimization for Variational Imaging Problems. In: Roth, V., Vetter, T. (eds) Pattern Recognition. GCPR 2017. Lecture Notes in Computer Science(), vol 10496. Springer, Cham. https://doi.org/10.1007/978-3-319-66709-6_22

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  • DOI: https://doi.org/10.1007/978-3-319-66709-6_22

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