Regularization with Sparse Vector Fields: From Image Compression to TV-type Reconstruction

Conference paper

DOI: 10.1007/978-3-319-18461-6_16

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9087)
Cite this paper as:
Brinkmann EM., Burger M., Grah J. (2015) Regularization with Sparse Vector Fields: From Image Compression to TV-type Reconstruction. In: Aujol JF., Nikolova M., Papadakis N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2015. Lecture Notes in Computer Science, vol 9087. Springer, Cham


This paper introduces a novel variational approach for image compression motivated by recent PDE-based approaches combining edge detection and Laplacian inpainting. The essential feature is to encode the image via a sparse vector field, ideally concentrating on a set of measure zero. An equivalent reformulation of the compression approach leads to a variational model resembling the ROF-model for image denoising, hence we further study the properties of the effective regularization functional introduced by the novel approach and discuss similarities to TV and TGV functionals. Moreover we computationally investigate the behaviour of the model with sparse vector fields for compression in particular for high resolution images and give an outlook towards denoising.


Image compression Denoising Reconstruction Diffusion inpainting Sparsity Total variation 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Eva-Maria Brinkmann
    • 1
  • Martin Burger
    • 1
  • Joana Grah
    • 1
    • 2
  1. 1.Institute for Computational and Applied MathematicsWestfälische Wilhelms-Universität MünsterMünsterGermany
  2. 2.Department of Applied Mathematics and Theoretical PhysicsUniversity of Cambridge, Centre for Mathematical SciencesCambridgeUK

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