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

  • Eva-Maria Brinkmann
  • Martin BurgerEmail author
  • Joana Grah
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9087)


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
    Email author
  • 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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