Image Denoising Using the Lyapunov Equation from Non-uniform Samples

  • João M. Sanches
  • Jorge S. Marques
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4141)


This paper addresses two problems: an image denoising problem assuming dense observations and an image reconstruction problem from sparse data. It shows that both problems can be solved by the Sylvester/Lyapunov algebraic equation. The Sylvester/Lyapunov equation has been extensively studied in Control Theory and it can be efficiently solved by well known numeric algorithms. This paper proposes the use of these equations in image processing and describes simple and fast algorithms for image denoising and reconstruction.


Sparse Data Noisy Image Image Denoising Lyapunov Equation Discrete Image 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • João M. Sanches
    • 1
  • Jorge S. Marques
    • 1
  1. 1.Instituto Superior Técnico / Instituto de Sistemas e Robótica 

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