Abstract
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.
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Sanches, J.M., Marques, J.S. (2006). Image Denoising Using the Lyapunov Equation from Non-uniform Samples. In: Campilho, A., Kamel, M.S. (eds) Image Analysis and Recognition. ICIAR 2006. Lecture Notes in Computer Science, vol 4141. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11867586_33
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DOI: https://doi.org/10.1007/11867586_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44891-4
Online ISBN: 978-3-540-44893-8
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