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May  2016, 10(2): 305-325. doi: 10.3934/ipi.2016002

Forward and backward filtering based on backward stochastic differential equations

 1 Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Received  March 2013 Revised  January 2015 Published  May 2016

In this paper we explore the problem of reconstruction of blurred and noisy images. The idea presented here provides a new methodology based on advanced tools of stochastic analysis which can be successfully used to solve the inverse problem. In order to solve this problem we use backward stochastic differential equations. The reconstructed image is characterized by smoothing noisy pixels and at the same time enhancing and sharpening edges. Our experiments show that the new approach gives very good results and compares favourably with deterministic partial differential equation methods.
Citation: Dariusz Borkowski. Forward and backward filtering based on backward stochastic differential equations. Inverse Problems & Imaging, 2016, 10 (2) : 305-325. doi: 10.3934/ipi.2016002
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