TY - JOUR
T1 - Image enhancement and denoising by complex diffusion processes
AU - Gilboa, Guy
AU - Sochen, Nir
AU - Zeevi, Yehoshua Y.
N1 - Funding Information:
This research has been supported in part by the Ollendorf Minerva Center, the Fund for the Promotion of Research at the Technion, Israel Academy of Science, Tel-Aviv University fund, the Adams Center and the Israeli Ministry of Science, the HASSIP Research Network Program HPRN-CT-2002-00285, sponsored by the European Commission and the BME Imaging Group of Columbia University and the ONR-MURI Grant N000M-01-1-0625, administered by Columbia University.
PY - 2004/8
Y1 - 2004/8
N2 - The linear and nonlinear scale spaces, generated by the inherently real-valued diffusion equation, are generalized to complex diffusion processes, by incorporating the free Schrödinger equation. A fundamental solution for the linear case of the complex diffusion equation is developed. Analysis of its behavior shows that the generalized diffusion process combines properties of both forward and inverse diffusion. We prove that the imaginary part is a smoothed second derivative, scaled by time, when the complex diffusion coefficient approaches the real axis. Based on this observation, we develop two examples of nonlinear complex processes, useful in image processing: a regularized shock filter for image enhancement and a ramp preserving denoising process.
AB - The linear and nonlinear scale spaces, generated by the inherently real-valued diffusion equation, are generalized to complex diffusion processes, by incorporating the free Schrödinger equation. A fundamental solution for the linear case of the complex diffusion equation is developed. Analysis of its behavior shows that the generalized diffusion process combines properties of both forward and inverse diffusion. We prove that the imaginary part is a smoothed second derivative, scaled by time, when the complex diffusion coefficient approaches the real axis. Based on this observation, we develop two examples of nonlinear complex processes, useful in image processing: a regularized shock filter for image enhancement and a ramp preserving denoising process.
UR - https://www.scopus.com/pages/publications/3242723371
U2 - 10.1109/TPAMI.2004.47
DO - 10.1109/TPAMI.2004.47
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AN - SCOPUS:3242723371
SN - 0162-8828
VL - 26
SP - 1020
EP - 1036
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
JF - IEEE Transactions on Pattern Analysis and Machine Intelligence
IS - 8
ER -