Image sharpening in the presence of noise is formulated as a non-convex variational problem. The energy functional incorporates a gradient-dependent potential, a convex fidelity criterion and a high order convex regularizing term. The first term attains local minima at zero and some high gradient magnitude, thus forming a triple well-shaped potential (in the one-dimensional case). The energy minimization flow results in sharpening of the dominant edges, while most noisy fluctuations are filtered out.
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Gilboa, G., Sochen, N. & Zeevi, Y.Y. Image Sharpening by Flows Based on Triple Well Potentials. Journal of Mathematical Imaging and Vision 20, 121–131 (2004). https://doi.org/10.1023/B:JMIV.0000011320.81911.38
- image filtering
- image enhancement
- image sharpening
- nonlinear diffusion
- variational image processing