Multiscale Tikhonov-Total Variation Image Restoration Using Spatially Varying Edge Coherence Exponent

Abstract: 

Edge preserving regularization using partial differential equation (PDE) based schemes are now widely used in image restoration. We propose an adaptive multiscale variable exponent-based anisotropic variational PDE scheme that avoids current limitations such as over smoothing and blockiness artifacts while still retaining and enhancing edge structures across scale. The innovative model automatically balances between Tikhonov and total variation (TV) regularization effects using scene content information by adopting a spatially varying edge coherence exponent term constructed from the eigenvalues of the smoothed structure tensor. The multiscale exponent model considered here leads to a novel denoising method which preserves edges and provides selective denoising without generating artifacts for both additive and multiplicative noise models. Mathematical analysis of the proposed method in variable exponent space demonstrates its robustness, unconditional stability of the scheme supporting large (time evolution) step sizes and that the approach theoretically satisfies the maximum-minimum principle which guarantees that artificial edge regions are not created. Extensive experimental results on synthetic and real biomedical images indicate that the proposed Multiscale Tikhonov-Total Variation (MTTV) and Dynamical MTTV (D-MTTV) schemes perform better than sixteen other denoising algorithms in terms of several metrics including signal-to-noise ratio improvement and structure preservation. Promising extensions to handle multiplicative noise models and multichannel imagery are also provided.

Reference:

V. B. S. Prasath, D. Vorotnikov, R. Pelapur, S. Jose, G. Seetharaman, K. Palaniappan. Multiscale Tikhonov-total variation image restoration using spatially varying edge coherence exponent.  IEEE Transactions on Image Processing, 24(12), 5220-5235, December 2015. doi:10.1109/TIP.2015.2479471

See our related works in general vectorial p(x) map-based diffusion flows were analysis and experiments undertaken in image smoothing, restoration and edge detection:

V. B. S. Prasath, D. Vorotnikov. On time adaptive critical variable exponent vectorial diffusion flows and their applications in image processing I. Analysis. Nonlinear Analysis, 168, pp. 176-197, Mar 2018. doi:10.1016/j.na.2017.11.013. Preliminary version at arXiv, March 2016. doi:10.48550/arXiv.1603.06337. This part explains the theoretical analysis of the diffusion models.

V. B. S. Prasath, D. Vorotnikov. On time adaptive critical variable exponent vectorial diffusion flows and their applications in image processing II. Experiments. In Preparation, 2025. doi:10.48550/arXiv.25xx.abcde This part presents the image processing applications (smoothing, restoration, edge detection) of the VarEx diffusion models.

For Vectorial (= Color, Multispectral & Hyperspectral) image processing projects please visit this page.