Unified Approach to Adaptive Total Variation Regularization (ATV) in Image Processing


we consider adaptive total variation (TV) based regularization models for image processing. Adaptive TV (ATV) based methods try to avoid the staircasing artifacts associated with the traditional regularization based energy minimization models. We review these based on the techniques utilized as well as applications where these ATV models were exploited.

Standard Test Images - Restoration:

Gaussian Noise:

Noisy (15%)


Weighted TV with ae(x)

Weighted TV with ad(x)

Rician Noise:

The following example shows denoising results for XA angiogram - dynamic images of a cerebral angiogram after coil embolization of cerebral arteriovenous malformation. The file angio5to9_noisy shows input slices (5 to 9), angio5to9_gaussiansmoothed_sd5 shows slices obtained with Gaussian smoothing with standard deviation 5, and angio5to9_wTV shows our weighted TV result.

Here are the snap shots of the files (Click on the image to see bigger versions). The MATLAB figure files1 are attached in the last row:

Poisson/Quantum Noise:

The following example shows denoising results for X-ray - image of a hand.



Weighted TV with ah(x)  [1]

Standard Test Images - Decomposition:

Input image


Weighted TV with ad(x) Smooth





[1] V. B. S. Prasath*. Quantum noise removal in X-ray images with adaptive total variation regularization. Informatica, 28(3), 505-515, September 2017. doi:10.15388/Informatica.2017.141

[2] V. B. S. Prasath. Unified approach to adaptive total variation regularization for image processing. In preparation, 2024. Preliminary version at arXiv, doi:10.48550/arXiv.24xx.abcde

Related works:

[3] V. B. S. Prasath, A. singh. A hybrid convex variational model for image restoration. Applied Mathematics and Computation, 215(10), 3655-3664, January 2010. doi:10.1016/j.amc.2009.11.003 

[4] V. B. S. Prasath, A. Singh, Well-posed inhomogeneous nonlinear diffusion scheme for digital image denoising, Journal of Applied Mathematics, article ID 763847, 14 pages, April 2010. doi:10.1155/2010/763847 

[5] V. B. S. Prasath. A Well-posed multiscale regularization scheme for digital image denoising. International Journal of Applied Mathematics and Computer Science, 21(4), 769-777, December 2011. doi:10.2478/v10006-011-0061-7 

[6] V. B. S. prasath, A. Singh. An adaptive anisotropic diffusion scheme for image restoration and selective smoothing. International Journal of Image and Graphics, 12(1), January 2012. doi:10.1142/S0219467812500039 


*Part of this work was done while the author was at the Fields Institute, Toronto, Canada. He thanks the Institute for their great hospitality and support during the Thematic Program on Inverse Problems and Imaging. The author thanks Prof. Arindama Singh (IITM) for the initiation on adaptive regularization methods while he was at IITM (2004-2009), India.

1You need MATLAB (or atleast MCR) to open/view/rotate these figures.

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