, Volume 4, Issue 1, pp 80-92
Date: 11 Apr 2014

Optimal selection of regularization parameter in total variation method for reducing noise in magnetic resonance images of the brain

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In the image processing community total variation (TV) is widely acknowledged as a popular and state-of-the-art technique for noise reduction because of its edge-preserving property. This attractive feature of TV is dependent on optimal selection of regularization parameter. Contributions in literature on TV focus on applications, properties and the different numerical solution methods. Few contributions which address the problem of regularization parameter selection are based on regression methods which pre-exist introduction of TV. They are generic and elegantly formulated, and their operation is in series with TV framework. For these reasons they render TV computationally inefficient and there is significant manual tuning when they are deployed in specific applications.


This paper describes a non-regression approach for selection of regularization parameter. It is based on a new concept, the Variational-Bayesian (VB) cycle. Within the context of VB cycle we derive two important results. First, we confirm the notion held for a long time by researchers, within image processing and computer vision community, that variational and Bayesian techniques are equivalent. Second, the value of regularization parameter is equal to noise variance, and is determined, at no computational cost to TV denoising algorithm, from a mathematical model that describes relationship between Markov random field energy and noise level in magnetic resonance images (MRI) of brain. The second result is similar to one reported in [1] in which the authors, for special choice of regularization operator in different regression methods, derive value of regularization parameter as equal to noise variance.


Our proposal was evaluated on brain MRI images with different acquisition protocols from two clinical trials study management centers. It was based on visual quality, computation time, convergence and optimality.


The result shows that our proposal is suitable in applications where high level of automation is demanded from image processing software.

Data used this article were obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database.
An erratum to this article can be found at http://dx.doi.org/10.1007/s13534-014-0141-3.