Category Archives: denoising

Adaptive regularization of NL-means

The denoising algorithm that has been developed is based on an adaptive regularization of the NL-means [1]. The proposed model is the following:

(1)   \begin{align*} u_{\text{TVNL}} &= \underset{u \in \mathbb{R}^N}{\operatorname{argmin}} \sum_{i \in \Omega} \lambda_i \left(u_i-u^{\text{NL}}_i\right)^2 + \text{TV}(u),\\ \lambda_i &= \gamma \left(\frac{\sigma_{\text{residual}}(i)}{\sigma_{\text{noise}}(i)}\right)^{-1} = \gamma \Big(\sum_j w_{i,j}^2\Big)^{-1/2}. \end{align*}

where u_{\NL} is the solution obtained with the NL-means algorithm, TV refers to the total variation of the image and w_{i,j} is the weight that measures the similarity between the patch of index i and the patch of index j in the NL-means algorithm. The ratio \left(\frac{\sigma_{\text{residual}}(i)}{\sigma_{\text{noise}}(i)}\right)^{-1} reflects the noise variance reduction performed by the NL-means. This formulation allows locally adaptive regularization of the NL-means solution u_{\NL}, thanks to a confidence index \lambda_i that reflects the quality of the denoising performed by the NL-means.

This model can be adapted to the different noise statistics belonging to the exponential family (Gaussian, Poisson, multiplicative…). It can also be adapted to video denoising thanks to the use of 3D patches combined to a spatio-temporal TV regularization.

Matlab implementation of RNL

Results of video denoising with R-NL and comparisons

Related papers:
1. C. Sutour, C.-A. Deledalle et J.-F. Aujol. Adaptive regularization of the NL-means : Application to image and video denoising. IEEE Transactions on image processing, vol. 23(8) : 3506-3521, 2014.

2. C. Sutour, J.-F. Aujol, C.-A. Deledalle et J.-P. Domenger. Adaptive regularization of the NL-means for video denoising. International Conference on Image Processing (ICIP), pages 2704–2708. IEEE, 2014.

3. C. Sutour, J.-F. Aujol et C.-A. Deledalle. TV-NL : Une coopération entre les NL-means et les méthodes variationnelles. Gretsi, 2013.

References

[1] Buades, A., Coll, B., and Morel, J.-M. (2005). A review of image denoising algorithms, with a new one. Multiscale Modeling and Simulation, 4(2): 490–530.

Non-local models

Several imaging systems provide large amount of images with complex degradation models and low signal to noise ratio. Specific adapted restoration methods should be developed. With the computing power currently available, new paradigms emerge, such as the “non-local” one (Buades et al., 2005), with very good performance (see, e.g., Lebrun et al. 2012; Milanfar, 2013). However, extensions of this methods to specific image modality might not be trivial. We focus on extensions of such methods for the restoration of non-conventional image modalities (low-light imagery, coherent imagery, tomography, …): presence of complex degradation models (blur, missing data, non-Gaussian, non-stationary and correlated noise) and requirement of fast computation large volume of data.