For various inverse problems including image denoising or restoration techniques, stochastic modeling for patch characterization has been recently studied. Using a global Gaussian mixture modeling (GMM), Yu etal.  proposed a patch-based Bayesian approach. For the SR problem, Sandeep et al. [3,5] extend the previous modeling, i.e. GMM, for joint HR-LR modeling given the opportunity to compute an optimal estimator based on the conditional expectation. Various works [1, 2, 4] have shown the possibility to consider pdf models which have more flexibility to adapt the shape of data and less sensibility for over-fitting the number of classes than the GMM. Indeed, including Gaussian and Laplacian distributions as special cases, generalized Gaussian mixture modeling (GGMM) are potentially interesting for modeling the statistical properties of various images or features extracted from these images.
In [2, 4], we have proposed different algorithms for estimating GGM parameters. The first goal of this PhD thesis is to extend the previous works to the GGMM case. We intend to capture the HR statistics from the LR image in a more appropriate way by using this richer modeling. The second goal of this PhD thesis is to use GMM and/or GGMM on other representations of the image such as the output of some neural networks.
- Interdisciplinary project involving 3 laboratories from Bordeaux campus (ICMCB, IMB, IMS) in connection with 2 international projects (European network MUMMERING, ANR/DFG project SUPREMATIM (collaboration with Kaiserslautern University)).
- PhD thesis (funded by ANR/DFG project SUPREMATIM). Starting date: September 2019.
- Joint supervision by J-F Aujol, Y Berthoumieu, and D Bernard.
- Strong background in image processing and applied mathematics is required.
Send a detailed CV, a letter stating the reasons of your application.
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