Solving Inverse Problems With Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

@article{Yu2010SolvingIP,
  title={Solving Inverse Problems With Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity},
  author={Guoshen Yu and Guillermo Sapiro and St{\'e}phane Mallat},
  journal={IEEE Transactions on Image Processing},
  year={2010},
  volume={21},
  pages={2481-2499}
}
A general framework for solving image inverse problems with piecewise linear estimations is introduced in this paper. The approach is based on Gaussian mixture models, which are estimated via a maximum a posteriori expectation-maximization algorithm. A dual mathematical interpretation of the proposed framework with a structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared with traditional sparse inverse problem… CONTINUE READING

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