Solving inverse problems with piecewise linear estimators: from Gaussian mixture models to structured sparsity.

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 techniques. We demonstrate that, in a number of image inverse problems, including interpolation, zooming, and deblurring of narrow kernels, the same simple and computationally efficient algorithm yields results in the same ballpark as that of the state of the art.

Full Text

Duke Authors

Cited Authors

  • Yu, G; Sapiro, G; Mallat, S

Published Date

  • May 2012

Published In

Volume / Issue

  • 21 / 5

Start / End Page

  • 2481 - 2499

PubMed ID

  • 22180506

Electronic International Standard Serial Number (EISSN)

  • 1941-0042

Digital Object Identifier (DOI)

  • 10.1109/TIP.2011.2176743


  • eng