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A general framework for solving image inverse problems is introduced in thispaper. The approach is based on Gaussian mixture models, estimated via acomputationally efficient MAP-EM algorithm. A dual mathematical interpretationof the proposed framework with structured sparse estimation is described, whichshows that the resulting piecewise linear estimate stabilizes the estimationwhen compared to traditional sparse inverse problem techniques. Thisinterpretation also suggests an effective dictionary motivated initializationfor the MAP-EM algorithm. We demonstrate that in a number of image inverseproblems, including inpainting, zooming, and deblurring, the same algorithmproduces either equal, often significantly better, or very small margin worseresults than the best published ones, at a lower computational cost.

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