20,312 research outputs found
Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity
A general framework for solving image inverse problems is introduced in this
paper. The approach is based on Gaussian mixture models, estimated via a
computationally efficient MAP-EM algorithm. A dual mathematical interpretation
of the proposed framework with structured sparse estimation is described, which
shows that the resulting piecewise linear estimate stabilizes the estimation
when compared to traditional sparse inverse problem techniques. This
interpretation also suggests an effective dictionary motivated initialization
for the MAP-EM algorithm. We demonstrate that in a number of image inverse
problems, including inpainting, zooming, and deblurring, the same algorithm
produces either equal, often significantly better, or very small margin worse
results than the best published ones, at a lower computational cost.Comment: 30 page
A comparative numerical study of meshing functionals for variational mesh adaptation
We present a comparative numerical study for three functionals used for
variational mesh adaptation. One of them is a generalisation of Winslow's
variable diffusion functional while the others are based on equidistribution
and alignment. These functionals are known to have nice theoretical properties
and work well for most mesh adaptation problems either as a stand-alone
variational method or combined within the moving mesh framework. Their
performance is investigated numerically in terms of equidistribution and
alignment mesh quality measures. Numerical results in 2D and 3D are presented.Comment: Additional example (H1), journal referenc
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