Advanced multiscale representations such as wedgelets and curvelets can represent images with edges much more effectively than classical wavelet methods. However, often these representations are considerably more computationally demanding than fast wavelet methods. In this talk I will introduce a new data-adaptive, coarse-to-fine approach to wedgelet based image reconstruction from noisy data. The new method is much less computationally intense than standard wedgelet methods without compromising near-minimax optimality enjoyed by wedgelets for certain interesting classes of images. This improvement is particularly advantageous for large images. I will also discuss coarse-to-fine estimation in more general settings and the strengths and limitations of such methods.
This is joint work with Robert Nowak and Rui Castro.
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