Abstract

Image estimation requires a compromise between reconstruction flexibility and computational tractability. A commonly adopted approach to the estimation problem is to decompose the observed image in a suitable basis, where the compression of the decomposition simplifies subsequent analysis. Much effort has been expanded in designing appropriate 2-D decompositions, but of great importance is also the statistical estimation procedure chosen, and this talk will focus on the estimation of any set of decomposition coefficients.

A new estimation method that can be combined with a local decomposition method is introduced. Under the assumption that structured features correspond to highly concentrated and connected regions of the spatial and spatial frequency space additional image replicates with the same local structure as the observed image are constructed from the observed image. The decomposition of the image is estimated not only using the observed image decomposition coefficients, but also using a set of local coefficients constructed from the replicate images. Given the tractable form of the first and second order structure of the full set of decomposition coefficients of both the image and replicate images at any given scale and spatial position, the full procedure can be specified analytically, and its risk calculated explicitly. The proposed method is implemented on several examples, and theoretical risk calculations substantiated, as well as visually appealing reconstructions presented.

The slides of the seminar are available at http://stats.ma.ic.ac.uk/sco/public_html/seminarsIC.htm

This work was part of an EPSRC supported project.