This project will address new, statistically based methods for
image restoration and reconstruction. The fundamental approach consists of using
representations of natural images yielding sparse and
near-independent coefficients. This goal will be pursued along two
main lines:

1. Methods relying on a fixed, wavelet-based representation. The
project shall extend existing methods of denoising, and of
deblurring using a known blur operator, to the blind deblurring /
denoising situation. The main approach will consist of taking the
blur operator as an additional unknown in a Bayesian formulation
of the problem.

2. Methods relying on a learned, ICA-based, spatially invariant
representation. The project shall address new image models,
consisting of an i.i.d. source followed by a learned, linear or
nonlinear, spatially invariant filter, and their application to
the blind deblurring problem.

Besides blurred natural images, the project will also address the
reconstruction of other classes of images, namely those formed
through tomographic methods.

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