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Recent Advances in Biomedical Image Reconstruction

M. Unser

Plenary talk, Second International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP'07), St. Thomas, U.S. Virgin Islands, December 12-14, 2007.



State-of-the art image reconstruction algorithms are typically derived from the optimization of a cost functional that includes a regularization term whose role is to favor solutions with desirable properties. Another important aspect is the discretization of the inverse problem which can be accomplished by projecting the solution on an adequate set of basis functions; e.g., wavelets, splines or radial basis functions. In this presentation, we will discuss three complementary strategies (sparse representation, invariance to coordinate transformations, and physical modeling) for narrowing down the specification of the regularization functional as well as the selection of the basis functions. We will argue that the two latter aspects are intimately related, which justifies the use of “joint” techniques such as wavelet-regularized image reconstruction. We will illustrate our point with a number of concrete examples, starting with the simplest task of image denoising. We will also present new algorithms for the deconvolution of 3D fluorescence micrographs, the reconstruction of vector fields from incomplete pulsed-mode echo Doppler data, the reconstruction of dynamic PET data, and the extraction of neuronal activation profiles in functional magnetic resonance imaging.


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