BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

Sparse Stochastic Processes with Application to Biomedical Imaging

M. Unser

Keynote address, International Conference on Image Analysis and Recognition (ICIAR'14), Vilamoura, Portuguese Republic, October 22-24, 2014.

Sparse stochastic processes are defined in terms of a generalized innovation model: they are characterized by a whitening operator that shapes their Fourier spectrum, and a Lévy exponent that controls their intrinsic sparsity. Starting from the characteristic form of these processes, we derive an extended family of Bayesian signal estimators. While our family of MAP estimators includes the traditional methods of Tikhonov and total-variation (TV) regularization as particular cases, it opens the door to a much broader class of potential functions (associated with infinitely divisible priors) that are inherently sparse and typically nonconvex. We apply our framework to the reconstruction of magnetic resonance images and phase-contrast tomograms and to the deconvolution of fluorescence micrographs; we also present simulation examples where the proposed scheme outperforms the more traditional convex optimization techniques (in particular, TV). 

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