Reconstruction Of Biomedical Images And Sparse Stochastic Modeling

We propose a novel statistical formulation of the image-reconstruction problem from noisy linear measurements. We derive an extended family of MAP estimators based on the theory of continuous-domain sparse stochastic processes. We highlight the crucial roles of the whitening operator and of the Levy exponent of the innovations which controls the sparsity of the model. While our family of 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 also provide an algorithmic scheme-naturally suggested by our framework-that can handle arbitrary potential functions. Further, we consider the reconstruction of simulated MRI data and illustrate that the designed estimators can bring significant improvement in reconstruction performance.

Published in:
2012 9Th Ieee International Symposium On Biomedical Imaging (Isbi), 880-883
Presented at:
9th IEEE International Symposium on Biomedical Imaging (ISBI) - From Nano to Macro, Barcelona, SPAIN, MAY 02-05, 2012
New York, Ieee

 Record created 2013-03-28, last modified 2019-08-12

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