Sparse Stochastic Processes and Discretization of Linear Inverse Problems

被引:27
作者
Bostan, Emrah [1 ]
Kamilov, Ulugbek S. [1 ]
Nilchian, Masih [1 ]
Unser, Michael [1 ]
机构
[1] Ecole Polytech Fed Lausanne, Biomed Imaging Grp, CH-1015 Lausanne, Switzerland
关键词
Innovation models; maximum a posteriori (MAP) estimation; nonconvex optimization; non-Gaussian statistics; sparse stochastic processes; sparsity-promoting regularization; IMAGE-RECONSTRUCTION; OPTIMIZATION; ALGORITHM; MRI;
D O I
10.1109/TIP.2013.2255305
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
We present a novel statistically-based discretization paradigm and derive a class of maximum a posteriori (MAP) estimators for solving ill-conditioned linear inverse problems. We are guided by the theory of sparse stochastic processes, which specifies continuous-domain signals as solutions of linear stochastic differential equations. Accordingly, we show that the class of admissible priors for the discretized version of the signal is confined to the family of infinitely divisible distributions. Our estimators not only cover the well-studied methods of Tikhonov and l(1)-type regularizations as particular cases, but also open the door to a broader class of sparsity-promoting regularization schemes that are typically nonconvex. We provide an algorithm that handles the corresponding nonconvex problems and illustrate the use of our formalism by applying it to deconvolution, magnetic resonance imaging, and X-ray tomographic reconstruction problems. Finally, we compare the performance of estimators associated with models of increasing sparsity.
引用
收藏
页码:2699 / 2710
页数:12
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