Title :
Generation of anisotropic-smoothness regularization filters for EIT
Author :
Borsic, Andrea ; Lionheart, William R B ; McLeod, Christopher N.
Author_Institution :
Sch. of Eng., Oxford Brookes Univ., UK
fDate :
6/1/2002 12:00:00 AM
Abstract :
In the inverse conductivity problem, as in any ill-posed inverse problem, regularization techniques are necessary in order to stabilize inversion. A common way to implement regularization in electrical impedance tomography is to use Tikhonov regularization. The inverse problem is formulated as a minimization of two terms: the mismatch of the measurements against the model, and the regularization functional. Most commonly, differential operators are used as regularization functionals, leading to smooth solutions. Whenever the imaged region presents discontinuities in the conductivity distribution, such as interorgan boundaries, the smoothness prior is not consistent with the actual situation. In these cases, the reconstruction is enhanced by relaxing the smoothness constraints in the direction normal to the discontinuity. In this paper, we derive a method for generating Gaussian anisotropic regularization filters. The filters are generated on the basis of the prior structural information, allowing a better reconstruction of conductivity profiles matching these priors. When incorporating prior information into a reconstruction algorithm, the risk is of biasing the inverse solutions toward the assumed distributions. Simulations show that, with a careful selection of the regularization parameters, the reconstruction algorithm is still able to detect conductivities patterns that violate the prior information. A generalized singular-value decomposition analysis of the effects of the anisotropic filters on regularization is presented in the last sections of the paper.
Keywords :
electric impedance imaging; image reconstruction; inverse problems; medical image processing; minimisation; singular value decomposition; smoothing methods; anisotropic filters; anisotropic-smoothness regularization filters generation; conductivity distribution; conductivity profiles reconstruction; interorgan boundaries; measurements-model mismatch; medical diagnostic imaging; reconstruction is enhancement; regularization functionals; regularization parameters; smooth solutions; Anisotropic magnetoresistance; Conductivity; Image reconstruction; Impedance; Information filtering; Information filters; Inverse problems; Matched filters; Reconstruction algorithms; Tomography; Algorithms; Anisotropy; Computer Simulation; Electric Impedance; Finite Element Analysis; Image Enhancement; Models, Biological; Models, Statistical; Normal Distribution; Signal Processing, Computer-Assisted; Stochastic Processes; Tomography;
Journal_Title :
Medical Imaging, IEEE Transactions on
DOI :
10.1109/TMI.2002.800611