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Image reconstruction based on L1 regularization and projection methods for electrical impedance tomography.

Qi Wang¹, Huaxiang Wang, Ronghua Zhang

¹School of Electronics and Information Engineering, Tianjin Polytechnic University, Tianjin 300387, People's Republic of China. wangqitju@hotmail.com

The Review of Scientific Instruments

|November 7, 2012

Summary

Electrical impedance tomography (EIT) image reconstruction is improved using L(1) regularization, which better handles sharp changes than L(2) methods. Combining L(1) with a projection method reduces computation time without sacrificing image quality.

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Area of Science:

Medical Imaging
Computational Science
Applied Mathematics

Background:

Electrical impedance tomography (EIT) reconstructs conductivity distributions from boundary voltage measurements.
EIT image reconstruction is a nonlinear, ill-posed inverse problem.
Standard L(2) regularization smooths sharp features in EIT reconstructions.

Purpose of the Study:

To improve EIT image reconstruction by addressing limitations of L(2) regularization.
To introduce and evaluate L(1) regularization for sharper EIT images.
To reduce the computational cost associated with L(1) regularization.

Main Methods:

Implemented L(1) regularization by using a sum of absolute values instead of sum of squares.
Employed the barrier method to solve the L(1) regularization problem.
Combined L(1) regularization with a projection method to solve the problem in a coarse subspace, reducing computational expense.

Main Results:

L(1) regularization produced sharper EIT images compared to L(2) regularization.
The L(1) method demonstrated improved tolerance to noise in voltage measurements.
The projected L(1) method significantly reduced computational time without compromising image reconstruction quality.

Conclusions:

L(1) regularization offers superior performance for EIT image reconstruction, particularly in preserving sharp conductivity changes.
The projected L(1) method provides an efficient and effective approach for EIT, balancing computational speed and image fidelity.
This technique enhances the practical applicability of EIT in various fields.