Modified sparse regularization for electrical impedance tomography.

Electrical impedance tomography (EIT) aims to estimate the electrical properties at the interior of an object from current-voltage measurements on its boundary. It has been widely investigated due to its advantages of low cost, non-radiation, non-invasiveness, and high speed. Image reconstruction of EIT is a nonlinear and ill-posed inverse problem. Therefore, regularization techniques like Tikhonov regularization are used to solve the inverse problem. A sparse regularization based on L1 norm exhibits superiority in preserving boundary information at sharp changes or discontinuous areas in the image. However, the limitation of sparse regularization lies in the time consumption for solving the problem. In order to further improve the calculation speed of sparse regularization, a modified method based on separable approximation algorithm is proposed by using adaptive step-size and preconditioning technique. Both simulation and experimental results show the effectiveness of the proposed method in improving the image quality and real-time performance in the presence of different noise intensities and conductivity contrasts.

[1]  Stephen J. Wright,et al.  Sparse Reconstruction by Separable Approximation , 2008, IEEE Transactions on Signal Processing.

[2]  Andrea Borsic,et al.  Regularisation methods for imaging from electrical measurements. , 2002 .

[3]  Lothar Reichel,et al.  Invertible smoothing preconditioners for linear discrete ill-posed problems , 2005 .

[4]  Roger Fletcher,et al.  On the Barzilai-Borwein Method , 2005 .

[5]  David Barber,et al.  An Image Reconstruction Algorithm for 3-D Electrical Impedance Mammography , 2014, IEEE Transactions on Medical Imaging.

[6]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[7]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[8]  Huaxiang Wang,et al.  Image reconstruction based on L1 regularization and projection methods for electrical impedance tomography. , 2012, The Review of scientific instruments.

[9]  Andy Adler,et al.  A primal–dual interior-point framework for using the L1 or L2 norm on the data and regularization terms of inverse problems , 2012 .

[10]  T. Günther,et al.  Constraining 3-D electrical resistance tomography with GPR reflection data for improved aquifer characterization , 2012 .

[11]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[12]  Andy Adler,et al.  In Vivo Impedance Imaging With Total Variation Regularization , 2010, IEEE Transactions on Medical Imaging.

[13]  Michael Elad,et al.  L1-L2 Optimization in Signal and Image Processing , 2010, IEEE Signal Processing Magazine.

[14]  Lihui Peng,et al.  Image reconstruction algorithms for electrical capacitance tomography , 2003 .

[15]  Bin Zhou,et al.  Gradient Methods with Adaptive Step-Sizes , 2006, Comput. Optim. Appl..

[16]  Weifu Fang,et al.  A nonlinear image reconstruction algorithm for electrical capacitance tomography , 2004 .

[17]  E. Somersalo,et al.  Inverse problems with structural prior information , 1999 .

[18]  Te Tang,et al.  Normalization of a spatially variant image reconstruction problem in electrical impedance tomography using system blurring properties , 2009, Physiological measurement.

[19]  José M. Bioucas-Dias,et al.  A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration , 2007, IEEE Transactions on Image Processing.

[20]  A. Adler,et al.  A Primal Dual-Interior Point Framework for Using the L 1-Norm or the L 2-Norm on the Data and Regularization Terms of Inverse Problems , 2009 .

[21]  Lihui Peng,et al.  Window function-based regularization for electrical capacitance tomography image reconstruction , 2007 .

[22]  Wenru Fan,et al.  A preconditioned hybrid reconstruction algorithm for electrical impedance tomography , 2008, International Symposium on Instrumentation and Control Technology.

[23]  Stephen J. Wright,et al.  Sparse reconstruction by separable approximation , 2009, IEEE Trans. Signal Process..

[24]  Bong Seok Kim,et al.  Electrical resistance imaging of two-phase flow using direct Landweber method , 2015 .

[25]  Andy Adler,et al.  An experimental clinical evaluation of EIT imaging with ℓ1 data and image norms , 2013, Physiological measurement.

[26]  Lixin Shen,et al.  A proximity algorithm accelerated by Gauss–Seidel iterations for L1/TV denoising models , 2012 .

[27]  Turgut Durduran,et al.  Compressed sensing in diffuse optical tomography. , 2010, Optics express.

[28]  Wuqiang Yang,et al.  Independent component analysis of interface fluctuation of gas/liquid two-phase flows - experimental study , 2009 .

[29]  Manuchehr Soleimani,et al.  EIT image reconstruction with four dimensional regularization , 2008, Medical & Biological Engineering & Computing.

[30]  Michael A. Saunders,et al.  Proximal Newton-type methods for convex optimization , 2012, NIPS.

[31]  Raul Gonzalez Lima,et al.  Dynamic Imaging in Electrical Impedance Tomography of the Human Chest With Online Transition Matrix Identification , 2010, IEEE Transactions on Biomedical Engineering.

[32]  D. Geselowitz.  An application of electrocardiographic lead theory to impedance plethysmography. , 1971, IEEE transactions on bio-medical engineering.

[33]  Feng Dong,et al.  A fast sparse reconstruction algorithm for electrical tomography , 2014 .

[34]  A. V. Schaik,et al.  L1 regularization method in electrical impedance tomography by using the L1-curve (Pareto frontier curve) , 2012 .