An accelerated version of alternating direction method of multipliers for TV minimization in EIT

Abstract

Existing total variation (TV) solvers that have been applied in Electrical Impedance Tomography (EIT) smooth the TV function in order to cope with its nondifferentiability around the origin, and thus imposes some numerical errors on the solution. Furthermore, these solvers require storage of Hessian, and are thus very impractical for large-scale computations, especially 3D EIT. These shortcomings were addressed by TV solvers that are based on first-order optimization methods. However, the application of these solvers to EIT remains scarce. In this manuscript, we proposes an accelerated version of a gradient-based TV solver based on Augmented Lagrangian and alternating direction method of multipliers, referred to as TVAL3, and apply it to EIT. The results demonstrate the superiority of the accelerated algorithm over existing TV solvers in EIT with regard to both accuracy and speed.

A Stacked Autoencoder Neural Network Algorithm for Breast Cancer Diagnosis With Magnetic Detection Electrical Impedance Tomography

“…12 is a comparison of the reconstruction error curves of three algorithms at different SNR levels. The relative error of reconstruction is calculated as shows in (15). where σ Reconstruction represents the reconstruction conductivity vector and σ Actural represents the real conductivity vector.…”

“…13(b), the anomaly couldn't be reconstructed and the background of the image is not uniform. According to (15), the BP algorithm reconstruction error is 246.17%, and the SAE algorithm reconstruction error is 14.56%. It shows the promising application of the SAE algorithm for breast cancer diagnosis with MDEIT.…”

“…The inverse problem of MDEIT is ill-posed. Sensitivity matrix algorithm (SM algorithm) [14] with regularization techniques has been used to solve the conductivity reconstruction in MDEIT such as total variation (TV) methods [15], [16], joint L-1 and TV regularization methods [17] et al Although regularized reconstruction methods have been shown to be effective in dealing with simple imaging tasks, their limited capability may cause difficulties in coping with more complicated imaging targets. Recently, deep learning is widely used in many fields such as fault detection [18]- [20], image processing [21], emotion recognition [22], and so on.…”

A nonlinear weighted anisotropic total variation regularization for electrical impedance tomography

“…TV regularization has the advantage of preserving the inter-medium discontinuities [34] especially for a piecewise constant images and definitely has promising in EIT clinical applications. [35] introduced the TV regularization in EIT, [13] introduce a primal dual interior-point-method for the minimizing process.…”

Total fractional-order variation regularization based image reconstruction method for capacitively coupled electrical resistance tomography

“…However, the edge of an image is not well preserved with this method [16]. Comparatively, total variation regularization tends to search solution of piecewise constant function and is advantageous for edge preservation [17]- [20]. The disadvantage is that blocky effect is yielded when reconstructing images with smooth edge [21].…”