A Non-Linear Reweighted Total Variation Image Reconstruction Algorithm for Electrical Capacitance Tomography

Abstract

A new iterative image reconstruction algorithm for electrical capacitance tomography (ECT) is proposed that is based on iterative soft thresholding of a total variation penalty and adaptive reweighted compressive sensing. This algorithm encourages sharp changes in the ECT image and overcomes the disadvantage of the l1 minimization by equipping the total variation with an adaptive weighting depending on the reconstructed image. Moreover, the non-linear effect is also partially reduced due to the adoption of an updated sensitivity matrix. Simulation results show that the proposed algorithm recovers ECT images more precisely than existing state-of-the-art algorithms and therefore is suitable for the imaging of multiphase systems in industrial or medical applications. Index Terms-Electrical capacitance tomography (ECT), iterative reconstruction, reweighted total variation, non-linear effect.

A machine learning approach for electrical capacitance tomography measurement of gas–solid fluidized beds

“…This can be done by three potential ways in the future. The first way is to replace the Landweber iteration algorithm with more advanced image reconstruction algorithms, such as those based on total variation . The second way is to perform synchronous measurements by ECT with another technique that can obtain key hydrodynamic parameters more accurately.…”

“…The first way is to replace the Landweber iteration algorithm with more advanced image reconstruction algorithms, such as those based on total variation. 5,54 The second way is to perform synchronous measurements by ECT with another technique that can obtain key hydrodynamic parameters more accurately. Some direct techniques (i.e., no image reconstruction is needed) like pressure drop measurements and some process tomographic techniques with higher spatial resolution like electron beam X-ray tomography 55 and magnetic resonance imaging technique 56 can be used.…”

Stochastic Gradient Matching Pursuit Algorithm Based on Sparse Estimation

“…This notion is general enough to address many important sparse models such as group sparsity and low rankness (see studies [31,32] for examples). Then, we can express Equation (9) in the form of…”

“…For a sparse signal recovery problem, the sparse basis Ψ consists of n basic vectors, each of size n in the Euclidean space. This problem can be regarded as a special case of Equation (9) 2 and M = m. The observation vector u is decomposed into the non-overlapping block observation vectors u b i with a size of b. Φ b i ×n denotes the block-matrix of the measurement matrix of size b. According to Equations (8) and (9), the objective function F(x) can be represented as in the following form:…”

“…Among the existing recovery algorithms, two major approaches are the l 1 -norm minimization (or convex optimization) and l 0 -norm minimization (or greedy pursuit) methods. Convex optimization methods approach the signal by changing the non-convex problem into convex ones such as the basis pursuit (BP) [6] algorithm, the gradient projection for sparse reconstruction (GPSR) [7] algorithm, the interior-point method Bergman iteration (BT) [8] and total-variation (TV) [9]. While the convex optimization methods work correctly for all sparse signals and provide theoretical performance guarantees, its high computational complexity may prevent it from encountering practical large-scale recovery problems.…”