Image Reconstruction Algorithm For Electrical Capacitance Tomography Based On Non-Convex Compressive Sensing

The Electrical Capacitance Tomography?ECT?resolves the field medium distribution by the capacitance between the electrodes and the sensitivity matrix.However,the solution of the inverse problem is ill-conditioned and underdetermined.Traditional algorithms cannot balance imaging accuracy and imaging speed,which limits the practical application of ECT.The theory of compressed sensing breaks through the limitation of the traditional Nyquist sampling theorem.It can restore the original signal accurately with only a small amount of sampled data,which is an effective means to alleviate the ill-posedness.Therefore,the non-convex compression perception?the objective function is a non-convex optimization problem with L₀ norm constraint?is introduced into the ECT imaging process to improve its ill-conditionedness.Firstly,aiming at the weak correlation between sensitivity matrix and sparse basis in ECT system,a new method of observation matrix optimization is proposed.The rows of sensitivity matrix are rearranged based on Gaussian random array,then SVD decomposition is performed,and the correction factor is added.Obtained an observation matrix has higher column independence.At the same time,the corresponding capacitance matrix also performs the same row transformation.Secondly,aiming at the problem that there is pseudo-inverse and no accurate sparse solution in the FOCUSS algorithm,an improved FOCUSS algorithm is proposed.Based on the regularized FOCUSS based on L_P norm,the quasi-Newton method is applied to solve the intermediate sparse variables and obtain a more accurate sparse solution.Finally,for the problem that the penalty term is not smooth at the origin in the half-threshold iterative algorithm based on L_1/2 norm,an iterative algorithm with improved half-threshold is proposed.The L₂ constraint is introduced into the penalty function to improve the original.The smoothness of the original algorithm at the origin is improved.The experimental results show that the optimized observation matrix can better satisfy the RIP property.The two non-convex optimization algorithms proposed in this paper can simultaneously consider the imaging speed and imaging accuracy,and the sparse search ability is stronger.The imaging effect is better than the classical algorithm and based on Partial reconstruction algorithm of compressed sensing theory.This paper provides a new research idea for ECT image reconstruction algorithms.