Research On ERT Image Reconstruction Algorithm Based On Compressed Sensing

Electrical Resistance Tomography(ERT)is a high-tech detection technology that has been booming in recent years to reconstruct the conductivity distribution of the medium in the measured field.It is based on the conductance(resistance)sensing mechanism,and has the characteristics of simple structure,rapid response,and relatively low cost.At present,through the unremitting efforts of relevant experts,scholars and research institutions,ERT imaging technology is gradually mature and has been widely used in many fields such as industry and medicine.However,problems such as ERT soft field characteristics have not been fundamentally solved or improved,and the imaging effect is often not ideal.Therefore,it is of great significance to continue to carry out in-depth research on the ERT image reconstruction algorithm.By reading relevant literature at home and abroad,and referring to ERT imaging application cases in the industrial and medical fields,this paper studies and designs the optimal algorithm for the structural parameters of the resistance sensor to indirectly improve the effect of the soft field characteristics of the sensitivity field on image reconstruction;At the same time,in accordance with the ERT image reconstruction theory,combined with the research ideas of dictionary learning and Bayesian prior theory,an image reconstruction algorithm based on improved compressed sensing is proposed.This article discusses through the following aspects:1.In view of the nonlinear problem of the sensitivity field of the ERT system,the Nelder-Mead simplex method is selected to optimize the structural parameters of the resistance sensor,and the penalty function is set to limit the optimization iteration results,and the optimal structural parameters are selected based on the penalty function.solution.Through COMSOL 5.5 software simulation modeling and the condition number and eigenvalue spectrum parameter evaluation of the sensitivity field,the optimized plate and the non-optimized plate were respectively constructed and compared with the sensitivity field.The experiment showed that the optimized plate position The condition number of the constructed sensitivity field matrix is significantly discreased,and the eigenvalue spectrum image is more stable and smooth,which verifies that the plate optimization scheme using the Nelder-Mead simplex method has a certain improvement in the soft field characteristics of the sensitivity matrix.2.The compressed sensing algorithm is a relatively mature algorithm,and the similarity between the compressed sensing algorithm based on dictionary learning and the inverse problem of the ERT system,the combination of the two is applied to the ERT system to improve the ERT imaging accuracy.On the basis of compressed sensing theory,the linear back-projection method is used to obtain the conductivity matrix as the initial signal,the dictionary learning method is selected to construct the orthogonal sparse base,the sparse coefficient is decomposed as the signal feature,and the normalized sensitivity field matrix is processed randomly and complemented by rows.With zero continuation as the observation matrix,it further explores the method of constructing a comprehensive model of dictionary learning through the improved SGK algorithm to solve the correlation coefficients,so that the under-deterministic problem of ERT can be solved through dictionary learning to solve the l0-norm problem,and relying on CVM The tool solves the NP-Hard problem of the compressed sensing problem very well,and finally solves the conductivity matrix information of the field medium.This paper selects different reconstruction algorithms to perform simulation experiments,introduces errors and correlation coefficients to compare the reconstructed images,and verifies that compared with other algorithms,this algorithm can effectively reduce errors and increase the correlation coefficient,which proves the feasibility of this algorithm.3.Because there is a problem of signal noise that cannot be ignored in the actual application of ERT,add additive noise interference based on the previous article,and add different percentages of noise to simulate the effect of noise in different detection environments on the signal in actual situations.On the basis of compressed sensing theory,an ERT image reconstruction algorithm based on Bayesian theory and dictionary learning is proposed.Introduce the Bayesian prior model and combine it with the ERT system to generate the SGK dictionary based on the block representation of the intermediate image,construct the Bayesian prior distribution suitable for the ERT system,and combine the prior information with the detection voltage value to construct the structure.Through the alternating iterative model,the sparse coefficient is gradually reduced and the iterative noise is updated,and then the conductivity matrix information is reconstructed to restore the image.Finally,through the comparison of signal-to-noise ratio and structural similarity,quantitative analysis from the data verifies the denoising effect of Bayesian theory;by comparing the error and correlation coefficient of the reconstructed image effect,it verifies that the dictionary is improved by Bayesian theory.The effectiveness and feasibility of learning algorithms.