Research Of ECG Inverse Problem Based On ADMM Iterative Algorithm

The electrocardiogram is a reflection of the electrical activity of the heart which can be obtained by measuring the body surface potential by the sensor.ECG is one of the most widely used clinical diagnostic tools,it can accurately reflect the patient's heart health,reduce the cost of diagnosis,which is of great significance for heart disease.The main goal of the study of ECG inverse problem is to restore the ECG,by first obtaining the body surface potential through the body surface potential measuring instrument,then obtaining the transfer matrix from the geometrical information of the heart and torso obtained by CT image,and then using the mathematical method to solve the ECG inverse problem Equation,so as to obtain the distribution of epicardial potential and finally diagnose the pathology of the heart.The most difficult part of solving the inverse problem of ECG is ill-posedness and non-uniqueness.In this thesis,we study the inverse problem of ECG based on epicardial potentials,which can overcome the difficulty of non-uniqueness.In order to overcome the ill-posedness,regularization techniques need to be introduced.The usual regularization methods are Tikhonov,TSVD,TTLS and so on.All of these regularization methods are based on the idea of pseudo-inverse,but they still have many errors in the calculation of the true value of epicardial potentials.Therefore,this thesis is devoted to the new algorithms,so that the epicardium potential obtained from the calculation of the body surface potential distribution can be closer to its true value.In order to solve the problem of ECG accurately,this thesis proposed three methods respectively.Firstly,this thesis establish objective function,then use the mathematical idea of the Ridge regression ADMM iterative algorithm to derive its solution,and then use the L-curve method to obtain the regularization parameters.We can find that this algorithm can solve the ECG problem more accurately through the multi-group experiment.In order to make the iterative process more smooth and get more accurate results,this thesis improve the objective function,and slow down the update speed of the iteration process.The experimental results show that the improved method can accurately reconstruct the epicardial potential,which is less error than the other three regularization methods(Tikhonov,TTLS and TSVD).Finally,in order to accelerate the convergence speed of the iterative process and solve the problem of ECG more quickly,some improvements are made to the objective function in this thesis,and the calculation process are also based on ADMM iterative algorithm.Through experimental comparison,we can see that this method can solve the problem of ECG more accurately.In conclusion,the three mathematical models proposed in this thesis and the method of solving the model can solve the problem of ECG more accurately.Therefore,the iterative algorithm based on ADMM has great value in the application of solving the ECG inverse problem.