Comparative Study Of Simulation Of The Back Projection Algorithm With Polar Driven Pattern And The PD-IPM Algorithm Based On Total Variation Regularization

Electrical Impedance Tomography (EIT) is an imaging technique which started in the 1980s and has great practical potential in the medical field. Compared to the conventional imaging approaches, EIT is convenient, harmless, non-invasive and has low cost. It is able to perform real-time dynamic bedside monitoring for a long period of time. Thus EIT is likely to become a clinical monitoring method that is complementary to the traditional medical imaging approaches. The Back Projection Algorithm (BP) is a dynamic EIT algorithm applied to clinical monitoring due to its fast imaging rate and fine noise immunity. However, the inherent defectiveness of the algorithm leads to the fact that the reconstructed image has relatively large artifacts and poor edge preservation of the target, which cannot perfectly meet the requirements of medical image in terms of spatial resolution and sharpness.In order to solve the problem mentioned above, an algorithm with fine ability of edge preservation is discussed in this thesis----the PD-IPM Algorithm (PD-IPM) based on Total Variation Regularization. Currently the algorithm applied in clinical monitoring has better performance than BP but has the inconvenience of adjusting reconstruction parameters, whereas there is no need for BP to do so. For more convenient evaluation of algorithms, this thesis adopts the simplest BP as the contrast. In the first place, BP with polar driven pattern is realized and preliminary evaluation of its edge preservation is carried out. Second, according to the shortages the study of PD-IPM which has fine edge preservation is conducted. Finally, comprehensive evaluation of edge preservation of the two algorithms with quantitative indexes as the standards is made through simulation. The thesis can be generally divided into three parts:(1) Elaboration of basic EIT problemsFirstly the physiological basis, the fundamental principle and process of EIT are introduced. Subsequently the key components of EIT----image reconstruction algorithms are introduced. Finally the mathematic model of EIT as well as the forward problem and the inverse problem is described from the mathematic point of view.(2) Retrospection of BP and introduction of PD-IPMThe retrospection of classical BP starts from its mathematical and physical basis and the back projection process is formulated. Subsequently the improved BP with polar driven pattern is introduced and the key part of the algorithm----the calculation of back projection matrix is given. At last the formula is presented and preliminary evaluation of its edge preservation is made. For the other algorithm, the edge preservation characteristic of total variation regularization and the derivation of PD-IPM algorithm are formulated. Finally the iterative formula of dynamic EIT based on the algorithm is given and iterations as well as the parameters are discussed.(3) Comparative study of simulationComparative study is carried out between the two algorithms on the platform of MATLAB. For the purpose of evaluating the quality of the reconstruction quantificationally, three indexes are introduced, which are: reconstruction quality function D , image structure deviation function SSIM and edge gradient function G . First, one-target and two-target reconstructions without noise are simulated and compared. The results indicate that PD-IPM is sensitive to the selection of regularization parameter. In the cases of both one-target reconstruction (6 imaging positions) and two-target reconstruction (4 imaging positions), the reconstructions of PD-IPM are more clear and have evidently better edge preservation of the target, which are also supported by the indexes. Second, the anti-noise performance of the two algorithms is compared in the case of one-target reconstruction (1 imaging position). The results show that PD-IPM has moderate noise immunity and has better reconstructions than BP with same noise levels. However PD-IPM is more sensitive to noise.Conclusions are made through the comparative study of simulation that PD-IPM has fine edge preservation property and moderate noise immunity, thus it is a relatively better algorithm. It is necessary to carry out further experiments on physical models and humans so that the foundation of future clinical application of the algorithm is laid.