| Magneto-acoustic Tomography is a promising medical imaging technology.The technology consists of positive and negative problems.The direct problem is the process of using Lorentz force excited in a static magnetic field to make biological tissue become a spontaneous sound source radiating sound field,and the radiated sound field is detected externally The inverse problem is that the sound source distribution is obtained from the sound field information detected from the outside.Finally,the sound source distribution is transformed into the conductivity distribution and the imaging results are obtained.Compared with the traditional single-field imaging technology,Magneto-acoustic Tomography technology has the advantages of high contrast and high sensitivity without trauma.The Method of Moment(also known as matrix model method)is often used to solve MAT problems.However,this method needs to solve the discrete global integral equations at the same time,then the scale of the complex fullrank matrix formed in the process of solution will increase rapidly,and it is difficult to solve on ordinary computer because of its high demand on memory and computing power,this has become one of the obstacles to the application of this method in Magneto-acoustic Tomography.In this paper,based on the matrix model formed by the Method of Moment in Magneto-acoustic Tomography technology,a large scale problem is solved,based on layer by layer discretization and layer by layer solution,the Boundary Element Method and Wave Superposition Method in near-field acoustic holography are combined respectively in the framework of Magneto-acoustic Tomography acoustics theory,two layer by layer calculation methods are proposed to reduce the size of the sound field distribution in the medium.The Boundary Element Method and the Wave Superposition Method concentrate all known and unknown variables on the boundary,which has the advantage of dimension reduction compared with the Finite Element Method and the Method of Moment which need global discretization and global solution,it is widely used in acoustic radiation,acoustic scattering and near-field acoustic holography.Firstly,a mathematical model for the reconstruction of sound field in Magneto-acoustic Tomography media is established by combining layer by layer calculation and Boundary Element Method,then a Layer by Layer algorithm based on Boundary Element Method is proposed.Secondly,in order to avoid the problem of singular integrals and strong singular integrals in the boundary element integral equation caused by point collocation at the source boundary in Layer by Layer algorithm,this paper combines the Wave Superposition Method without point collocation at the source boundary,a new Layer by Layer algorithm based on Wave Superposition Method is proposed by establishing the corresponding mathematical model and introducing the complex vector radius method to overcome the non-uniqueness problem.In this paper,the theoretical formulas of the above two methods are derived in detail,the calculation flow is described,and the mechanism of reducing the solution scale is analyzed.In order to verify the feasibility of the proposed method in the reconstruction of the sound field in the medium domain and the effectiveness of reducing the calculation scale,numerical simulation is used to compare the computational effect and memory consumption of the proposed method with the classical method of moments.The results show that both of the proposed Layer by Layer algorithms can reconstruct the sound field in the medium domain correctly and effectively,and the solving scale is greatly reduced.In addition,the computational efficiency and stability of the two Layer by Layer algorithms are compared and analyzed.The results show that the Layer by Layer algorithm based on wave superposition method has lower computational difficulty and higher computational efficiency,while the Layer by Layer algorithm based on Boundary Element Method has lower matrix condition number and better solving stability. |
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