Research On Vector Field Radon Transform Spectrum Analysis Technology

In this paper,the surface magnetic field tomography method based on amorphous wire is proposed for the first time at home and abroad.For time-varying signals such as eddy current excitation,the time-varying field tomography method is studied in this paper.The research results can be used in many fields such as non-destructive testing,automatic identification and medical testing.There is no research on time-varying field tomography.The final processing results of the existing related technologies are all in the spatial dimension,and this paper extends the time-varying field imaging to the space-time dimension.Therefore,it is necessary to establish corresponding processing guidelines and treatment methods.In this paper,Radon tran sform is used to reconstruct the image.Only the Radon transform is completely sampled,and the Radon transform can be accurately determined.In principle,the iRadon transform can be used to reconstruct the image.Therefore,for space-independent imaging and space-time joint imaging in time-varying fields,it is necessary to study the sampling conditions that can accurately determine the Radon transform,and to clarify the correlation of space-time projection data,which lays a foundation for time-varying field tomography.In this paper,a no-scatter vector field tomography technique based on Radon transform theory is studied.The Radon transform related technology is analyzed,and the principle of vector field image reconstruction is studied.The double straight wire non-scatter vector field tomography based on Radon transform is proposed and simulated by MATLAB.Image reconstruction is better.It provides the possibility to perform time-varying vector field reconstruction based on the Radon transform.For the spatial independent imaging in time-varying field,an optimized two-dimensional Radon transform sampling grid is proposed.Traditionally,the two-dimensional Radon transform is regarded as a univariate parametric function.In this paper,the two-dimensional Radon transform is regarded as a bivariate function.The theoretical derivation of the two-dimensional Radon transform spectrum shape is “finite-length bowtie” and verified by MATLAB simulation.According to the two-dimensional spectral characteristics,the sampling condition that can accurately determine the two-dimensional Radon transform is sampled on a hexagonal sampling grid or a rectangular sampling grid,and the hexagonal sampling grid is more optimized,which lays the foundation for space independent imaging in time-varying fields.For space-time joint imaging in time-varying field,a three-dimensional Radon transform sampling condition is proposed.Based on the two-dimensional Radon transform spectrum,this paper deduces the three-dimensional Radon transform spectrum shape as a “bowtie” expansion.By discretizing the three-dimensional continuous Radon transform,following the continuous theory,the discrete Fourier slice theorem is proposed,and the accurate shape of the three-dimensional Radon transform spectrum is obtained as a three-dimensional “bowtie”,and verified by MATLAB simulation.According to the three-dimensional spectral characteristics,the three-dimensional Radon transform sampling conditions and the correlation of space-time projection data are obtained,and the image can be reconstructed according to the sampling conditions,which lays the foundation for space-time joint image reconstruction in time-varying field.