Research On Super-resolution Of Electromagnetic Inverse Scattering Imaging Algorithm

When electromagnetic waves are irradiated onto an object,the object scatters the electromagnetic waves.The inverse electromagnetic scattering problem involves using the scattered data to perform inversion calculations on the unknown object,thereby obtaining information about its size,position,shape,and electromagnetic parameters.Due to significant advantages such as non-contact operation,safety,and lightweight characteristics,electromagnetic inverse scattering shows great potential for applications in medical imaging.However,the current inverse scattering algorithms still face challenges and are not yet fully satisfactory.The main difficulty at present is that the accuracy of the calculation results of inverse scattering algorithms is not high enough;specifically,the resolution does not meet the requirements of practical problems.This is due to the inherent nonlinearity and ill-posedness of the inverse scattering problem.Despite these mathematical challenges,researchers are committed to improving the resolution of inverse scattering algorithms.Although existing electromagnetic inverse scattering imaging algorithms can achieve super-resolution imaging in some cases,the underlying principles are not yet clear.There is even a lack of unified standards for evaluating the resolution of existing algorithms,which hinders the further development of inverse scattering imaging in practical applications.This dissertation focuses on the core scientific issue of resolution in inverse scattering imaging algorithms,with the main work and innovations summarized as follows:Resolution Analysis: This dissertation draws on the resolution calculation methods of Fourier optics and applies them to the electromagnetic inverse scattering problem.By determining the point spread function(PSF)and optical transfer function(OTF)of the inverse scattering problem and combining them with the Sparrow criterion,the resolution of inverse scattering algorithms based on the Born approximation is quantitatively evaluated.The effectiveness of this method is verified through numerical examples.On this basis,the reasons for achieving super-resolution in the electromagnetic inverse scattering problem are attributed to three points: first,the scatterer affects the resolution calculation,and when the scatterer’s size increases,the resolution also improves,achieving super-resolution.Second,the iterative computation in Born iterative methods cannot be regarded as decoupling the multiple scattering effects.The actual reason iterative methods improve resolution is that the high-frequency components of the OTF increase during the iteration process,and due to the anti-aliasing effect,the PSF becomes steeper,thereby improving the resolution calculated under the Sparrow criterion.Third,in the iterative process,using the result of the previous step as the initial value for the next step expands the OTF of the inverse scattering problem,thus obtaining information beyond the Ewald sphere,which enhances the algorithm’s resolution.This analysis explains why inverse scattering algorithms can achieve super-resolution and provides a theoretical basis for further optimizing these algorithms.Working Parameters for Inverse Scattering Problems: This dissertation proposes a calculation method based on resolution analysis for working parameters such as the working frequency of the imaging algorithm and the number of antennas.For the determination of the working frequency,it is divided into upper and lower limits.The upper limit depends on the error between the incident field and the total field,while the lower limit is determined by the minimum resolution required by the problem.As for the number of antennas,it is calculated based on the theory that the antenna measures the scattered field in the spatial frequency domain,combining the target imaging size with the Nyquist sampling theorem.This analysis provides a reasonable basis for judging whether the inverse scattering imaging algorithm can be successfully applied to different problems.Improving Resolution Using Prior Knowledge: This dissertation proposes two methods to improve the resolution of inverse scattering imaging algorithms using prior knowledge.One method is to enhance the resolution of electromagnetic inverse scattering algorithms by integrating radar imaging methods.At an appropriate working frequency,radar imaging and inverse scattering imaging show good compatibility at the hardware level.Although the images generated by radar algorithms do not contain dielectric constant information,their high sensitivity to abnormal regions can be used as prior information in inverse scattering imaging algorithms to improve the latter’s resolution.The second method involves incorporating Kalman filtering to enhance the resolution of dynamic electromagnetic inverse scattering algorithms.Specifically,Kalman filtering is introduced into the dynamic inverse scattering imaging problem.By utilizing the intrinsic relationship between dielectric constants at different times,the accuracy of prior knowledge during the iterative process is improved,thereby enhancing the resolution of the imaging algorithm.Numerical results show that the two hybrid algorithms proposed in this dissertation can effectively improve the resolution of inverse scattering problems.Through this research,this dissertation provides new ideas and methods for improving the resolution of electromagnetic inverse scattering imaging algorithms,which may promote the further development of inverse scattering algorithms in practical applications.