Research On Image Reconstruction Based On Inversion

Image reconstruction based on inversion is a technique that uses some acquired information to reconstruct internal structure of a specific object,and is widely used in the fields of computed tomography and seismic tomography nowadays.However,in real applications,especially when combined with sensor networks,artificially acquired data is limited.Traditional image reconstruction techniques cannot reconstruct high-quality images in this case.Therefore,how to perform image reconstruction with incomplete projection is a major issue that researchers in related fields have considered in recent years.This paper first elaborates the principles and mathematics involved in the image reconstruction based on inversion,introduces several commonly used classical algorithms,and analyzes their advantages and disadvantages.Based on this,we carried out some research work:(1)Aiming at the artifacts and noise of image reconstruction in finite data sampling,an image reconstruction algorithm based on Bregman iteration and soft thresholding is proposed.Influenced by the Tikhonov regularization method and the idea of total variational optimization,a general variational model considering eight directions is added above the regularization of the traditional L1-norm.When solving the model,the Bregman distance is introduced,then the base tracking method is used to solve the image,and the image is restored.At the same time,an update strategy for regularization parameters based on each reconstruction image is defined.The algorithm not only accelerates the convergence speed of each iteration,but also avoids the staircase effect in the reconstruction and effectively protects the detailed information.The experimental results show that the proposed algorithm can effectively remove the strip artifacts,protect the details of the image and have good noise immunity in image reconstruction,especially when the projection data is little.(2)For LSQR algorithm,in the case of incomplete projection,although the calculation speed is fast,but the reconstruction image quality is not high,the convergence cannot be continued,and artifacts and noise are easily generated.An algorithm combining LSQR and Bregman iteration therefore is proposed.Firstly,the traditional image reconstruction model is improved.Then the Bregman distance is introduced on the basis of LSQR,then the LandB image reconstruction algorithm is proposed.The algorithm can not only rely on the noise reduction characteristics of Bregman iteration itself to process the noise,but also can obtain higher reconstruction quality with fewer iteration steps and effectively avoid the "semi-convergence" problem of LSQR.At the same time,due to the addition of the full variational constraint in the algorithm,the image artifacts and noise are also well suppressed.Comparing with the classical reconstruction algorithms ART and FBP,the algorithm has achieved better reconstruction effect in the absence of noise.Compared with the algorithms proposed in recent years such as BTV and LSQR-STF,this algorithm can be achieved when the projection is more sparse.The results of LandB have good characteristics of restoration performance,detailed preservation and high contrast.(3)As a traditional algorithm,LSQR is widely used in seismic tomography,meanwhile the reconstruction quality is limited by the amount of sensing data,and it is often impossible to complete the reconstruction of the image delineating the distribution of regional geological structure with high quality.This paper analyzes the problem of seismic tomography,combines the common detection methods and sensor placement methods,then applies the LandB reconstruction algorithm to seismic tomography.The experimental results show that the Land B algorithm can be effectively applied to seismic tomography,and the geologic layer structure can be well restored when the amount of perceived data is little.Compared with the LSQR,the image noise suppression and detail presentation are both significant,and has a better performance.