Research On The Projections Sampling Optimized Algorithm Based On Lattice Theory In Time-Varying Tomograph

The tomographic imaging problem consists of reproducing an image or distribution from a set of its line-integral projections.If this set is large enough in which certain sampling requirements are met,the reproduced image will be of acceptable quality with no significant reconstruction error.For the step of projections sampling during tomographic imaging,the conventional approach is to use a linear angular sampling order,in which a scan consists of projections taken progressively around the object.However,this natural extension of time-invariant tomographic techniques to the time-varying problem requires high and sometimes infeasible scan rates to meet stringent sampling requirements.If these sampling requirements are not met,the resulting reconstruction will suffer from motion artifacts.Hence,this paper focuses on the sampling schedule which can significantly lower the scan rate required to eliminate motion artifacts,while preserving image quality.We consider time-varying images with different temporal variation spatially localized to a circular region.In order to solve the problem of high scan rate in time-varying tomography,we construct a spectral supporting model of samples projections and describe the optimization problem as a B_?-reconstructive TS sampling schedules minimizing,in some sense,the temporal sampling rate.Meanwhile,we discuss the lattice model,sampling requirements and efficiency of the linear sampling in the scene.Based on this model,the simulations results show that the linear sampling is ineffectively in the scene of time-varying tomography.Then,based on spectrum support in the angel-time slice of time-varying field spectrum support,we discuss the polar lattice related to the projection of the frequency spectrum of sampling,the generating lattice and spatial structure lattice related to the sampling period and sampling angels.We put forward the LSB algorithm to turn any base matrix related to lattice into upper and lower triangular matrix,and then the original sampling optimization problem is converted into the tightest packing problem in lattice,which is a purely geometric problem.Based on these theory,the critical packing configurations in different regions based on different time varying parameters is derived.Furthermore,the specific critical packing configurations of subregions are designed to satisfy the densest packing requirements at different time-varying points.Finally,by using the performance evaluation methods,it is proved that by using an optimally scrambled rather than linear angular sampling order,a significant reduction in the scan rate required to eliminate motion artifacts can be obtained.