【摘要】 将最小二乘准则与平滑准则相结合,提出了一个关于SIRT型CT代数重建模型的实用的最优准则,根据这一准则推导出相应的代数重建方程·分别应用预优共轭梯度算法和另一种新兴的迭代格式SOR like算法对该方程进行求解·在理论上证明了:对任意的迭代初值,预优共轭梯度法的收敛速度至少不低于广义SOR或SOR like算法·在数值实验中,验证了预优共轭梯度算法比SOR like算法具有更好的CT重建效果和消噪能力·由此导出的预优共轭梯度重建算法提高了CT代数重建的效率·更多还原

【Abstract】 ?A practical optimal criterion for SIRT model of CT reconstruction was proposed by combining least square criterion and smooth criterion into one. Based on this criterion, an algebraic reconstruction equation was derived. The equation was solved by use of the preconditioned conjugate gradient (PCG) and SOR-like algorithms separately. It was proved theoretically that the convergence rate of PCG is at least not slower than generalized SOR or SOR-like algorithm for any initial value of iteration. The numerial experiment showed that PCG algorithm is better than SOR-like in CT reconstruction and noise removal. The PCG algorithm derived is thus confirmed preferable to improve the efficiency of CT algebraic reconstruction.更多还原