基于ASD-POCS框架的高阶TpV图像重建算法

High Order TpV Image Reconstruction Algorithms Based on ASD-POCS Framework

总变差(TV)最小化模型目前已广泛应用于图像重建领域,其通过最小化一阶图像梯度大小变换的L1范数实现,能在稀疏投影采集下得到精确的重构。然而,TV模型是基于分段平滑的图像的假设提出的,有时会产生阶梯效应。研究发现,高阶总变差(HOTV)模型可以有效压制阶梯效应,提高重建精度。此外,TpV模型使用Lp范数来逼近L0范数,有望进一步提高稀疏重建能力。鉴于此,本文将HOTV模型与TpV模型结合,提出一种新的高阶TpV(HOTpV)重建模型,采用自适应梯度下降-投影到凸集(ASD-POCS)算法进行求解,分别在理想和有噪声条件下对灰度渐变仿真模体以及真实CT图像仿真模体进行稀疏重建实验。实验结果显示,相比于TV、TpV以及HOTV三种重建模型,HOTpV能得到精度最高的图像。

Total variation(TV) minimization model has been widely used in the field of image reconstruction. It can achieve accurate reconstruction under sparse projection acquisition by minimizing L1 norm of first-order image gradient size transformation. However, the TV model is based on the assumption of segmented smooth image, which sometimes leads to staircase effect. Researches show that the high-order Total Variation(HOTV) model can suppress the staircase effect effectively and improve the reconstruction accuracy. In addition, total p-variation(TpV, 0 < p ≤ 1) model uses Lpnorm to approximate L0 norm, which is expected to further improve the sparse reconstruction ability. In view of this, this paper combines HOTV model with TpV model, a new high-order TpV(HOTpV) reconstruction model is proposed, which is solved by adaptive steepest descent-projection onto convex sets(ASD-POCS) algorithm, sparse reconstruction experiments are carried out on grayscale gradual simulation phantom and real CT image simulation phantom under ideal and noisy conditions. The experimental results show that compared with TV, TpV and HOTV, HOTpV can get the highest accuracy image.