基于Chambolle-Pock算法框架的高阶TV图像重建算法

传统的总变差(TV)最小算法是一种基于压缩感知(CS)的经典迭代重建算法,可以从稀疏数据或含噪数据中高精度地重建图像。然而,TV算法在重建分段常数特征不明显的图像时可能会引入块状伪影,通过研究得出,在图像去噪中使用高阶总变差(HOTV)能有效压制TV模型引入的块状伪影。鉴于此,提出了一种HOTV图像重建模型及其Chambolle-Pock(CP)求解算法。具体来说,以二阶梯度构建二阶TV范数,进而设计了一种数据保真约束的二阶TV最小重建模型,并推导出了相应的CP算法。在理想数据投影和含噪数据投影条件下,分别采用基于波浪背景的Shepp-Logan模体、灰度渐变模体以及真实CT图像模体进行重建实验,并进行定性和定量分析。理想数据投影的重建结果表明,和传统TV算法相比,HOTV算法能有效压制块状伪影并提高重建精度。含噪数据投影的重建结果表明,HOTV算法和TV算法均有良好的抗噪能力,但HOTV算法的保边性能更好且抗噪性更强。在重建分段常数特征不明显而灰度波动特征明显的图像时,HOTV算法是一种比TV算法更优的重建算法。所提HOTV算法可以被推广到各种扫描模式下的CT重建及其他成像模态中。

High order TV image reconstruction algorithm based on Chambolle-Pock algorithm framework

The traditional Total Variation (TV) minimization algorithm is a classical iterative reconstruction algorithm based on Compressed Sensing (CS), and can accurately reconstruct images from sparse and noisy data. However, the block artifacts may be brought by the algorithm during the reconstruction of image having not obvious piecewise constant feature. Researches show that the use of High Order Total Variation (HOTV) in the image denoising can effectively suppress the block artifacts brought by the TV model. Therefore, a HOTV image reconstruction model and its Chambolle-Pock (CP) solving algorithm were proposed. Specifically, the second order TV norm was constructed by using the second order gradient, then a data fidelity constrained second order TV minimization model was designed, and the corresponding CP algorithm was derived. The Shepp-Logan phantom in wave background, grayscale gradual changing phantom and real CT phantom were used to perform the image reconstruction experiments and qualitative and quantitative analysis under ideal data projection and noisy data projection conditions. The reconstruction results of ideal data projection show that compared to the traditional TV algorithm, the HOTV algorithm can effectively suppress the block artifacts and improve the reconstruction accuracy. The reconstruction results of noisy data projection show that both the traditional TV algorithm and the HOTV algorithm have good denoising effect but the HOTV algorithm is able to protect the image edge information better and has higher anti-noise performance. The HOTV algorithm is a better reconstruction algorithm than the TV algorithm in the reconstruction of image having not obvious piecewise constant feature and obvious grayscale fluctuation feature. The proposed HOTV algorithm can be extended to CT reconstruction under different scanning modes and other imaging modalities.