压缩感知理论为低采样率下稀疏性信号的高质量重建提供理论基础和广泛的应用前景,然而现有大部分研究通常假设原始图像是分段光滑的,不适用于纹理丰富的图像。基于多成分分析理论将原始图像分为卡通和纹理两部分,并且利用各成分在不同变换下稀疏的性质,提出一种多成分正则化的断层图像重建模型。采用分裂Bregman方法将多正则项解耦合,分解成最小二乘问题和去噪问题求解,提出该模型的交替迭代算法。对MRI和CT图像进行仿真实验,并同新近的多种算法进行比较。实验结果表明,该模型能够较好地保持图像纹理等中小尺度信息,收敛速度快。

Recently a number of algorithms have been proposed to overcome the data insufficiency for certain compressible signals.Most of the existing methods are appropriate for piecewise smooth objects,but do not behave very well on texture-rich object.In this paper,a new optimization model for tomography reconstruction for texture-rich object is proposed based on morphological components analysis,in which compound regularizations are exploited.Furthermore,an alternating iterative algorithm is presented to solve the relevant optimization problem.We compare its numerical performance with two recent algorithms,which demonstrate that the proposed method is highly efficient especially in preserving texture features.