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优化加权TV的复合正则化压缩感知图像重建

DOI: 10.11834/jig.20140206

Keywords: 压缩感知|加权全变差|非局部结构相似|局部自回归

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Abstract:

目的压缩感知理论突破了传统的Shanon-Nyquist采样定理的限制,能够以较少的采样值来进行原信号的恢复。针对压缩感知图像重建问题,提出一种基于优化加权全变差(TV)的复合正则化压缩感知图像重建模型。方法提出的重建模型是以TV正则化模型为基础。首先,为克服传统TV正则化会导致重建图像的边缘和纹理细节部分模糊或丢失的缺点,引入图像的梯度信息估计权重,构建加权TV的重建模型。其次,利用全变差去噪(ROF)模型对权重进行优化估计,从而减少计算权重时受噪声的影响。再次,将非局部结构相似性先验和局部自回归性先验引入提出的加权TV模型,得到优化加权TV的复合正则化重建模型。最后,结合投影法和算子分裂法对优化模型求解。结果针对自然图像的不同特性,使用复合正则化先验进行建模,实验结果表明上述重建问题通过本文方法得到了很好的解决,加权TV正则化先验使得图像的平坦区域和强边重建较好,而非局部结构相似性先验和局部自回归性先验能够保证图像的精细结构部分的重建效果。结论与其他基于TV正则化的重建模型相比,本文模型的重建性能无论是在视觉效果还是在客观评价指标上都有明显的提高。

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