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费选1, 韦志辉1, 肖亮1, 李星秀2(1.南京理工大学计算机科学与工程学院, 南京 210094;2.南京理工大学理学院, 南京 210094)

摘 要
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。
Compound regularized compressed sensing image reconstructionbased on optimal reweighted TV

Fei Xuan1, Wei Zhihui1, Xiao Liang1, Li Xingxiu2(1.School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China;2.School of Science, Nanjing University of Science and Technology, Nanjing 210094, China)

Objective Breaking the limitations of the traditional Shanon-Nyquist sampling theorem,compressed sensing is a recent paradigm, which allows a signal to be sampled at sub-Nyquist rates and proposed a methodology of recovery that incurs no loss. The field of compressed sensing is related to other topics in signal processing. Especially,imaging techniques having a strong affinity with compressed sensing include coded aperture and computational photography. In recent years,compressed sensing image reconstruction has caused widespread concern,and the total variation (TV) regularization, which describes the sparsity of the image gradient, has been widely used for image reconstruction. Inspired by these ideas,we propose a novel compound regularized compressed sensing image reconstruction model based on optimal reweighted TV. Method Our reconstruction modeling is based on the classical TV regularization recovery model,and some actions have been taken to improve the reconstruction performance. At first,the TV regularization always results in a piecewise constant solutions. This will make the reconstructed image too smooth and some details, such as edges and textures, are lost. To overcome this drawback,the gradient information of the image is utilized to estimate weights,and build a reweighted TV-based compressed sensing image reconstruction model. Then,for reducing the noise or other degradation influence,we introduce a TV denoising (Rudin-Osher-Fatemi,ROF)model into the optimal estimation of weights. Next,the characters of the natural image are introduced into image modeling as the priors such as the nonlocal structure similarity and local regression priors. We introduce these priors into the reconstruction model to preserve the image details,and propose a novel compound regularized optimization model based on optimal reweighted TV. At last,the optimization model could be reduced to a series of convex minimization problems that can be efficiently solved with a combination of the projection method and operator splitting method,leading to fast and easy-to-code algorithms. Result In the conventional TV regularization reconstruction model,there is not enough prior information which is utilized to represent different characters of the natural image. Therefore, a compound regularized model is proposed to use these corresponding priors of different characters in this paper. The experimental results demonstrate the more refined image reconstruction in our proposed method. Especially,the sparsity prior of the image gradient is fully considered as reweighted TV regularizer, which could guarantee the reconstructed effects of the smoothed areas and strong edges,while the nonlocal structure similarity and local regression priors are also exploited to improve the reconstructed performance of weak edges or textures. Conclusion TV regularization model is a widely-used compressed sensing image reconstruction method. However,this process is easy to be affected by noise or other degradation. Meanwhile, it is difficult to obtain refined reconstruction result because image prior information is rarely utilized. We propose a novel compound regularized compressed sensing image reconstruction model. Here,we integrate the sparsity prior,the nonlocal structure similarity prior and the local regression prior into reconstruction model as compound regularizers. Extended experiment results indicate that the proposed compressed sensing reconstruction method has a better improvement in terms of objective criterion and visual fidelity over other related TV-based reconstruction methods.