稀疏准则下的图像复原与重建方法研究

发布时间：2018-05-11 01:02

本文选题：非局部均值 + 字典学习　；参考：《东南大学》2016年博士论文

【摘要】：近来,随着压缩感知理论的出现,基于稀疏的图像复原与图像重建研究取得了较大的进展。压缩感知理论指出,只要原始信号满足一定的有限等距性(Restricted Isometry Property, RIP),当所采集的信号数目低于奈奎斯特-香农采样定律(Nyquist-Shannon Sampling Theorem)所规定的采样数目的情况下,仍有极高的可能性恢复出原始信号。对于稀疏信号的稀疏性的描述,最佳的选择是l0范数,但是由于其不可导等缺点,压缩感知理论进一步指出基于l1范数的约束在一定情况下可以近似取代l0范数。此外,在图像处理问题中,基于Total Variation (TV)的约束可以看做是一种l1范数的约束。本文针对稀疏准则下的约束项做了进一步改进,研究了其在图像复原与低剂量计算机断层(Computed Tomography, CT)重建问题中的应用。具体来讲,本文在图像复原方面的工作可以归纳为以下两个方面：(1)提出了一种基于局部与非局部均值诱导的双重稀疏图像复原算法(L-NL)。该算法充分利用了TV图像复原模型与逆滤波图像复原模型的优点,同时融入了非局部均值滤波算法的思想。为了使逆滤波能够避免噪声的影响更好地发挥其复原性能,本文将逆滤波模型改进为无约束优化模型,并用非局部均值滤波后的图像替代模型中的退化图像。为了提高非局部均值算法的速率,本文对其进行了加速改进,提出了基于相关加速的快速非局部均值去噪算法。此时,直接使用逆滤波复原,仍不能达到理想的复原效果,因为非局部均值滤波不能完全滤除噪声且在去噪的过程中引入了新的方法噪声。于是,本文结合改进的逆滤波优化模型与TV模型提出了基于局部与非局部均值诱导的双重稀疏图像复原算法。为了评价所提算法的复原效果,本文进行了大量的实验,并与其它复原算法进行了对比,根据Peak Signal to Noise Ratio (PSNR)与Structural Similarity Index Measurement (SSIM)客观评价指标以及视觉效果,证实了所提算法的优越性。(2)提出了一种基于局部与字典表示诱导的双重稀疏的图像复原算法(L-DR)。该算法可以看做是对上文所提的基于局部与非局部均值诱导的双重稀疏算法(L-NL)的进一步改进。本文首先利用正交匹配追踪算法与K-Singular Value Decomposition (K-SVD)算法对要复原的图像进行训练获得一自适应字典,然后基于所学的字典对要复原的图像进行滤波,获得一幅近似的只含模糊退化的图像。最后结合逆滤波模型与经典的基于TV的图像复原模型,提出了基于局部与字典表示诱导的双重稀疏图像复原算法。为了验证本算法的性能,本文进行了大量的实验,并与其它复原算法进行了对比,根据P SNR与SSIM客观度量指标以及视觉效果,证实了所提算法的优越性。本文在图像重建方面的工作可以归纳为以下两个方面：(1)提出了基于Gamma准则的稀疏角CT图像重建算法。本文首先分析了基于l0的稀疏准则模型,基于l1的TV准则模型以及基于l2的稀疏准则模型。分析了它们之间的区别与联系,并提出了一个更为通用的的稀疏准则模型。利用所提的通用模型,结合Gamma概率分布方面的知识,提出了基于Gamma准则的稀疏角度重建算法。所提Gamma准则,成功弥补了l1准则与l0准则之间的空白,因此也称为分数阶准则。为了验证所提算法有效性,本文基于仿真的Modified Shepp-Logan(MSL)体模与Non-Uniform Rational B-Splines Based Cardiac-Torso(NCAT)体模的稀疏角度投影数据以及真实临床数据进行了稀疏角度的重建实验。实验结果与基于l2准则与基于l1准则方法重建结果进行了对比,依据PSNR的客观衡量标准以及视觉效果,证实了所提算法的优势。(2)提出了基于自适应Gamma准则的低剂量CT重建算法。基于对低电流(低电压)情况下投影数据中噪声的分析,以及前文所提出的Gamma准则,本文提出了基于Gamma准则的加权最小方模型。本文首先对Gamma准则模型中的两个参数进行了分析,发现其中的形状参数与尺度参数在Gamma准则函数逼近l0函数的过程中发挥了相反的作用。基于此,本文采用固定变量法的设置策略。然后,依据两个参数的比值与Gamma函数逼近l0函数之间的关系对参数进行自适应设定。为了验证所提算法的性能,本文基于MSL与NACT体模进行了低剂量仿真投影数据的重建实验以及基于Catphan600物理体模的低剂量投影数据重建实验,并与其它重建算法进行了对比,根据PSNR,SNR与SSIM客观度量指标以及视觉效果,证实了所提算法较其它算法在伪影抑制以及噪声消除方面具有明显优越。
[Abstract]:Recently, with the emergence of compressed sensing theory, the research on sparse image restoration and image reconstruction has made great progress. The theory of compressed sensing indicates that as long as the original signal satisfies certain Restricted Isometry Property (RIP), the number of signals collected is lower than the Nyquist Shannon sampling law (Nyquist-Sha In the case of the number of samples given by nnon Sampling Theorem, there is still a high possibility to restore the original signal. The best choice for the sparsity of the sparse signal is the l0 norm, but because of its shortcomings, the compression perception theory further points out that the constraints based on the L1 norm can be approximated to the L in a certain case. 0 norm. In addition, in the problem of image processing, the constraints based on Total Variation (TV) can be considered as a constraint of L1 norm. This paper further improves the constraints under sparse criterion, and studies its application in image restoration and low dose computer tomography (Computed Tomography, CT) reconstruction. The image restoration work can be summed up in the following two aspects: (1) a double sparse image restoration algorithm based on local and non local mean induction (L-NL) is proposed. The algorithm makes full use of the advantages of the TV image restoration model and the inverse filtering image restoration model, and combines the idea of the non local mean filtering algorithm. In this paper, inverse filtering can avoid the influence of noise to better play its recovery performance. In this paper, the inverse filter model is improved to unconstrained optimization model, and the image of non local mean filter is used to replace the degraded image in the model. In order to improve the rate of non local mean algorithm, this paper improves it and proposes the correlation addition. The fast fast non local mean denoising algorithm. In this case, the inverse filtering can not achieve the ideal recovery effect, because the non local mean filter can not completely filter the noise and introduce the new method noise in the process of denoising. Therefore, this paper proposes a local and TV model based on the improved inverse filter optimization model and the model. In order to evaluate the restoration effect of the proposed algorithm, a lot of experiments are carried out and compared with other restoration algorithms. According to the objective evaluation index and visual effect of Peak Signal to Noise Ratio (PSNR) and Structural Similarity Index Measurement (SSIM), it is proved that The superiority of the proposed algorithm. (2) a double sparse image restoration algorithm based on local and dictionary representation (L-DR) is proposed. This algorithm can be regarded as a further modification of the dual sparse algorithm (L-NL) based on the local and non local mean induction proposed in the previous article. The AR Value Decomposition (K-SVD) algorithm trains the reconstructed image to get a self-adaptive dictionary, then filters the reconstructed image based on the dictionary, and obtains an approximate image containing only fuzzy degradation. Finally, it combines the inverse filter model and the classic image restoration model based on TV, and proposes a local and local based on the image restoration model. In order to verify the performance of the dual sparse image restoration, a dictionary is used to verify the performance of this algorithm. A lot of experiments are carried out in this paper, and compared with other restoration algorithms. The superiority of the proposed algorithm is confirmed according to the objective metrics and visual effects of P SNR and SSIM. The next two aspects are: (1) a sparse angle CT image reconstruction algorithm based on Gamma criterion is proposed. In this paper, the sparse criterion model based on l0, the TV criterion model based on L1 and the L2 based sparse criterion model are analyzed. The difference and connection between them are analyzed, and a more general sparse criterion model is proposed. The general model, combined with the knowledge of Gamma probability distribution, proposes a sparse angle reconstruction algorithm based on Gamma criterion. The proposed Gamma criterion has successfully made up the gap between the L1 criterion and the l0 criterion, so it is also called fractional order criterion. In order to verify the effectiveness of the proposed algorithm, this paper is based on the simulated Modified Shepp-Logan (MSL) body model and No. The sparse angle projection data of the n-Uniform Rational B-Splines Based Cardiac-Torso (NCAT) body model and the real clinical data are reconstructed with sparse angle. The experimental results are compared with the reconstruction results based on the L2 criterion and the L1 criterion method. The proposed algorithm is based on the objective criterion of PSNR and the visual effect. (2) (2) a low dose CT reconstruction algorithm based on adaptive Gamma criterion is proposed. Based on the analysis of the noise in the projection data under low current (low voltage), and the Gamma criterion proposed in the previous article, a weighted least square model based on the Gamma criterion is proposed. First, the paper divides the two parameters in the Gamma criterion model. It is found that the shape parameter and the scale parameter play the opposite role in the process of the Gamma criterion function approximation to the l0 function. Based on this, this paper adopts the setting strategy of the fixed variable method. Then, according to the relation between the ratio of the two parameters and the approximation of the l0 function by the Gamma function, the parameters are adaptively set. The performance of the method is based on the reconstruction experiments of low dose simulation projection data of MSL and NACT body mode, and the experiment of low dose projection data reconstruction based on the physical model of Catphan600, and compared with other reconstruction algorithms. According to the objective metrics of PSNR, SNR and SSIM and visual effect, it is proved that the proposed algorithm is compared with other algorithms. It has obvious superiority in artifact suppression and noise elimination.

【学位授予单位】：东南大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP391.41

【参考文献】