本文提出了一种基于加权Schatten p范数最小化(Weighted Schatten p-Norm Minimization,WSNM)的磁共振图像重构算法,该方法利用磁共振图像的非局部自相似性,并结合Schatten p范数和不同秩元素重要性的加权因子,实现磁共振图像重构过程...本文提出了一种基于加权Schatten p范数最小化(Weighted Schatten p-Norm Minimization,WSNM)的磁共振图像重构算法,该方法利用磁共振图像的非局部自相似性,并结合Schatten p范数和不同秩元素重要性的加权因子,实现磁共振图像重构过程的低秩约束.此外,采用交替方向乘子算法(Alternating Direction Method of Multipliers,ADMM)来求解基于WSNM磁共振图像重构的非凸最小化问题.实验结果表明,相比于最近的磁共振重构算法,基于WSNM的磁共振图像重构方法具有更好的重建效果,可获得更高的峰值信噪比(Peak Signal to Noise Ratio,PSNR)和更好的结构相似性(Structural Similarity,SSIM).展开更多
Image denoising is a fundamental and important task in image processing and computer vision fields. A lot of methods are proposed to reconstruct clean images from their noisy versions. These methods differ in both met...Image denoising is a fundamental and important task in image processing and computer vision fields. A lot of methods are proposed to reconstruct clean images from their noisy versions. These methods differ in both methodology and performance. On one hand, denoising methods can be classified into local and nonlocal methods. On the other hand, they can be marked as spatial and frequency domain methods. Sparse coding and low-rank are two popular techniques for denoising recently. This paper summarizes existing techniques and provides several promising directions for further studying in the future.展开更多
鲁棒主成分分析(Robust principal component analysis,RPCA)模型中秩函数和L0范数的求解是非确定性多项式(Nondeterministic polynominal,NP)难问题,凸近似模型的求解通常会导致过收缩。本文结合加权方法和Lp范数提出了一种基于双加权L...鲁棒主成分分析(Robust principal component analysis,RPCA)模型中秩函数和L0范数的求解是非确定性多项式(Nondeterministic polynominal,NP)难问题,凸近似模型的求解通常会导致过收缩。本文结合加权方法和Lp范数提出了一种基于双加权Lp范数的RPCA模型,利用加权S p范数低秩项和加权Lp范数稀疏项分别对RPCA框架中的低秩恢复问题和稀疏恢复问题进行建模,使其更接近秩函数和L0范数最小化问题的解,提升了矩阵秩估计和稀疏估计的准确性。为了验证模型性能,本文利用图像的非局部自相似性,结合相似图像块组的低秩性与椒盐噪声的稀疏性,将双加权Lp范数鲁棒主成分分析模型应用于去除椒盐噪声过程中。定量与定性的实验结果表明,本文模型性能优于其他模型,同时奇异值过收缩分析也表明本文模型能够有效抑制秩成分的过度收缩。展开更多
针对Shearlet收缩去噪引入的Gibbs伪影和"裂痕"现象,提出一种结合非局部自相似的Shearlet自适应收缩图像去噪方法。首先,对噪声图像进行多方向多尺度的Shearlet分解;然后,基于高斯比例混合(GSM)模型的Shearlet系数分布建模,...针对Shearlet收缩去噪引入的Gibbs伪影和"裂痕"现象,提出一种结合非局部自相似的Shearlet自适应收缩图像去噪方法。首先,对噪声图像进行多方向多尺度的Shearlet分解;然后,基于高斯比例混合(GSM)模型的Shearlet系数分布建模,利用贝叶斯最小二乘估计对Shearlet系数进行自适应收缩去噪,重构得到初始去噪图像;最后,利用非局域自相似模型对初始去噪图像进行滤波处理,得到最终的去噪图像。实验结果表明,所提方法在更好地保留边缘特征的同时,有效地去除噪声和收缩去噪引入的Gibbs伪影,该方法获得的峰值信噪比(PSNR)和结构自相似指标(SSIM)比基于非抽样剪切波变换(NSST)的硬阈值去噪方法提高1.41 d B和0.08;比非抽样Shearlet域GSM模型去噪方法提高1.04 d B和0.045;比基于三变量模型的剪切波去噪方法提高0.64 d B和0.025。展开更多
文摘本文提出了一种基于加权Schatten p范数最小化(Weighted Schatten p-Norm Minimization,WSNM)的磁共振图像重构算法,该方法利用磁共振图像的非局部自相似性,并结合Schatten p范数和不同秩元素重要性的加权因子,实现磁共振图像重构过程的低秩约束.此外,采用交替方向乘子算法(Alternating Direction Method of Multipliers,ADMM)来求解基于WSNM磁共振图像重构的非凸最小化问题.实验结果表明,相比于最近的磁共振重构算法,基于WSNM的磁共振图像重构方法具有更好的重建效果,可获得更高的峰值信噪比(Peak Signal to Noise Ratio,PSNR)和更好的结构相似性(Structural Similarity,SSIM).
基金Supported by Independent Innovation Foundation of Shandong University,IIFSDU(No.2012TB013)Scientific Research Foundation of Shandong Province of Outstanding Young Scientist Award(No.BS2013DX041,No.BS2013DX048)+1 种基金Shandong Province Natural Fund(zr2011FM031)Ji'nan Science and Technology Development Project(No.201202015)
文摘Image denoising is a fundamental and important task in image processing and computer vision fields. A lot of methods are proposed to reconstruct clean images from their noisy versions. These methods differ in both methodology and performance. On one hand, denoising methods can be classified into local and nonlocal methods. On the other hand, they can be marked as spatial and frequency domain methods. Sparse coding and low-rank are two popular techniques for denoising recently. This paper summarizes existing techniques and provides several promising directions for further studying in the future.
文摘针对Shearlet收缩去噪引入的Gibbs伪影和"裂痕"现象,提出一种结合非局部自相似的Shearlet自适应收缩图像去噪方法。首先,对噪声图像进行多方向多尺度的Shearlet分解;然后,基于高斯比例混合(GSM)模型的Shearlet系数分布建模,利用贝叶斯最小二乘估计对Shearlet系数进行自适应收缩去噪,重构得到初始去噪图像;最后,利用非局域自相似模型对初始去噪图像进行滤波处理,得到最终的去噪图像。实验结果表明,所提方法在更好地保留边缘特征的同时,有效地去除噪声和收缩去噪引入的Gibbs伪影,该方法获得的峰值信噪比(PSNR)和结构自相似指标(SSIM)比基于非抽样剪切波变换(NSST)的硬阈值去噪方法提高1.41 d B和0.08;比非抽样Shearlet域GSM模型去噪方法提高1.04 d B和0.045;比基于三变量模型的剪切波去噪方法提高0.64 d B和0.025。
