MR image reconstruction based on comprehensive sparse prior

In this paper, a novel Magnetic Resonance (MR) reconstruction framework which combines image-wise and patch-wise sparse prior is proposed. For addressing, a truncated beta-Bernoulli process is firstly employed to enforce sparsity on overlapping image patches emphasizing local structures. Due to its properties, beta-Bernoulli process can adaptive infer the sparsity (number of nonzero coefficients) of each patch, an appropriate dictionary, and the noise variance simultaneously, which are prerequisite for iterative image reconstruction. Secondly, a General Gaussian Distribution (GGD) prior is introduced to engage image-wise sparsity for wavelet coefficients, which can be then estimated by a threshold denoising algorithm. Finally, MR image is reconstructed by patch-wise estimation, image-wise estimation and under-sampled k-space data with least square data fitting. Experimental results have demonstrated that proposed approach exhibits excellent reconstruction performance. Moreover, if the image is full of similar low-dimensional-structures, proposed algorithm has dramatically improved Peak Signal to Noise Ratio (PSNR) 7～9 dB, with comparisons to other state-of-art compressive sampling methods.     

MR image reconstruction from highly undersampled k-space data by dictionary learning

Compressed sensing (CS) utilizes the sparsity of magnetic resonance (MR) images to enable accurate reconstruction from undersampled k-space data. Recent CS methods have employed analytical sparsifying transforms such as wavelets, curvelets, and finite differences. In this paper, we propose a novel framework for adaptively learning the sparsifying transform (dictionary), and reconstructing the image simultaneously from highly undersampled k-space data. The sparsity in this framework is enforced on overlapping image patches emphasizing local structure. Moreover, the dictionary is adapted to the particular image instance thereby favoring better sparsities and consequently much higher undersampling rates. The proposed alternating reconstruction algorithm learns the sparsifying dictionary, and uses it to remove aliasing and noise in one step, and subsequently restores and fills-in the k-space data in the other step. Numerical experiments are conducted on MR images and on real MR data of several anatomies with a variety of sampling schemes. The results demonstrate dramatic improvements on the order of 4-18 dB in reconstruction error and doubling of the acceptable undersampling factor using the proposed adaptive dictionary as compared to previous CS methods. These improvements persist over a wide range of practical data signal-to-noise ratios, without any parameter tuning.     

自适应稀疏约束图像超分辨力重建方法

简要介绍了基于稀疏字典约束的超分辨力重建算法,提出了具有低复杂度的基于K均值聚类的自适应稀疏约束图像超分辨力重建算法。所提算法从两个方面降低其计算复杂度:分类训练字典,对图像块归类重建,降低每个图像块所用字典的大小;对图像块的特征进行分析,自适应地选择重建方法。实验结果表明,提出的快速重建方法在重建质量与原算法相当的前提下,可以较大程度地降低重建时间。     

Coupled dictionary learning in wavelet domain for Single-Image Super-Resolution

In this paper a coupled dictionary learning mechanism with mapping function is proposed in the wavelet domain for the task of Single-Image Super-Resolution. Sparsity is used as the invariant feature for achieving super-resolution. Instead of using a single dictionary multiple compact dictionaries are proposed in the wavelet domain. Such dictionaries will exhibit the properties of the wavelet transform such as compactness, directionality and redundancy. Six pairs of dictionaries are designed using a coupled dictionary mechanism with mapping function which helps in strengthening the similarity between the sparse coefficients. Low-resolution image is assumed as the approximation image of the first-level wavelet decomposition. High resolution is achieved by estimating the wavelet sub-bands of this low-resolution image by dictionary learning and sparsity. The proposed algorithm outperforms a well-known spatial domain and wavelet domain algorithm as evaluated on the existing comparative parameters such as structural similarity index measure and peak signal-to-noise ratio.     

融合解析模型和综合模型的压缩感知算法

如何利用更多的图像先验知识来提高图像的重构质量是压缩感知的一个关键问题.本文将综合稀疏模型与近几年提出的Cosparse解析模型结合,利用图像在综合字典和解析字典下的稀疏性提出了一种融合两种稀疏先验的图像重构算法,并利用交替方向乘子法(ADMM)求解对应的复杂优化问题.为进一步提高算法性能,该算法还充分利用了图像中任意位置图像块的稀疏性.实验结果表明,本文算法能有效提高图像重构质量.     

基于深度学习的单像素相机超分辨率成像优化

基于压缩感知和单像素成像的基本原理,设计了一种用于图像超分辨率重建的新型深度卷积神经网络架构.这种单像素超分辨率成像算法成功地将深度学习图像超分辨率重建技术与压缩感知单像素成像技术相结合,从而发展出一种全新的深度学习单像素成像优化方法.与传统的常规压缩感知图像重构算法相比,该算法有效提升了图像超分辨率重建精度和单像素成像质量.通过图像重建的仿真实验和单像素相机的成像实验验证,结果表明这种基于深度学习的新型单像素相机成像方式具有良好的性能表现.     

基于耦合特征空间下改进字典学习的图像超分辨率重建

针对目前基于字典学习的图像超分辨率重建效果欠佳或字典训练时间过长的问题,本文提出了一种耦合特征空间下改进字典学习的图像超分辨率重建算法.该算法首先利用高斯混合模型聚类算法对训练图像块进行聚类,然后使用更改字典更新方式的改进KSVD字典学习算法来快速获得高、低分辨率特征空间下字典对和映射矩阵.重建时根据测试样本与各个类别的似然概率自适应地选择最匹配的字典对和映射矩阵进行高分辨率重建.最后利用图像非局部相似性,将其与迭代反向投影算法相结合对重建后的图像进行后处理获得最佳重建效果.实验结果表明了本文方法的有效性.     

Joint modeling and reconstruction of a compressively-sensed set of correlated images

Employing correlation among images for improved reconstruction in compressive sensing is a conceptually attractive idea, although developing efficient modeling strategies and reconstruction algorithms are often the key to achieve any potential benefit. This paper presents a novel modeling strategy and an efficient reconstruction algorithm for processing a set of correlated images, jointly taking into consideration inter-image correlation, intra-image correlation and inter-channel correlation. The approach starts with joint modeling of the entire image set in the gradient domain, which supports simultaneous representation of local smoothness, nonlocal self-similarity of every single image, and inter-image correlation. Then an efficient algorithm is proposed to solve the joint formulation, using a Split-Bregman-based technique. Furthermore, to support color image reconstruction, the proposed algorithm is extended by using the concept of group sparsity to explore inter-channel correlation. The effectiveness of the proposed approach is demonstrated with extensive experiments on both grayscale and color image sets. Results are also compared with recently proposed compressive sensing recovery algorithms.     

基于块稀疏的电阻抗成像算法

该文提出一种基于自适应块稀疏字典学习的电阻抗图像重建算法,构建了分块稀疏字典,较好地保留了重建图像的细节信息;同时,将字典学习与图像重建交替进行,并将迭代重建的中间结果作为稀疏字典的训练样本,有效提高了字典学习效果。数值仿真与实验重建结果表明,新方法对电阻抗成像系统测量噪声具有较好的鲁棒性,能准确重构电导率分布图像,特别是对突变细节的准确恢复。     

基于图像块分类稀疏表示的超分辨率重构算法

 目前基于图像块稀疏表示的超分辨率重构算法对所有图像块都用同一字典表示,不能反映不同类型图像块间的差别.针对这一缺点,本文提出基于图像块分类稀疏表示的方法.该方法先利用图像局部特征将图像块分为平滑、边缘和不规则结构三种类型,其中边缘块细分为多个方向.然后利用稀疏表示方法对边缘和不规则结构块分别训练各自对应的低分辨率和高分辨率字典.重构时对平滑块利用简单双三次插值方法,边缘和不规则结构块由其对应的高、低分辨率字典通过正交匹配追踪算法重构.实验结果表明,与单字典稀疏表示算法相比,本文算法对图像边缘部分重构质量明显改善,同时重构速度显著提高.     

Dictionary learning based reconstruction for distributed compressed video sensing

Distributed compressed video sensing (DCVS) is a framework that integrates both compressed sensing and distributed video coding characteristics to achieve a low-complexity video coding. However, how to design an efficient reconstruction by leveraging more realistic signal models that go beyond simple sparsity is still an open challenge. In this paper, we propose a novel “undersampled” correlation noise model to describe compressively sampled video signals, and present a maximum-likelihood dictionary learning based reconstruction algorithm for DCVS, in which both the correlation and sparsity constraints are included in a new probabilistic model. Moreover, the signal recovery in our algorithm is performed during the process of dictionary learning, instead of being employed as an independent task. Experimental results show that our proposal compares favorably with other existing methods, with 0.1–3.5 dB improvements in the average PSNR, and a 2–9 dB gain for non-key frames when key frames are subsampled at an increased rate.     

基于稀疏编码的鲁棒型人脸超分辨率重建

为了减少人脸超分图像的边缘伪影和图像噪点,利用基于稀疏编码的单幅图像超分辨率重建算法,在字典学习阶段,结合L1范数引入在线字典学习方法,使字典根据当前输入图像块和上次迭代生成的字典逐列更新,得到更加精确的超完备字典对,用于图像重建.实验中进行的仿真结果表明,改进算法超分结果的峰值信噪比(PSNR)和结构相似性(SSIM)比同类型的稀疏编码超分法(SCSR)和应用在线字典学习算法的超分方法(ODLSR)均有较大幅度提升,比后者平均提升0.72 dB和0.0187.同时,视觉上有效地消除了边缘伪影,且在处理含噪人脸图像时,具备更强的去噪能力和更好的鲁棒性.     

压缩感知中测量矩阵与重建算法的协同构造

本文提出基于感知字典的迭代硬阈值(SDIHT)算法,以此协同构造压缩感知中测量矩阵与重建算法.将成对测量矩阵与感知字典分别用于压缩投影和构造重建算法,重建迭代至残差为零,从而精确恢复原始稀疏信号.本文证明了SDIHT算法精确恢复原始稀疏信号的充分条件.SDIHT算法的优点是重建精度高和计算复杂度低.仿真实验表明,当信号稀疏度或测量次数相同时,相比IHT、OMP和BIHT算法,SDIHT算法重建0-1稀疏信号和二维图像效果更好、算法效率更高.     

基于压缩感知的月球探测器着陆图像超分辨重建

嫦娥工程二期的任务要求中,嫦娥3号的安全降落是最为关键的任务。因此,提出了一种基于压缩感知的超分辨率图像重建方法,根据经过模糊处理并加入噪声的低分辨率图像重建原始的高分辨率图像,实现了月球探测器着陆图像的超分辨率重建。算法采用局部Sparse-Land模型,从美国阿波罗计划获取的月球影像、嫦娥1、2号卫星影像和嫦娥工程二期试验中获取的月球探测器图像中提取了大量训练图块,采用K-SVD算法完成了高、低分辨率过完备字典Al和Ah的学习,通过求解优化问题,获得待处理低分辨率图块的稀疏表示,并将表示系数用于Ah以生成对应的高分辨率图块。最后,运用最小二乘算法,得到满足重构约束的高分辨率图像。实验验证了算法的有效性,表明其在视觉效果及PSNR指标上均优于插值方法和Yang的方法。     

基于改进K-SVD字典学习的超分辨率图像重构

 针对已有算法中字典训练的时间消耗巨大的问题,提出了一种改进的基于字典学习的超分辨率图像重构算法.本文将K-SVD字典算法和高低分辨率联合生成的思想结合起来,形成新的字典训练方法,并将由该算法生成的高低分辨率字典应用于基于稀疏表示的超分辨率重构.重构仿真实验证明算法不仅有效降低了字典训练所消耗的时间,而且能够改善重构高分辨图像的质量.     

基于聚类字典的图像超分辨率重构算法

针对图像超分辨率(SR)重构在空间邻域选取过程中 细节特征易被大幅度特征分量淹没的问题,提出 一种基于聚类字典的SR重构(DD-NE)算法。图像SR重构是利用信号处理方 法来提高图像分辨 率,针对NE算法在空间邻域选取时细节信号易被大幅度信号淹没的问题,对输入图像及邻域 利用聚类字典进行 稀疏分解。从大、小幅值表示系数中分别重构大、小幅度特征子图,保护邻域计算中的小幅 度特征,并将 低分辨率(LR)图像库及输入图像使用聚类字典表示。细节信号以字典原子的形式得到表达 ,空间邻域度 量转换为字典原子间的度量,从而细节特征对邻域的选择更加准确。实验结果表明,相对于 NE算法,本文算法图像SR 重构的峰值信噪比(PSNR)值平均提升了1.1dB,有效改善了重构效果;重构时间仅为NE算法的30.9%。     

一种改进的压缩感知信号重构算法

针对支撑集未知且变化时的稀疏信号的重构问题,本文基于卡尔曼滤波思想,结合压缩感知算法,给出了一种改进的卡尔曼-压缩感知（Modified Kalman Filter Compressive Sensing,MKFCS）信号重构算法,该算法首先利用Kalman滤波获得信号残差的有效估计,然后根据残差变突情况,用改进的CS算法估计突变位置以确定信号的新的支撑集,最后用最小二乘方法重构信号,从而自适应的实现支撑集未知且变化的稀疏信号的重构。最后对所改进的通过重构精度、重构误差、稳健性等方面进行了仿真,仿真结果表明所提算法重构信号具有需要量测个数少、重构精度高、鲁棒性强等特点。      

连续波太赫兹成像系统的单幅图像超分辨重建

针对现有的太赫兹成像系统所需硬件设备复杂且昂贵的问题,设计了基于单幅图像超分辨重建的连续波太赫兹成像系统,降低设备复杂度和硬件成本。通过对该成像系统生成的太赫兹图像进行双维度预处理,降低图像处理的占用内存,提高后续处理速度。引入限制对比度自适应直方图均衡方法对太赫兹图像进行分区域对比度提升,有效解决太赫兹图像对比度低的问题。利用稀疏表示和字典学习实现太赫兹图像的超分辨重建,提出了反余割拟牛顿平滑零范数的算法解决零范数优化问题,提高了重建精度。通过对该成像系统采集的单幅太赫兹图像进行超分辨重建,在边缘强度上提高了3.232,在平均梯度对比中提高了0.300,验证了对单幅太赫兹图像超分辨重建的有效性与优越性。     

基于正则化稀疏表示的图像超分辨率算法

为了从单幅低分辨率(LR)图像恢复出高分辨率(H R)图像,提出了一种应用正则化稀疏表示和基于机器学习 的超分辨率(SR)图像恢复算法。构造了一种基于稀疏表示的SR凸变模型,为了提高 恢复效果,针对模型 提出了两种稀疏正则化约束条件,一是将分类效果更好的图表拉普拉斯作为正则化约束条件 ,从而找到与 输入LR图像块在结构上最接近的学习样本;另一种是针对冗余的学习样本进行约 束,保证了图像边 缘的锐利。将输入的每一块LR图像应用正则化稀疏表示,经过学习得到与之对应的HR图像块 , 最终得到整幅HR图像。试验结果表明,算法恢复出的HR图像峰值信噪比(PSNR )值较双三次插值算法最高提升约2dB,主观目视清晰、边缘锐利。     

基于稀疏优化的图像压缩感知重建算法

在信号的稀疏表示方法中,传统的基于变换基的稀疏逼近不能自适应性地提取图像的纹理特征,而基于过完备字典的稀疏逼近算法复杂度过高.针对该问题,文章提出了一种基于小波变换稀疏字典优化的图像稀疏表示方法.该算法在图像小波变换的基础上构建图像过完备字典,利用同一场景图像的小波变换在纹理上具有内部和外部相似的属性,对过完备字典进行灰色关联度的分类,有效提高了图像表示的稀疏性.将该新算法应用于图像信号进行稀疏表示,以及基于压缩感知理论的图像采样和重建实验,结果表明新算法总体上提升了重建图像的峰值信噪比与结构相似度,并能有效缩短图像重建时间.