基于压缩传感和代数重建法的CT图像重建

代数重建法(ART)是一种重要的CT图像重建方法,适合于不完全投影数据的图像重建,其缺点是重建速度慢。为提高图像重建的质量和速度,利用压缩传感理论提出了一种基于ART的高质量图像重建算法。该算法将CT图像的梯度稀疏性结合到ART图像重建中,在每次迭代中的投影操作结束后用梯度下降法调整全变差,减小图像梯度的l1范数。实验结果验证了该算法的有效性。     

一种基于编码孔径的压缩传感图像重构算法的改进

针对压缩传感理论应用于实际系统成像时重构图像质量随图像采样率变化的问题,通过对正交匹配追踪算法进行改进,提出了一种利用空间光调制器实现编码孔径成像的压缩传感图像重构方法。该方法对传统的正交匹配追踪法迭代计算中已选入支撑集的列向量进行标记,并在下一次迭代计算中予以排除,从而减少了重构时间。在此基础上提出了将测量矩阵分别按行和按列排列进行重构后平均的图像增强算法。增强算法在达到同样重构质量时,减小了图像采样率,有利于图像数据的传输和存储。仿真实验验证了方法的有效性和稳定性,可为压缩传感技术的应用提供技术参考。     

确定性相位掩膜可压缩双透镜成像

压缩成像是压缩传感理论的一个重要应用领域.本文将确定性测量引入压缩成像,提出一种确定性相位掩膜可压缩双透镜成像方法.模拟实验结果表明,新的成像方法可以在显著地降低物理实现成本的同时,有效地捕获图像信息来重建原始图像.此方法改变了经典的模拟-数字转换的光学成像思路,减少模数转换开销,并有利于图像的传输和存储,可以为照相机...     

确定性相位掩膜可压缩双透镜成像

压缩成像是压缩传感理论的一个重要应用领域.本文将确定性测量引入压缩成像,提出一种确定性相位掩膜可压缩双透镜成像方法.模拟实验结果表明,新的成像方法可以在显著地降低物理实现成本的同时,有效地捕获图像信息来重建原始图像.此方法改变了经典的模拟-数字转换的光学成像思路,减少模数转换开销,并有利于图像的传输和存储,可以为照相机的设计提供若干理论、计算和技术支撑.     

确定性矩阵可分离压缩成像

针对可分离压缩传感使用的可分离随机正交矩阵在处理大尺度图像等高维信号感知时难度太大或成本过高的问题,引入确定性测量矩阵,提出确定性矩阵可分离压缩传感,可将如托普利兹矩阵及循环矩阵等具有确定性结构的矩阵作为可分离压缩传感的左、右可分离矩阵.该方案可以降低独立元素的数目,从而显著降低前端物理实现的难度与成本.数值模拟实验分别评估了该方法在不同采样率及不同图像尺寸下的压缩重建性能,结果表明该方法在独立元素非常少的情形下得到与原随机正交矩阵相近的重建质量,证明了其可行性.     

基于高斯混合尺度模型的压缩传感图像重构

在图像处理领域中,压缩传感重构是稀疏表示下的最重要的病态反问题之一。压缩传感图像重构利用图像可稀疏表示的先验知识,从比奈奎斯特采样率低得多的随机投影观测值中重构原始图像。为了克服传统的压缩传感算法中收敛速度慢和未利用变换系数的邻域统计特性的缺点,提出了基于高斯混合尺度模型的压缩传感图像重构算法,证明了独立的高斯混合尺度分布作为压缩传感重构的稀疏先验知识的可行性,结合全变差调整进一步提高算法的性能。实验结果表明,该算法有效地提高了重构图像的主观视觉效果和峰值信噪比,加快了压缩传感图像重构算法的收敛速度。     

基于改进的分块压缩感知红外图像重建

针对基于压缩感知理论的红外图像重建问题,提出一种基于改进的分块压缩感知红外图像重建方法。该方法首先对原始红外图像进行分块,并对每个子块用相同的观测矩阵进行随机观测,获得少量的观测数据;然后利用谱图小波变换优异的稀疏特性,将其引入平滑投影Landweber算法进行迭代优化重建,同时采用混合中值滤波进行处理以增加图像的平滑度和减少块伪影,最后输出满足要求的高质量红外图像。实验结果表明,在相同采样率下,该方法对于不同类型红外图像的重建性能均优于目前广为采用的一些小波压缩感知方法,可获得更高质量的红外图像。     

基于近似l0范数最小化的NMR波谱稀疏重建算法

在核磁共振（NMR）波谱中,过长的数据采集时间会使很多化学以及分子生物学领域的高分辨率多维谱应用难以实现. 传统的解决办法是使用随机非均匀采样代替奈奎斯特采样,但这样会使谱图质量受损. 压缩传感的出现为此提供了更好的解决办法,合适的压缩传感重建算法可以通过很少的随机非均匀采样将谱图高质量的重建出来. 该文先介绍了一种可用于谱图重建的压缩传感重建算法,名为“平滑l₀范数最小化法”,然后针对该算法对采样噪声鲁棒性较差的缺点进行了改进. 通过将改进后的算法与原算法在一维实数域信号以及NMR波谱信号重建实验中进行对比后表明,改进后的算法对噪声的鲁棒性明显提高,并能获得更好的重建性能.     

基于lp范数的压缩感知图像重建算法研究

图像重建是光学成像、光声成像、声纳成像、核磁共振成像、 天体成像等物理成像领域中的关键技术之一. 近年来提出的压缩感知理论指出: 对稀疏或者可压缩信号进行少量非自适应线性投影,投影信号含有足够的信息, 从而能对信号进行高概率重建. 压缩感知已被应用于多种物理成像系统. 将罚函数法和修正Hesse阵序列二次规划方法相结合, 并采用了分块压缩感知思想, 提出一种基于l_p范数的压缩感知图像重建算法. 以cameraman, barbara和mandrill图像为例, 采用该算法进行图像重建. 首先, 在不同采样率下对图像重建. 即便采样率低至0.3时, 也能获得高达32.23dB的信噪比, 重建图像清晰可辨. 验证了该算法的正确性. 其次, 将该算法与正交匹配追踪算法进行对比, 在采样率达到0.5以上时, 能够获得高信噪比的重建图像, 成像时间也大为减少, 特别是采样率为0.7时, 成像时间减少88%. 最后, 与现有基于l_p 范数的压缩感知图像重建算法进行对比, 计算结果表明在成像质量有所提高的基础上, 成像时间大为缩短. 关键词： 图像重建 压缩感知 罚函数 修正Hesse阵序列二次规划     

循环-托普利兹块相位掩模可压缩双透镜成像

压缩成像是压缩传感理论的重要应用领域之一,可以用比Nyquist测量数目少的测量值捕获充分信息重建稀疏或可压缩图像.在研究现有的压缩成像方法的基础上,给出一种新的循环-托普利兹块相位掩模矩阵可压缩双透镜成像方法.模拟实验结果表明新的相位掩模矩阵成像方法可以在欠采样的情况下有效地获得图像信息来重建原始图像.新方法的研究为...     

选择性双向顺序压缩感知重建动态磁共振成像

压缩感知是一种新兴技术,该技术能够用远低于奈奎斯特采样频率采集的信号恢复出原始信号. 压缩感知成像方法大大提高了心脏磁共振成像的采集速度,已有的方法主要利用动态图像时间相关及心脏的周期性运动特征,如采用在时间维做傅立叶变换或求解每帧数据跟参考帧数据的差异获取稀疏数据,满足压缩感知重建的要求. 该文提出了选择性双向顺序压缩感知重建算法,利用相邻帧的差异更小的特点,获取更加稀疏的差异数据,同时利用动态图像的周期性,以目标函数积分为判据,在时间顺序和时间逆序两个方向选择效果更好的方向进行数据重建,降低图像伪影和噪声. 该选择算法,可以在不增加重建时间的情况下,选择双向顺序重建中最佳的结果. 该文对心脏磁共振图像数据进行了数据处理实验,并且跟传统压缩感知算法、参考帧差异方法及匙孔成像方法进行了比较. 结果表明：该方法无论从视觉效果还是从统计结果上,都有很大的改善.     

Compressed sensing MR image reconstruction using a motion-compensated reference

Compressed sensing (CS)-based methods have been proposed for image reconstruction from undersampled magnetic resonance data. Recently, CS-based schemes using reference images have also been proposed to further reduce the sampling requirement. In this study, we propose a new reference-constrained CS reconstruction method that accounts for the misalignment between the reference and the target image to be reconstructed. The proposed method uses a new image model that represents the target image as a linear combination of a motion-dependent reference image and a sparse difference image. We then use an efficient iterative algorithm to jointly estimate the motion parameters and the difference image from sparsely sampled data. Simulation results from a numerical phantom data set and an in vivo data set show that the proposed method can accurately compensate the motion effects between the reference and the target images and improve reconstruction quality. The proposed method should prove useful for several applications such as interventional imaging, longitudinal imaging studies and dynamic contrast-enhanced imaging.     

An infrared image super-resolution reconstruction method based on compressive sensing

Limited by the properties of infrared detector and camera lens, infrared images are often detail missing and indistinct in vision. The spatial resolution needs to be improved to satisfy the requirements of practical application. Based on compressive sensing (CS) theory, this thesis presents a single image super-resolution reconstruction (SRR) method. With synthetically adopting image degradation model, difference operation-based sparse transformation method and orthogonal matching pursuit (OMP) algorithm, the image SRR problem is transformed into a sparse signal reconstruction issue in CS theory. In our work, the sparse transformation matrix is obtained through difference operation to image, and, the measurement matrix is achieved analytically from the imaging principle of infrared camera. Therefore, the time consumption can be decreased compared with the redundant dictionary obtained by sample training such as K-SVD. The experimental results show that our method can achieve favorable performance and good stability with low algorithm complexity.     

压缩感知理论在图像处理领域的应用

针对传统的采样方法得到的图像数据量巨大,给图像信息的后续处理造成极大压力的问题,对压缩感知理论（Compressed Sensing,CS）进行了研究。压缩感知理论使采集很少一部分数据并且从这些少量数据中重构出更大量信息的想法变成可能,突破了奈奎-斯特采样定理的限制。综述了CS理论及关键技术问题,并着重介绍了CS理论在成像系统、图像融合、图像目标识别与跟踪等方面的应用与发展状况。文章指出CS理论开拓了信息处理的新思路,随着该理论的进一步完善,会有更广泛的应用领域。     

压缩感知理论在图像处理领域的应用

针对传统的采样方法得到的图像数据量巨大,给图像信息的后续处理造成极大压力的问题,对压缩感知理论(Compressed Sensing,CS)进行了研究。压缩感知理论使采集很少一部分数据并且从这些少量数据中重构出更大量信息的想法变成可能,突破了奈奎-斯特采样定理的限制。综述了CS理论及关键技术问题,并着重介绍了CS理论在成像系统、图像融合、图像目标识别与跟踪等方面的应用与发展状况。文章指出CS理论开拓了信息处理的新思路,随着该理论的进一步完善,会有更广泛的应用领域。     

Joint Reconstruction of Multi-contrast Images and Multi-channel Coil Sensitivities

Magnetic resonance imaging (MRI) has an important feature that it provides multiple images with different contrasts for complementary diagnostic information. However, a large amount of data is needed for multi-contrast images depiction, and thus, the scan is time-consuming. Many methods based on parallel magnetic resonance imaging (pMRI) and compressed sensing (CS) are applied to accelerate multi-contrast MR imaging. Nevertheless, the image reconstructed by sophisticated pMRI methods contains residual aliasing artifact that degrades the quality of the image when the acceleration factor is high. Other methods based on CS always suffer the regularization parameter-selecting problem. To address these issues, a new method is presented for joint multi-contrast image reconstruction and coil sensitivity estimation. The coil sensitivities can be shared during the reconstruction due to the identity of coil sensitivity profiles of different contrast images for imaging stationary tissues. The proposed method uses the coil sensitivities as sharable information during the reconstruction to improve the reconstruction quality. As a result, the residual aliasing artifact can be effectively removed in the reconstructed multi-contrast images even if the acceleration factor is high. Besides, as there is no regularization term in the proposed method, the troublesome regularization parameter selection in the CS can also be avoided. Results from multi-contrast in vivo experiments demonstrated that multi-contrast images can be jointly reconstructed by the proposed method with effective removal of the residual aliasing artifact at a high acceleration factor.     

Computational ghost imaging with deep compressed sensing

Computational ghost imaging (CGI) provides an elegant framework for indirect imaging, but its application has been restricted by low imaging performance. Herein, we propose a novel approach that significantly improves the imaging performance of CGI. In this scheme, we optimize the conventional CGI data processing algorithm by using a novel compressed sensing (CS) algorithm based on a deep convolution generative adversarial network (DCGAN). CS is used to process the data output by a conventional CGI device. The processed data are trained by a DCGAN to reconstruct the image. Qualitative and quantitative results show that this method significantly improves the quality of reconstructed images by jointly training a generator and the optimization process for reconstruction via meta-learning. Moreover, the background noise can be eliminated well by this method.     

Photoacoustic image reconstruction based on Bayesian compressive sensing algorithm

The photoacoustic tomography (PAT) method, based on compressive sensing (CS) theory, requires that, for the CS reconstruction, the desired image should have a sparse representation in a known transform domain. However, the sparsity of photoacoustic signals is destroyed because noises always exist. Therefore, the original sparse signal cannot be effectively recovered using the general reconstruction algorithm. In this study, Bayesian compressive sensing (BCS) is employed to obtain highly sparse representations of photoacoustic images based on a set of noisy CS measurements. Results of simulation demonstrate that the BCS-reconstructed image can achieve superior performance than other state-of-the-art CS-reconstruction algorithms.     

光子计数集成成像的压缩与重构

集成成像技术作为一种重要的裸眼三维显示技术,在完整记录三维场景信息的同时,庞大的数据量给传输和存储带来了压力。为了实现图像的有效压缩和重构,根据光子计数集成成像的特点,基于分布式压缩感知理论,提出用于图像压缩与重构的方案。该方案将图像分为参考图像和非参考图像两类,对其设置不同的测量率并分别进行重构。为保证非参考图像的重构质量,提出一种联合重构算法。该算法首先对非参考图像进行分块测量,依据与参考图像之间的相关性进行图像块分类,然后结合参考图像测量值信息构建新的测量矢量,利用新的测量矢量完成初次图像重构。为了进一步提升图像重构质量,对初次重构结果进行二次残差补偿重构,获得最终重构结果。最后通过设置不同的测量率进行了大量实验,实验结果表明,所提算法在测量率为0.25时,图像重构质量可以达到30 dB,测量率为0.4时,图像质量可以达到35 dB,算法性能具有一定的优越性。