基于数据驱动紧框架的含泊松噪声的图像恢复

首先提出了基于数据驱动紧框架的含泊松噪声的图像恢复变分模型。在该模型中,赋权的l2范数项作为保真项,包含数据驱动紧框架的l1范数项作为正则项。然后,又提出了解该模型的重新赋权的分裂Bregman算法。另外,又将所提出的模型与算法拓展应用到了含泊松高斯混合噪声的图像恢复中。最后,利用仿真实验以及PSNR指标对该模型的图像恢复效果进行评估,评估结果表明该算法可行、有效。     

欧拉弹性正则化的图像泊松去噪

利用泊松噪声分布与图像灰度值相关这一特性,结合图像的水平集曲线对图像灰度值的刻画能力,在Bayesian-MAP框架下,提出了欧拉弹性正则与泊松似然保真的图像泊松去噪变分正则化模型.利用交替方向乘子法,将原问题转化为几个不同低阶子问题的求解.对于子问题中出现的高阶非线性项,利用滞后扩散不动点迭代进行线性化,从而得到模型的快速迭代求解算法.通过数值模拟实验,证明了当图像受不同强度泊松噪声影响时,所提出的泊松去噪方法都能够有效的抑制泊松噪声,同时具有良好的结构保持性能.     

改进的迭代算法在图像恢复正则化模型中的应用

根据图像成像过程容易受泊松噪声的影响,提出用Kullback-Leibler距离描述保真项,用平方根复合函数描述正则项,建立具有自适应权系数的能量泛函正则化模型.由于模型的梯度退化和海森矩阵的规模较大,使得无法应用牛顿迭代算法.本文利用退化梯度幅值作为约束集,建立可对角化和容易求逆的海森矩阵,提出改进的牛顿投影迭代算法.仿真表明,该方法取得较小的相对误差、偏差,较高的信噪比和良好的视觉效果.     

稀疏性正则化的图像泊松去噪算法

去除医学、天文图像中的泊松噪声是一个重要问题,基于图像在过完备字典下的稀疏表示,在BayesianMAP框架下建立了稀疏性正则化的图像泊松去噪凸变分模型,采用负log的泊松似然函数作为模型的数据保真项,模型中非光滑的正则项约束图像表示系数的稀疏性,并附加非负件约束,保证去噪图像的非负性.基于分裂Bregman方法,提出...     

基于向量相关的高光谱图像真实性检验

提出了一种对高光谱图像的真实性进行检验的方法,借助地物光谱仪获取的光谱分辨率更高的同步地物光谱数据,使用光谱角度匹配的方法对高光谱图像光谱信息定量化分析,以此结果作为高光谱图像数据的真实性判据.计算前对参考光谱重采样及对光谱向量进行一阶微分变换,能够减少噪声影响、提高分析结果的可信度.实际飞行数据实验结果证明了这种方法的可行性.     

基于小波影响锥分析的图像去噪方法

采用非抽取小波变换(UDWT),在小波影响锥(COI)分析的基础上,提出一种新的图像去噪方法,能够有效地去除脉冲噪声同时保护图像的边缘.该方法与传统小波阈值去噪法结合,可以很好地抑制高斯噪声和泊松噪声,甚至混合形式的噪声.实验结果证实了该方法的有效性.     

基于低秩结构提取的高光谱图像压缩表示

为实现高效、精准的高光谱图像分类,该文利用低秩矩阵恢复从原始数据中提取低维特征,实现高光谱图像的压缩表示。针对高光谱应用的特殊性,该文算法基于结构相似性度量(Structural Similarity Index Measurement, SSIM)对矩阵恢复过程提出了信噪分离约束,有助于选择更优的模型参数,增强表示的准确性。实验证明,相比现有相关方法,该文算法能够有效去除高光谱图像中的噪声,表示结果更为鲁棒;在仅使用低维特征时,仍能达到较高的分类精度。     

基于卷积神经网络的高光谱图像重建方法

为了提高高光谱图像的成像质量，满足应用需求，提出基于卷积神经网络的高光谱图像重建方法研究。通过预处理方式消除高光谱图像中的暗电流信息与噪声数据，以此为基础，获取高光谱图像SIFT特征，选择高光谱图像最优波段，最大限度地保留高光谱图像的波段特征，有效融合卷积神经网络构建高光谱图像重建模型，将最优波段高光谱图像数据输入至构建模型中，输出结果即为高光谱图像重建结果。实验数据显示：应用提出方法获得的评价指标MSE最小值为6,评价指标Q最大值为6.8,PSNR与SSIM最大值分别为40.349 dB与0.964 4,充分证实提出方法高光谱图像重建质量较佳。     

基于小波变换的超声图像去噪算法研究

在超声无损检测中,图像在生成和传输过程中常常因受到各种噪声的干扰和影响而质量下降,这对缺陷的识别和定位将产生不利影响。在对超声检测信号和噪声的种类及特点进行深入分析的基础上,运用小波变换阈值去噪的理论,对四种不同的噪声(高斯噪声、泊松噪声、椒盐噪声和斑点噪声),分别运用软阈值去噪法、硬阈值去噪法及NeighShrink去噪法进行去噪,发现NeighShrink去噪法去噪后的图像性噪比提高最多,边缘模糊也最小。用这三种去噪法对超声B扫图像进行去噪,验证了NeighShrink去噪法对于超声B扫图像具有最出色的去噪效果。     

利用期望最大化算法的EMCCD噪声分布模型的参数估计

讨论了电子倍增CCD（EMCCD）图像的噪声来源及其统计特性,建立了混合泊松-高斯噪声分布模型。针对混合泊松-高斯噪声分布模型的极大似然函数难以求解的问题,对噪声模型进行了适当的初始化设置,利用期望最大化算法对噪声模型进行参数估计,有效实现了噪声参数的极大似然估计。Monte Carlo仿真结果及实验结果表明,期望最大化算法估计性能较好,对混合泊松-高斯分布有较好的拟合效果,能得到较高精度的参数估计值。     

泊松噪声模糊图像的边缘保持变分复原算法

从贝叶斯估计出发,构造了一种新的变分模型,用于复原被泊松噪声污染的模糊图像.首先讨论了模型正则化项中具有边缘保持能力的函数选取以及模型求解的相关问题,然后将变分模型的求解转化为可快速求解的非线性扩散方程,给出了正则化参数选取的初步空间自适应方法,可以区分平滑区域和图像边缘自适应的调节参数.实验结果表明,本文方法的复原效果整体上优于传统的迭代正则化方法,复原图像的边缘得到了有效的保护,泊松噪声的抑制效果明显,复原图像提高的改进信噪比(ISNR)要比迭代正则化方法平均提高1 dB以上.     

A Proximal Iteration for Deconvolving Poisson Noisy Images Using Sparse Representations

We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key contributions are as follows. First, we handle the Poisson noise properly by using the Anscombe variance stabilizing transform leading to a nonlinear degradation equation with additive Gaussian noise. Second, the deconvolution problem is formulated as the minimization of a convex functional with a data-fidelity term reflecting the noise properties, and a nonsmooth sparsity-promoting penalty over the image representation coefficients (e.g., lscr₁ -norm). An additional term is also included in the functional to ensure positivity of the restored image. Third, a fast iterative forward-backward splitting algorithm is proposed to solve the minimization problem. We derive existence and uniqueness conditions of the solution, and establish convergence of the iterative algorithm. Finally, a GCV-based model selection procedure is proposed to objectively select the regularization parameter. Experimental results are carried out to show the striking benefits gained from taking into account the Poisson statistics of the noise. These results also suggest that using sparse-domain regularization may be tractable in many deconvolution applications with Poisson noise such as astronomy and microscopy.     

Multi-frame super-resolution reconstruction based on mixed Poisson–Gaussian noise

In this paper, a non-blind multi-frame super-resolution (SR) model based on mixed Poisson–Gaussian noise (MPGSR) is proposed. Poisson noise arises from the stochastic nature of the photon-counting process. Readout noise and reset noise inherent to the readout circuitry can be modeled by an additive Gaussian noise. Therefore, a mixed Poisson–Gaussian noise model is more appropriate for real imaging system. Instead of deriving the data fidelity term from the perspective of error norms and the corresponding influence functions, we address the multi-frame SR problem based on a statistical noise model. The derived objective function is decomposed into sub-functions and solved by the alternating direction method of multipliers (ADMM) algorithm which allows using techniques of constrained optimization. The validation of the proposed MPGSR was performed quantitatively and qualitatively on natural and X-ray images. In comparison to the optimization-based and learning-based state-of-the-art methods, we have demonstrated the feasibility of MPGSR and the significance of applying a more appropriate noise model on the SR image reconstruction.     

二阶Hopfield型神经网络的稳定性 分析及收敛速度的估计

本文讨论二阶连续Hopfield型神经网络平衡点的全局稳定性问题,利用LMI方法和Lyapunov方法得到了网络平衡点全局渐近稳定和全局指数稳定的几个充分条件,并对其指数收敛速度进行了估计.     

Learning-based image restoration for compressed images

In this paper, we propose a novel learning-based image restoration scheme for compressed images by suppressing compression artifacts and recovering high frequency (HF) components based upon the priors learnt from a training set of natural images. The JPEG compression process is simulated by a degradation model, represented by the signal attenuation and the Gaussian noise addition process. Based on the degradation model, the input image is locally filtered to remove Gaussian noise. Subsequently, the learning-based restoration algorithm reproduces the HF component to handle the attenuation process. Specifically, a Markov-chain based mapping strategy is employed to generate the HF primitives based on the learnt codebook. Finally, a quantization constraint algorithm regularizes the reconstructed image coefficients within a reasonable range, to prevent possible over-smoothing and thus ameliorate the image quality. Experimental results have demonstrated that the proposed scheme can reproduce higher quality images in terms of both objective and subjective quality.     

An adaptive spatial–spectral total variation approach for Poisson noise removal in hyperspectral images

Poisson distributed noise, such as photon noise, is an important noise source in multi- and hyperspectral images. We propose a variational-based denoising approach that accounts the vectorial structure of a spectral image cube, as well as the Poisson distributed noise. For this aim, we extend an approach initially developed for monochromatic images, by a regularisation term, which is spectrally and spatially adaptive and preserves edges. In order to take the high computational complexity into account, we derive a split Bregman optimisation for the proposed model. The results show the advantages of the proposed approach compared with a marginal approach on synthetic and real data.     

Multigrid tomographic inversion with variable resolution data and image spaces.

A multigrid inversion approach that uses variable resolutions of both the data space and the image space is proposed. Since the computational complexity of inverse problems typically increases with a larger number of unknown image pixels and a larger number of measurements, the proposed algorithm further reduces the computation relative to conventional multigrid approaches, which change only the image space resolution at coarse scales. The advantage is particularly important for data-rich applications, where data resolutions may differ for different scales. Applications of the approach to Bayesian reconstruction algorithms in transmission and emission tomography with a generalized Gaussian Markov random field image prior are presented, both with a Poisson noise model and with a quadratic data term. Simulation results indicate that the proposed multigrid approach results in significant improvement in convergence speed compared to the fixed-grid iterative coordinate descent method and a multigrid method with fixed-data resolution.     

Wavelet-domain filtering for photon imaging systems

Many imaging systems rely on photon detection as the basis of image formation. One of the major sources of error in these systems is Poisson noise due to the quantum nature of the photon detection process. Unlike additive Gaussian white noise, the variance of Poisson noise is proportional to the underlying signal intensity, and consequently separating signal from noise is a very difficult task. In this paper, we perform a novel gedankenexperiment to devise a new wavelet-domain filtering procedure for noise removal in photon imaging systems. The filter adapts to both the signal and the noise, and balances the trade-off between noise removal and excessive smoothing of image details. Designed using the statistical method of cross-validation, the filter is simultaneously optimal in a small-sample predictive sum of squares sense and asymptotically optimal in the mean-square-error sense. The filtering procedure has a simple interpretation as a joint edge detection/estimation process. Moreover, we derive an efficient algorithm for performing the filtering that has the same order of complexity as the fast wavelet transform itself. The performance of the new filter is assessed with simulated data experiments and tested with actual nuclear medicine imagery.