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.     

Maximum entropy image reconstruction from sparsely sampled coherentfield data

There are many practical problems in which it is required to detect and characterize hidden structures or remote objects by virtue of the scattered acoustic or electromagnetic fields they generate. It remains an open question, however, as to which reconstruction algorithms offer the most informative images for a given set of field measurements. Commonly used time-domain beamforming techniques, and their equivalent frequency-domain implementations, are conceptually simple and stable in the presence of noise, however, large proportions of missing measurements can quickly degrade the image quality. We apply a new algorithm based on the maximum entropy method (MEM) to the reconstruction of images from sparsely sampled coherent field data. The general principles and limitations of the new method are discussed in the framework of regularization theory, and the results of monostatic imaging experiments confirm that superior resolution and artifact suppression are obtained relative to a commonly used linear inverse filtering approach     

Regularization of noisy ISAR images containing extended features

We present a regularization method that employs a cross-entropy functional and which deals with the three issues of complex-valued data, prior information, and noise mitigation. The basic model of this approach is similar to that used in usual maximum a posteriori analysis and allows for a more general relationship between the image and its configuration entropy than that usually employed.     

Edge-preserving tomographic reconstruction with nonlocal regularization

Tomographic image reconstruction using statistical methods can provide more accurate system modeling, statistical models, and physical constraints than the conventional filtered backprojection (FBP) method. Because of the ill posedness of the reconstruction problem, a roughness penalty is often imposed on the solution to control noise. To avoid smoothing of edges, which are important image attributes, various edge-preserving regularization methods have been proposed. Most of these schemes rely on information from local neighborhoods to determine the presence of edges. In this paper, we propose a cost function that incorporates nonlocal boundary information into the regularization method. We use an alternating minimization algorithm with deterministic annealing to minimize the proposed cost function, jointly estimating region boundaries and object pixel values. We apply variational techniques implemented using level-sets methods to update the boundary estimates; then, using the most recent boundary estimate, we minimize a space-variant quadratic cost function to update the image estimate. For the positron emission tomography transmission reconstruction application, we compare the bias-variance tradeoff of this method with that of a "conventional" penalized-likelihood algorithm with local Huber roughness penalty.     

Super resolution image reconstruction through bregman iteration using morphologic regularization

Multiscale morphological operators are studied extensively in the literature for image processing and feature extraction purposes. In this paper, we model a nonlinear regularization method based on multiscale morphology for edge-preserving super resolution (SR) image reconstruction. We formulate SR image reconstruction as a deblurring problem and then solve the inverse problem using Bregman iterations. The proposed algorithm can suppress inherent noise generated during low-resolution image formation as well as during SR image estimation efficiently. Experimental results show the effectiveness of the proposed regularization and reconstruction method for SR image.     

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.     

Fast maximum entropy approximation in SPECT using the RBI-MAP algorithm

In this work, we present a method for approximating constrained maximum entropy (ME) reconstructions of SPECT data with modifications to a block-iterative maximum a posteriori (MAP) algorithm. Maximum likelihood (ML)-based reconstruction algorithms require some form of noise smoothing. Constrained ME provides a more formal method of noise smoothing without requiring the user to select parameters. In the context of SPECT, constrained ME seeks the minimum-information image estimate among those whose projections are a given distance from the noisy measured data, with that distance determined by the magnitude of the Poisson noise. Images that meet the distance criterion are referred to as feasible images. We find that modeling of all principal degrading factors (attenuation, detector response, and scatter) in the reconstruction is critical because feasibility is not meaningful unless the projection model is as accurate as possible. Because the constrained ME solution is the same as a MAP solution for a particular value of the MAP weighting parameter, beta, the constrained ME solution can be found with a MAP algorithm if the correct value of beta is found. We show that the RBI-MAP algorithm, if used with a dynamic scheme for estimating beta, can approximate constrained ME solutions in 20 or fewer iterations. We compare results for various methods of achieving feasible images on a simulation of Tl-201 cardiac SPECT data. Results show that the RBI-MAP ME approximation provides images and quantitative estimates close to those from a slower algorithm that gives the true ME solution. Also, we find that the ME results have higher spatial resolution and greater high-frequency noise content than a feasibility-based stopping rule, feasibility-based low-pass filtering, and a quadratic Gibbs prior with beta selected according to the feasibility criterion. We conclude that fast ME approximation is possible using either RBI-MAP with the dynamic procedure or a feasibility-based stopping rule, and that such reconstructions may be particularly useful in applications where resolution is critical.     

Sparsity-driven reconstruction for FDOT with anatomical priors

In this paper we propose a method based on (2, 1)-mixed-norm penalization for incorporating a structural prior in FDOT image reconstruction. The effect of (2, 1)-mixed-norm penalization is twofold: first, a sparsifying effect which isolates few anatomical regions where the fluorescent probe has accumulated, and second, a regularization effect inside the selected anatomical regions. After formulating the reconstruction in a variational framework, we analyze the resulting optimization problem and derive a practical numerical method tailored to (2, 1)-mixed-norm regularization. The proposed method includes as particular cases other sparsity promoting regularization methods such as l(1)-norm penalization and total variation penalization. Results on synthetic and experimental data are presented.     

基于最大熵阈值分割的SAR图像溢油检测

近年来,海上溢油事故频发,使用(合成孔径雷达)SAR遥感图像进行溢油检测有着十分重要的意义。本文提出了一种基于最大熵阈值分割的SAR图像溢油检测算法,算法运算简单,适用于星载平台,可实现高效准确的检测。由于SAR成像存在固有的相干斑噪声,首先需要进行滤波对噪声进行抑制。图像中存在的陆地区域会对溢油检测产生影响,通过先验知识利用经纬度信息对其进行掩模处理,之后采用滑动窗口的方法,在窗口内部基于最大熵选取最佳的分割阈值,最后对分割产生的小块区域进行滤除,并依据距离信息合并相邻的区域。算法使用GF-3卫星图像进行验证测试,并与其他算法对比表明,本算法可满足遥感图像检测实时性、准确性的要求。      

基于非局部相似度约束的多通道复用压缩遥感成像方法

结合压缩感知成像原理和遥感成像系统的物理可实现性,提出了采用掩膜编码的多通道复用压缩成像方法。首先,采用多组随机二值伯努利分布的掩膜为不同光学通道视场进行压缩编码,在单位积分时间内采集一帧图像重构所需欠采样数据。然后,针对传统的全变分范数最小化的重构方法易受遥感图像局部突出特征干扰的问题,提出了以遥感图像空间域非局部相似度为正则化重构标准的先验约束。实验结果验证了本文提出的压缩成像方法的可行性。与传统算法相比,本文提出的重构算法能够在保留图像细节的同时实现快速有效重构。     

基于非局部相似度约束的多通道复用压缩遥感成像方法

结合压缩感知成像原理和遥感成像系统的物理可实现性,提出了采用掩膜编码的多通道复用压缩成像方法.首先,采用多组随机二值伯努利分布的掩膜为不同光学通道视场进行压缩编码,在单位积分时间内采集重构图像所需的欠采样数据.然后,针对传统的全变分范数最小化的重构方法易受遥感图像局部突出特征干扰的问题,提出了以遥感图像空间域非局部相似度为正则化重构标准的先验约束.实验结果验证了此压缩成像方法的可行性.与传统算法相比,此重构算法能够在保留图像细节的同时实现有效重构.     

基于SP-LSQR的综合孔径辐射成像方法

综合孔径微波辐射计是被动微波遥感领域中一种重要的探测器。综合孔径辐射计成像反演过程在数学上是病态的反问题,传统正则化方法虽然能够有效克服其病态性,但重构误差较大、对干扰噪声鲁棒性不强。与传统正则化方法相比,最小二乘Q-R矩阵(Least Square Q-R matrix, LSQR)分解算法具有计算精度高、数值稳定性好等优点,但收敛速度不够快。对此,文中提出利用子空间预处理LSQR(Subspace Preconditioned LSQR, SP-LSQR)算法进行综合孔径辐射计反演成像,提高收敛速度。仿真结果表明：与Tikhonov正则化和带限正则化相比,SP-LSQR方法不仅可以降低重构误差,而且对干扰噪声的鲁棒性更强。此外,与LSQR方法相比,SP-LSQR方法在不降低成像反演精度的情况下,有效提高了计算效率。     

Spatially adaptive high-resolution image reconstruction of DCT-based compressed images

The problem of recovering a high-resolution image from a sequence of low-resolution DCT-based compressed observations is considered in this paper. The introduction of compression complicates the recovery problem. We analyze the DCT quantization noise and propose to model it in the spatial domain as a colored Gaussian process. This allows us to estimate the quantization noise at low bit-rates without explicit knowledge of the original image frame, and we propose a method that simultaneously estimates the quantization noise along with the high-resolution data. We also incorporate a nonstationary image prior model to address blocking and ringing artifacts while still preserving edges. To facilitate the simultaneous estimate, we employ a regularization functional to determine the regularization parameter without any prior knowledge of the reconstruction procedure. The smoothing functional to be minimized is then formulated to have a global minimizer in spite of its nonlinearity by enforcing convergence and convexity requirements. Experiments illustrate the benefit of the proposed method when compared to traditional high-resolution image reconstruction methods. Quantitative and qualitative comparisons are provided.     

基于边缘定向扩散方程的图像复原方法

讨论了光学图像中同时存在噪声与模糊时的复原问题。采用一种能根据边缘方向自适应选取扩散系数的各向异性扩散方程来约束复原后的图像的光滑性质,将其和图像复原模型一起使用,得到了一种图像复原的正则化模型,并利用Eluer方程将该模型转换成一种可以快速求解的各向异性非线性扩散模型。在光滑性约束项的构造上,构造了一种基于边缘定向扩散的各向异性张量型扩散方程,能有效地根据边缘的方向确定是增强边缘还是滤除噪声。相比图像复原的迭代正则化方法,新方法能在复原图像的同时有效地抑制噪声,并有效地减轻边缘处的振铃效应。数值计算结果表明,新方法在整幅图像的复原效果上明显强于迭代正则化方法,尤其在对背景噪声的抑制上效果更明显,峰值信噪比（PSNR）也比迭代正则化方法平均提高了约2dB。     

otal curvature (TC) model and its alternating direction method of multipliers algorithm for noise removal

This paper develops a variational model for image noise removal using total curvature (TC), which is a high-order regularizer. The TC has the advantage of preserving image feature. Unfortunately, it also has the characteristics of nonlinear, non-convex and non-smooth. Consequently, the numerical computation with the curvature regularization is difficult. In order to conquer the computation problem, the proposed model is transformed into an alternating optimization problem by importing auxiliary variables. Furthermore, based on alternating direction method of multipliers, we design a fast numerical approximation iterative scheme for proposed model. Finally, numerous experiments are implemented to indicate the advantages of the proposed model in image edge preserving, image contrast and corners preserving. Meanwhile, the high computational efficiency of the designed model is verified by comparing with traditional models, including the total variation (TV) and total Laplace (TL) model.     

基于空谱联合和波段分类的高光谱压缩感知重构

卫星在获取地面信息时会受到大气、电磁波的干扰,导致高光谱影像本身产生坏线和噪声。针对这一问题,本文结合高光谱遥感影像的特性提出了一种基于空谱联合和波段分类的影像重构方法。首先,根据噪声影响程度将影像波段分为坏线强干扰波段和非干扰低噪声波段;其次,对波段进行分组,确定每组参考波段,并对参考波段进行独立重构;然后,根据参考波段构建双模式空谱联合预测模型,利用正则化交叉投影得到非参考波段重构影像;最后,对坏线强干扰波段,先进行独立重构,然后对重构影像进行小波分解,通过高频校正得到了干扰波段最终重构影像。实验表明,本文方法对重构高光谱影像的平均信噪比较传统方法提高了1~2dB。     

网格梯度曲率模型零度Metropolis-Hastings遥感图像缺失重建

针对矩形网格遥感图像可微随机域数据缺失重建过程中,存在重建效果不佳且计算效率不高的问题,提出一种网格化全局几何约束零度Metropolis-Hastings遥感图像缺失数据随机重建算法.首先,构建遥感图像的随机梯度-曲率重建模型,通过全局几何约束相互作用随机场模型,匹配整个网格样本的梯度和曲率,从而满足蒙特卡罗模拟应用条件;其次,采用蒙特卡罗算法改进版本零度Metropolis-Hastings算法,实现遥感图像缺失数据重建,该方式不承担对底层数据的概率分布参数描述,有助于降低用户参与度,提高计算效率,适用大型遥感图像数据集的无监督自动处理;最后,通过与其他分类或插值方法实验对比显示,所提算法在数据重建效果和计算效率上均要优于对比算法.     

A super-resolution reconstruction algorithm for hyperspectral images

The spatial resolution of a hyperspectral image is often coarse because of the limitations of the imaging hardware. Super-resolution reconstruction (SRR) is a promising signal post-processing technique for hyperspectral image resolution enhancement. This paper proposes a maximum a posteriori (MAP) based multi-frame super-resolution algorithm for hyperspectral images. Principal component analysis (PCA) is utilized in both parts of the proposed algorithm: motion estimation and image reconstruction. A simultaneous motion estimation method with the first few principal components, which contain most of the information of a hyperspectral image, is proposed to reduce computational load and improve motion field accuracy. In the image reconstruction part, different image resolution enhancement techniques are applied to different groups of components, to reduce computational load and simultaneously remove noise. The proposed algorithm is tested on both synthetic images and real image sequences. The experimental results and comparative analyses verify the effectiveness of this algorithm.     

A convex variational method for super resolution of SAR image with speckle noise

Super resolution (SR) is an attractive issue in image processing. In the synthetic aperture radar (SAR) image, speckle noise is a crucial problem that is multiplicative. Therefore, numerous custom SR methods considering additive Gaussian noise cannot respond to this image degradation model. The main contribution of this paper is to propose a novel variational convex optimization model for the single SAR image SR reconstruction with speckle noise that is one of the first works in this field. Employing maximum a posteriori (MAP) estimator and proposing an effective regularization based on combination of sparse representation, total variation (TV) and a novel feature space based soft projection tool to use merits of them is the main idea. To solve the proposed model, the split Bregman algorithm is employed efficiently. Experimental results for the multiple synthetic and realistic SAR images show the effectiveness of proposed method in terms of both fidelity and visual perception.