基于对数函数的非局部总变分图像修复模型

针对基于总变分最小化的图像修复模型容易造成阶梯效应及假边缘的问题,提出了基于对数函数的非局部总变分图像修复模型。新的总变分能量泛函的被积函数为一个关于梯度幅度的对数函数。在总变分模型与各向异性扩散模型的偏微分方程框架下,首先,从理论上证明了对数总变分模型满足良好扩散所需的所有性质,并对其局部扩散行为进行了理论分析,证明了其在等照度方向及梯度方向扩散的良好特性。其次,为考虑图像块的相似性及避免局部模糊,采用非局部对数总变分进行数值实现。实验结果表明,与经典的总变分修复模型相比,基于对数函数的非局部总变分模型对图像修复的效果良好,避免了局部模糊,且在图像平滑区域能较好地抑制阶梯效应;与基于样例的修复模型相比,所提模型对纹理图像能获得更为自然的修复效果。实验结果表明,与三类总变分模型和基于样例的修复模型相比,所提模型的性能最优,且与各对比模型的平均结果（图2、图3、图4）相比,其结构相似性指数（SSIM）分别提高了0.065、0.022和0.051,峰值信噪比（PSNR）分别提高了5.94 dB、4.00 dB和6.22 dB。含噪图像的修复结果表明所提模型具有较好的鲁棒性,对含噪声的图像也能获得良好的修复效果。     

Weighted and extended total variation for image restoration and decomposition

In various information processing tasks obtaining regularized versions of a noisy or corrupted image data is often a prerequisite for successful use of classical image analysis algorithms. Image restoration and decomposition methods need to be robust if they are to be useful in practice. In particular, this property has to be verified in engineering and scientific applications. By robustness, we mean that the performance of an algorithm should not be affected significantly by small deviations from the assumed model. In image processing, total variation (TV) is a powerful tool to increase robustness. In this paper, we define several concepts that are useful in robust restoration and robust decomposition. We propose two extended total variation models, weighted total variation (WTV) and extended total variation (ETV). We state generic approaches. The idea is to replace the TV penalty term with more general terms. The motivation is to increase the robustness of ROF (Rudin, Osher, Fatemi) model and to prevent the staircasing effect due to this method. Moreover, rewriting the non-convex sublinear regularizing terms as WTV, we provide a new approach to perform minimization via the well-known Chambolle's algorithm. The implementation is then more straightforward than the half-quadratic algorithm. The behavior of image decomposition methods is also a challenging problem, which is closely related to anisotropic diffusion. ETV leads to an anisotropic decomposition close to edges improving the robustness. It allows to respect desired geometric properties during the restoration, and to control more precisely the regularization process. We also discuss why compression algorithms can be an objective method to evaluate the image decomposition quality.     

Total variation constraint GAN for dynamic scene deblurring

Recovering the sharp image solely from the blurry image in dynamic scene is challenging due to the ill-defined nature of the problem. Through Wasserstein distance and L₁ norm of total variation combined regularization, we propose a novel TV-DRGAN optimization framework to obtain a latent sharp image from some observed blurry images. Our method benefits from two aspects: one is the improved object total variation energy to constrain the blurry image, and the other is the generator model combining (UPR)-Blocks and D-Blocks. An (UPR)-Block is composed of one upsampling layer and 3 convolution layers. Consisting of an average-pooling layer and multiple convolution layers, a D-Block comes with different kernel sizes that capture global, and local spatial information of the raw image, separately. By analyzing the information of gradient, we obtain a TV-based based on minimum lower bound of loss function of the generator. Our experiments show that the proposed method outperforms the state-of-the-art conventional algorithms significantly.     

基于非凸全变差正则的核磁共振图像重构算法

针对于核磁共振（MR）图像重构中由于欠采样导致的重构图像不够完整、边缘模糊以及噪声残留等问题,提出了一种基于L₂正则的非凸全变差正则重构模型。首先,以Moreau包络和最小最大凹罚函数为工具构造L₂范数的非凸正则;然后,将其应用于全变差正则上来构造各向同性的非凸全变差正则稀疏重构模型。所提的非凸正则可以有效地避免凸正则中对较大非零元欠估计现象,能够更有效地重构目标的边缘轮廓;同时,在一定条件下可以保证目标函数的整体凸性,从而最后可以利用交替方向乘子法（ADMM）对模型进行求解。仿真实验对若干MR图像在不同的采样模板和采样率下进行了重构。实验结果均表明,与几种典型的图像重构方法相比,所提模型性能更优,相对误差明显降低,峰值信噪比（PSNR）有明显改善,较经典的L₁非凸正则重构模型提升了大约4 dB,并且重构后的图像视觉效果显著提升,有效地保留了原始图像的边缘细节。     

彩色图约束的二阶广义总变分深度图超分辨率重建

目的 针对深度图像分辨率非常低的问题,结合同场景高分辨率彩色图像,提出一种基于彩色图约束的二阶广义总变分深度图超分辨率重建方法。方法 首先将低分辨率深度图映射到高分辨率彩色空间;然后利用二阶广义总变分模型,将带有边缘指示函数的高分辨率彩色约束项作为正则项,使得深度图像超分辨率重建问题变成最优求解问题;最后通过迭代重加权和原—对偶方法进行求解。结果 实验结果表明,本文方法可以有效地保护图像的边缘结构,在定性和定量两个方面都可达到很好的效果。结论 本文方法可以有效地解决深度图分辨率非常低的问题。     

自适应阈值HMRF模型超分辨率重建

针对Huber-Markov随机场作为图像先验进行MAP超分辨率重建时先验约束的有效性问题,通过分析重建过程中Huber惩罚函数与图像空间灰度变化分布特性的相互关系,提出一种根据图像空间灰度变化统计特性,在超分辨率重建迭代过程中动态确定Huber函数阈值的方法。实验结果表明,该方法可根据不同图像的边缘特性,自适应确定Huber惩罚函数阈值,在有效抑制噪声的同时,保持重建图像的边缘和细节信息。     

改进的整体变分模型在视频图像修补上的应用

改进了经典的图像修补变分模型,既考虑了图像区域中梯度不同给图像修补带来的不同影响,同时兼顾了视觉心理学对图像效果的影响。提出了新的变分泛函,给出了相应的欧拉-拉格朗日方程。将此模型应用到静态的图像上,和原来的模型在图像修补效果上进行了对比。将此图像修补模型应用到视频修补问题上,从一个新的角度,在两帧图像之间以增加一帧,把目标放在相应位置,形成新帧,使人物动作连贯,达到更好的视频图像的修补效果。     

非局部的变分正则化图像放大算法

针对Chambolle图像放大模型存在分块效应,提出一种非局部的变分正则化图像放大算法。该算法的思想是构造一个适用于图像放大的变分泛函,该泛函由正则项和数据保真项构成,其中图像的正则项是用非局部全变差范数进行估计,进而用迭代投影方法求泛函的最小解,即为放大后的图像。与传统的图像插值方法不同,该算法是用变分的思想进行图像放大,非局部全变差的引入更使得该算法不只是利用图像的单个像素点,或某一邻域内的灰度和梯度信息进行放大,而是更大范围地利用了图像本身的信息,这将更有效地保留图像特征,避免了Chambolle方法在图像放大时出现的分块效应。实验结果表明,该算法能更好地保留边缘和细节信息,放大图像的清晰度比Chambolle图像放大方法和样条插值的效果要好。     

基于张量总变分的模糊图像盲复原

现有模糊图像盲复原算法通常仅利用彩色图像的灰度信息估计模糊核,彩色图像转换成灰度图像的操作会造成信息丢失,在处理尺寸过小或显著边缘过少的图像时,模糊核的估计通常会失效,导致最后复原图像的质量不理想。针对上述问题,在新的张量框架下,把彩色模糊图像作为一个三阶张量,提出了一种基于张量总变分的模糊图像盲复原算法。首先通过调整张量总变分模型中的正则化参数获取彩色图像不同尺度的边缘信息,从而估计出模糊核;再利用张量总变分算法对模糊图像解模糊,复原出清晰图像。实验结果表明,所提算法得到的复原图像在峰值信噪比（PSNR）和主观视觉上均得到明显改善。     

Infrared dim target detection based on total variation regularization and principal component pursuit

Robust detection of infrared dim and small target contributes significantly to the infrared systems in many applications. Due to the diversity of background scene and unique characteristic of target, the detection of infrared targets remains a challenging problem. In this paper, a novel approach based on total variation regularization and principal component pursuit (TV-PCP) is presented to deal with this problem. The principal component pursuit model only considers the low-rank feature of background images, which will result in poor detection ability in non-uniform and non-smooth scenes. We take into account the total variation regularization term to thoroughly describe background feature, which can achieve good detection result as well as good background estimation result. Firstly, the input infrared image is transformed to a patch image model. Secondly, the TV-PCP model is presented on the patch image. An effective optimization algorithm is proposed to solve this model. Experiments on six real datasets show that the proposed method has superior detection ability under various backgrounds, especially with good background suppression performance and low false alarm rate.     

Stochastic ranking for constrained evolutionary optimization

Penalty functions are often used in constrained optimization. However, it is very difficult to strike the right balance between objective and penalty functions. This paper introduces a novel approach to balance objective and penalty functions stochastically, i.e., stochastic ranking, and presents a new view on penalty function methods in terms of the dominance of penalty and objective functions. Some of the pitfalls of naive penalty methods are discussed in these terms. The new ranking method is tested using a (μ, λ) evolution strategy on 13 benchmark problems. Our results show that suitable ranking alone (i.e., selection), without the introduction of complicated and specialized variation operators, is capable of improving the search performance significantly     

SAR image reconstruction and autofocus by compressed sensing

A new SAR signal processing technique based on compressed sensing is proposed for autofocused image reconstruction on subsampled raw SAR data. It is shown that, if the residual phase error after INS/GPS corrected platform motion is captured in the signal model, then the optimal autofocused image formation can be formulated as a sparse reconstruction problem. To further improve image quality, the total variation of the reconstruction is used as a penalty term. In order to demonstrate the performance of the proposed technique in wide-band SAR systems, the measurements used in the reconstruction are formed by a new under-sampling pattern that can be easily implemented in practice by using slower rate A/D converters. Under a variety of metrics for the reconstruction quality, it is demonstrated that, even at high under-sampling ratios, the proposed technique provides reconstruction quality comparable to that obtained by the classical techniques which require full-band data without any under-sampling.     

改进的二阶总广义变分图像前后景分割模型

针对总变分TV图像前后景分割模型易导致阶梯效应的缺陷,提出了二阶总广义变分TGV图像前后景分割模型。为进一步提升图像分割质量,在TGV前后景分割模型的正则项中引入边缘指示函数,使其在图像边缘区域减弱扩散,较好地保护边缘;在图像平滑区域增强扩散,有效地消除噪声。为突出前景信息,用矩形框标出图像的前景信息,对框内部、外部和边缘的像素做距离映射,并根据能量最小化原则,在二阶TGV模型的数据项中引入此距离映射函数,使模型总能量更小。最后,提出了一种有效的原始对偶分割算法来求解模型。实验表明,新模型不但能够去除阶梯效应现象,保持图像的边缘信息,还使得模型总能量更小,分割得到的图像视觉效果更好。     

Constrained Dimensionality Reduction Using a Mixed-Norm Penalty Function with Neural Networks

Reducing the dimensionality of a classification problem produces a more computationally-efficient system. Since the dimensionality of a classification problem is equivalent to the number of neurons in the first hidden layer of a network, this work shows how to eliminate neurons on that layer and simplify the problem. In the cases where the dimensionality cannot be reduced without some degradation in classification performance, we formulate and solve a constrained optimization problem that allows a trade-off between dimensionality and performance. We introduce a novel penalty function and combine it with bilevel optimization to solve the constrained problem. The performance of our method on synthetic and applied problems is superior to other known penalty functions such as weight decay, weight elimination, and Hoyer's function. An example of dimensionality reduction for hyperspectral image classification demonstrates the practicality of the new method. Finally, we show how the method can be extended to multilayer and multiclass neural network problems.     

单位法向量引导的自适应医学图像分割新算法

水平集方法已经广泛应用于图像分割,ChunmingLi等人早期的模型通过在能量方程中引入惩罚项可以避免重新初始化。但惩罚项中的函数会引起扩散率趋于无穷大的问题,因此ChumningLi等人通过改进惩罚项中的函数,解决了扩散率的问题。针对新模型采用高斯滤波去除图像噪声使图像边缘变模糊的问题,采用正则化的P-M方程滤波,去除噪声的同时保护图像边缘信息。同时,新模型仍然不能实现自适应分割。通过初始曲线内外梯度模值的信息改变曲线内法向量的方向,从而使曲线自适应地向内或者向外演化。最后,用改进的算法准确地提取出了医学图像的轮廓,算法的效率也有很大的提高。     

基于交叠组合稀疏高阶全变分的图像复原

针对传统全变分进行扩展,提出了一种高阶全变分结合交叠组合稀疏的新算法,将像素级别梯度信息推广为高阶交叠组合稀疏梯度信息,更好地抑制了因全变分产生的阶梯效应并保存了图像边缘等细节信息。为了解决提出的图像复原新算法的优化问题,采用交替方向乘子算法（ADMM）来交替求解优化问题。将提出的新算法与其他几种相关算法相比,并用峰值信噪比（PSNR）和结构相似性（SSIM）两个评价指标来评价图像复原后的质量,从而论证了新算法的优越性。     

基于图像结构纹理分解及局部总变分最小化的图像修复模型

在基于样例的图像修复算法中,由于优先权公式的计算容易受图像局部噪声和细小纹理的干扰,导致修复顺序错乱;而在搜索最优匹配块时,因忽略了图像块内部的结构影响,可能导致误匹配。针对以上问题提出了一种基于图像的结构-纹理分解及局部总变分最小化的图像修复模型。首先,根据对数总变分最小化模型,将待修复图像进行结构-纹理分解,得到图像的结构分量,并利用图像的结构分量来计算待修复点优先权,使优先权的计算排除局部纹理干扰而更具鲁棒性;其次,将优先权的计算改进为数据项和置信项的加权和,避免了乘积效应,确保数据项一直发挥作用,减少因修复顺序不合理造成的错误匹配;最后,根据图像的局部总变分最小化原则,将图像块的最优匹配转换为0-1优化问题,确保图像修复后的局部结构一致性。与3组参考文献的5组对比实验结果表明,峰值信噪比（PSNR）提高了1.12~3.56 dB,结构相似性指数提高了0.02~0.04。所提模型更好地遵循了修复优先性原则,具有更强的保持图像局部结构一致性的能力,改善了修复图像的视觉效果,适用于复杂结构的大面积毁损的图像的修复。     

改进的二阶总广义变分图像去噪算法

为了有效地去除含噪图像中的噪声,克服总变分（TV）去噪易于导致阶梯效应的缺陷,提出了一种改进的二阶总广义变分（TGV）的图像去噪方法。介绍了二阶TGV的理论基础,在二阶TGV中引入了各向异性扩散张量,利用张量函数引导扩散,获得了新的去噪模型,最后提出了一种扩展了的原始-对偶算法对新模型进行数值求解。新模型充分结合了二阶TGV作为正则项自动平衡了一阶和二阶导数项,以及张量函数的各向异性扩散,有效突出边缘结构的特性。实验结果表明,该方法在有效地去除含噪图像中噪声的同时,避免了阶梯效应,增强了对原始图像中边缘结构的保持。     

基于总变分的超分辨率图像重建

超分辨率图像重建是指从一组降晰的低分辨率图像重建出一帧清晰的高分辨率图像的过程。建立了超分辨率图像重建的数学模型,估计出场景在观测图像中的运动参数,选择总变分规整化克服问题的病态性得到重建结果。运用算法对模拟和实际图像序列进行重建,分别从主观效果和客观衡量标准两方面与基于Tikhonov规整化的超分辨率重建结果进行比较,结果表明该算法具有更好的处理效果。     

基于整体变分模型的岩心图像修复

针对岩心扫描图像信息缺失的修复问题,提出了基于整体变分模型的修复算法。利用图像待修复区域邻域的参考像素信息,从待修复区域边缘逐步向待修复区域内部扩散,同时采用了邻域相关系数来衡量待修复区域邻域边界对目标像素点的影响程度,对算法进行了改进。通过仿真实验表明,改进后的算法与原方法相比,修复效果得到了改善,可以有效完成对于岩心图像的修复。