Image denoising via sparse coding using eigenvectors of graph Laplacian

Image denoising plays an important role in image processing, which aims to separate clean images from the noisy images. A number of methods have been presented to deal with this practical problem in the past decades. In this paper, a sparse coding algorithm using eigenvectors of the graph Laplacian (EGL-SC) is proposed for image denoising by considering the global structures of images. To exploit the geometry attributes of images, the eigenvectors of the graph Laplacian, which are derived from the graph of noised patches, are incorporated in the sparse model as a set of basis functions. Sequently, the corresponding sparse coding problem is presented and efficiently solved with a relaxed iterative method in the framework of the double sparsity model. Meanwhile, as the denoising performance of the EGL-SC significantly depends on the number of the used eigenvectors, an optimal strategy for the number selection is employed. A parameter called as out-of-control rate is set to record the percentage of the denoised patches that suffer from serious residual errors in the sparse coding procedure. Thus, with the eigenvector number increasing, the appropriate number can be heuristically selected when the out-of-control rate falls below an empirical threshold. Experiments illustrate that the EGL-SC can achieve a better performance than some other well-developed denoising methods, especially in the structural similarity index for the noise of large deviations.     

A numerical study of variable coefficient elliptic Cauchy problem via projection method

In this paper, we investigate a numerical method for the solution of an inverse problem of recovering lacking data on some part of the boundary of a domain from the Cauchy data on other part for a variable coefficient elliptic Cauchy problem. In the process, the Cauchy problem is transformed into the problem of solving a compact linear operator equation. As a remedy to the ill-posedness of the problem, we use a projection method which allows regularization solely by discretization. The discretization level plays the role of regularization parameter in the case of projection method. The balancing principle is used for the choice of an appropriate discretization level. Several numerical examples show that the method produces a stable good approximate solution.     

FUZZIFYING THE “PRECISE”

Based on the fuzzy-integral model, methods and algorithms are developed for identifying the “input–output” operator of continuous and stationary discrete extremal fuzzy dynamic systems (EFDS). The EFDS “input–output” operator is restored by means of experimental data with possibilistic uncertainty, the source of which is extremal fuzzy time intervals. The regularization conditions for obtaining quasi-optimal estimates are substantiated by the proved theorems. The corresponding algorithms are provided. The results obtained are illustrated by examples in the case of a finite set of EFDS states.     

多视图交叉一致性学习的半监督水面目标检测

为缓解基于半监督学习的水面目标检测对有限标注样本过拟合的问题，提高无标注样本中目标提取的有效性，提出了基于多视图交叉一致性学习的半监督水面目标检测算法。首先，该算法通过数据增强的方式为训练样本生成不同的视图以丰富数据集的多样性；然后，利用所提出的多视图目标判别器为无标注样本在线生成伪标签，有助于提取无标注样本的有效信息；最后，利用所提出的多视图交叉一致性学习使同一目标实例的不同视图的输出实现交叉一致性正则化，以促进检测模型学习判别性的特征从而降低过拟合的风险。在海上和内河数据集上的实验结果表明：文中所提算法能够提高特征提取的判别性，对多类别的水面目标检测精度达到91.0%,比全监督检测算法提高了18.7%,比其他半监督检测算法提高了3.8%以上；在检测速度上，该算法达到13.1帧/s,基本满足实时性要求。所提算法通过多视图交叉一致性学习提高特征的判别性和缓解检测模型的过拟合风险，有助于提高半监督水面目标检测的性能。     

Half supervised coefficient regularization for regression learning with unbounded sampling

In this study, we investigate the consistency of half supervised coefficient regularization learning with indefinite kernels. In our setting, the hypothesis space and learning algorithms are based on two different groups of input data which are drawn i.i.d. according to an unknown probability measure ρ _X . The only conditions imposed on the kernel function are the continuity and boundedness instead of a Mercer kernel and the output data are not asked to be bounded uniformly. By a mild assumption of unbounded output data and a refined integral operator technique, the generalization error is decomposed into hypothesis error, sample error and approximation error. By estimating these three parts, we deduce satisfactory learning rates with proper choice of the regularization parameter.     

Identification of diffusion parameters in a non-linear convection–diffusion equation using adaptive homotopy perturbation method

This paper is concerned with the numerical identification of diffusion parameters in a non-linear convection–diffusion equation, which arises as the saturation equation in the fractional flow formulation of the two-phase porous media flow equations. In order to overcome the defect of the local convergence of traditional methods, an adaptive homotopy perturbation method is applied to solve this parameter identification inverse problem. The adaptive homotopy perturbation method provides a simple way to adapt computational refinement to the choice of the homotopy parameter. Numerical simulations illustrate that the proposed algorithm is globally convergent and computationallyefficient.     

基于机器学习的音频分类

为施行有效的音频分类以高效率处理日渐复杂的音频信息,研究采用包含多种神经网络在内的5种机器学习模型,实现多种决策下的音频分类以寻找最优模型,基于分类准确度对各模型分类效果进行评估,在使用正则化方法保证模型泛化能力的条件下,通过比较和实验,挖掘并验证出了相对最优的模型——卷积神经网络音频分类模型及对应参数,为现有音频分类模型的进一步优化提供了参考方向。     

Optimization of multiple region quantizer for Laplacian source

This paper proposes a multiple region quantizer composed of quantizers defined on different disjunctive regions of an input signal. In particular, for the two region and the three region cases, the paper provides a complete optimization of a multiple region companded quantizer for the Laplacian source of unit variance. The analysis of the multiple region quantizer is limited to a three region case due to the complexity of the optimization problem and due to the fact that much more complex multiple region quantizer models obtained for a higher number of regions could slightly improve the performances. Two-stage optimization is performed with respect to the number of reconstruction levels of each quantizer composing the considered multiple region companded quantizer and with respect to the region bounds. It is shown that optimal parameters depend only on the fractional part of the required average bit rate. In order to design the three region optimal quantizer, Lloyd–Max's algorithm and Newton–Kantorovich iterative method are used with the three region optimal companded quantizer as the initial solution. The gradient Newton–Kantorovich iterative method is used to provide better convergence speed than Lloyd–Max's algorithm, which is essential in cases where effective initialization solution of Lloyd–Max's algorithm is missing. It is shown that the three region optimal companded quantizer have signal to quantization noise ratio value close to the one of the three region optimal quantizer, where a simpler design procedure is the benefit of the three region optimal companded quantizer over the three region optimal one.     

Gaussian-Hermite moment-based depth estimation from single still image for stereo vision

Depth information of objects plays a significant role in image-based rendering. Traditional depth estimation techniques use different visual cues including the disparity, motion, geometry, and defocus of objects. This paper presents a novel approach of focus cue-based depth estimation for still images using the Gaussian-Hermite moments (GHMs) of local neighboring pixels. The GHMs are chosen due to their superior reconstruction ability and invariance properties to intensity and geometric distortions of objects as compared to other moments. Since depths of local neighboring pixels are significantly correlated, the Laplacian matting is employed to obtain final depth map from the moment-based focus map. Experiments are conducted on images of indoor and outdoor scenes having objects with varying natures of resolution, edge, occlusion, and blur contents. Experimental results reveal that the depth estimated from GHMs can provide anaglyph images with stereo quality better than that provided by existing methods using traditional visual cues.