Bayesian sparse hierarchical model for image denoising

Sparse models and their variants have been extensively investigated, and have achieved great success in image denoising. Compared with recently proposed deep-learning-based methods, sparse models have several advantages: (1) Sparse models do not require a large number of pairs of noisy images and the corresponding clean images for training. (2) The performance of sparse models is less reliant on the training data, and the learned model can be easily generalized to natural images across different noise domains. In sparse models, ${\ell }_0$ norm penalty makes the problem highly non-convex, which is difficult to be solved. Instead, ${\ell }_1$ norm penalty is commonly adopted for convex relaxation, which is considered as the Laplacian prior from the Bayesian perspective. However, many previous works have revealed that ${\ell }_1$ norm regularization causes a biased estimation for the sparse code, especially for high-dimensional data, e.g., images. In this paper, instead of using the ${\ell }_1$ norm penalty, we employ an improper prior in the sparse model and formulate a hierarchical sparse model for image denoising. Compared with other competitive methods, experiment results show that our proposed method achieves a better generalization for images with different characteristics across various domains, and achieves state-of-the-art performance for image denoising on several benchmark datasets.     

基于稀疏分解的指静脉图像去噪

手指静脉识别技术因其独特的优势,受到广泛的关注。然而由硬件系统获取的手指静脉图像常常含有严重的噪声、阴影等问题,所以对低质量的静脉图像的去噪成为了整个识别过程的关键。本文提出了一种基于稀疏分解的指静脉图像去噪新方法。基于稀疏分解的图像去噪是将含有噪声的图像信息进行稀疏分解,分解成稀疏成分和其他成分。其中的稀疏部分是有用信息,其他部分被认为是噪声,再由图像的稀疏部分重建原始信号,达到恢复原始信号并去除噪声的效果。本文根据指静脉图像的静脉的特点,应用高斯函数构造了过完备库。用合成图像和真实指静脉图像分别对新算法进行实验验证。实验结果证明,与传统的去噪算法相比,峰值信噪比提高1-2dB。      

Efficient time domain threshold for sparse channel estimation in OFDM system

A novel efficient time domain threshold based sparse channel estimation technique is proposed for orthogonal frequency division multiplexing (OFDM) systems. The proposed method aims to realize effective channel estimation without prior knowledge of channel statistics and noise standard deviation within a comparatively wide range of sparsity. Firstly, classical least squares (LS) method is used to get an initial channel impulse response (CIR) estimate. Then, an effective threshold, estimated from the noise coefficients of the initial estimated CIR, is proposed. Finally, the obtained threshold is used to select the most significant taps. Theoretical analysis and simulation results show that the proposed method achieves better performance in both BER (bit error rate) and NMSE (normalized mean square error) than the compared methods has good spectral efficiency and moderate computational complexity.     

自适应稀疏约束图像超分辨力重建方法

简要介绍了基于稀疏字典约束的超分辨力重建算法,提出了具有低复杂度的基于K均值聚类的自适应稀疏约束图像超分辨力重建算法。所提算法从两个方面降低其计算复杂度:分类训练字典,对图像块归类重建,降低每个图像块所用字典的大小;对图像块的特征进行分析,自适应地选择重建方法。实验结果表明,提出的快速重建方法在重建质量与原算法相当的前提下,可以较大程度地降低重建时间。     

Halftoning-based Block Truncation Coding image restoration

This paper presents a new image restoration method for improving the quality of halftoning-Block Truncation Coding (BTC) decoded image in a patch-based manner. The halftoning-BTC decoded image suffers from the halftoning impulse noise which can be effectively reduced and suppressed using the Vector Quantization (VQ)-based and sparsity-based approaches. The VQ-based approach employs the visual codebook generated from the clean image, whereas the sparsity-based approach utilizes the double learned dictionaries in the noise reduction. The sparsity-based approach assumes that the halftoning-BTC decode image and clean image share the same sparsity coefficient. In the sparse coding stage, it uses the halftoning-BTC dictionary, while in the reconstruction stage, it exploits the clean image dictionary. As suggested by the experimental results, the proposed method outperforms in the halftoning-BTC image reconstructed when compared to that of the filtering approaches.     

InSAR通道联合稀疏贝叶斯特征化成像

针对干涉合成孔径雷达(InSAR)成像,该文提出了一种通道联合结构化稀疏的贝叶斯成像算法,可实现图像稀疏特征化增强,以提升干涉相位噪声滤波和相干斑抑制性能。基于贝叶斯准则,利用多层级统计模型建立稀疏成像模型,结构化稀疏表示InSAR图像。在稀疏成像求解中,利用最大期望(EM)算法进行图像重构和多层级统计参数估计。由于能够联合利用通道稀疏统计特性,所提算法能够有效提升InSAR幅度和相位噪声滤波性能。最后,通过实验分析进一步验证该文算法的有效性。      

可见光与红外图像结构组双稀疏融合方法研究

传统的可见光与红外稀疏表示融合方法,采用图像块构造解析字典或者学习字典,利用字典的原子表征图像的显著特征。这类方法存在两个问题,一是没有考虑图像块与块之间的联系,二是字典的适应能力不够并且复杂度高。针对这两个问题,本文提出可见光与红外图像结构组双稀疏融合方法。该方法首先利用图像的非局部相似性,将图像块构建成图像相似结构组,然后对图像相似结构组进行字典训练,采用双稀疏分解模型,有效结合解析字典和学习字典的优势,降低了字典训练的复杂度,得到的结构字典更加灵活,适应性提高。该方法能够有效提高红外与可见光融合图像的视觉效果,经对比实验分析,在主观和客观评价上都优于传统的稀疏表示融合方法。     

融合图像块低维流形特性与解析轮廓波稀疏性的压缩成像算法

基于图像的整体稀疏表示和图像块的局部特性,融合图像块低维流形特性和整幅图像在解析轮廓波表示下的稀疏性两种先验知识,该文提出了一种高质量压缩成像算法。该算法利用迭代硬阈值法和流形投影法重构图像。为减小运算复杂度,该文用多个线性子流形的并集来近似表示包含所有图像块的非线性流形,并根据图像块的主方向进行初始分类后再用稀疏正交变换获得各线性子空间的基。实验结果表明,该文算法的重构图像在峰值信噪比和视觉效果两方面均有显著提高。     

非局部学习字典的图像修复

该文提出一种新的基于学习的图像修复算法。与经典的稀疏表示模型不同,该文将非局部自相似图像块统一进行联合稀疏表示,训练高效的学习字典,并使自相似块间保持相同的稀疏模式。该方法既确保自相似块投影到稀疏空间后也具有相似性,也较好地保留了自相似块间的相关性信息,更有效地建立了它们的联合稀疏关联,并将这种关联作为先验知识来指导图像的修复。该算法使用大量自然图像样本来训练初始的过完备字典,既利用了样本图像的先验知识,又充分考虑了待处理图像本身的相关信息,自适应性强。通过对自然图像进行大﹑小范围图像修复和文字去除实验,该文方法均取得不错的修复效果。     

Bayesian compressive sensing using reweighted laplace priors

Bayesian compressive sensing (BCS) plays an important role in signal processing for dealing with sparse representation related problems. BCS utilizes a Bayesian model to solve the compressing sensing (CS) problem, such as signal sampling processing and model parameters using the hierarchical Bayesian framework. The use of Gaussian and Laplace distribution priors on the basic coefficients has already been demonstrated in previous works. However, the two existing priors cannot more effectively encode sparsity representation for unknown signals. In this paper, a reweighted Laplace distribution prior is proposed for hierarchical Bayesian to fully exploit the sparsity of unknown signals. The proposed algorithm can automatically estimate all the coefficients of unknown signal, and the expected model parameters are solely gotten from observation by developing a fast greedy algorithm to solve the Bayesian maximum posterior and type-II maximum likelihood. Theoretical analysis on the sparsity of the proposed model is analyzed and compared with the Laplace priors model. Moreover, numerical experiments are conducted to prove that the proposed algorithm can achieve superior performance for reconstructing unknown sparse signal with low computational burden as well as high accuracy.     

非局部联合稀疏近似的超分辨率重建算法

该文结合联合稀疏近似和非局部自相似的概念,提出非局部联合稀疏近似的超分辨率重建方法。该方法将输入图像的跨尺度高、低分辨率图像块统一进行联合稀疏编码,建立它们之间的稀疏关联,并将这种关联作为先验知识来指导图像的超分辨率重建。该文方法保证跨尺度自相似集具有相同的稀疏性模式,能更有效地利用图像的自相似性先验信息,提高算法的自适应性。通过自然图像实验,与其它几种基于学习的超分辨率算法对比,超分辨率效果有较好改善。     

Sparse intrinsic decomposition and applications

This paper proposes an intrinsic decomposition method from a single RGB-D image. To remedy the highly ill-conditioned problem, the reflectance component is regularized by a sparsity term, which is weighted by a bilateral kernel to exploit non-local structural correlation. As shading images are piece-wise smooth and have sparse gradient fields, the sparse-induced ${\ell }_1$-norm is used to regularize the finite difference of the direct irradiance component, which is the most dominant sub-component of shading and describes the light directly received by the surfaces of the objects from the light source. To derive an efficient algorithm, the proposed model is transformed into an unconstrained minimization of the augmented Lagrangian function, which is then optimized via the alternating direction method. The stability of the proposed method with respect to parameter perturbation and its robustness to noise are investigated by experiments. Quantitative and qualitative evaluation demonstrates that our method has better performance than state-of-the-art methods. Our method can also achieve intrinsic decomposition from a single color image by integrating existed depth estimation methods. We also present a depth refinement method based on our intrinsic decomposition method, which obtains more geometry details without texture artifacts. Other application, e.g., texture editing, also demonstrates the effectiveness of our method.     

Gray-level image denoising with an improved weighted sparse coding

The nonlocal self-similarity of images means that groups of similar patches have low-dimensional property. The property has been previously used for image denoising, with particularly notable success via sparse coding. However, only a few studies have focused on the varying statistics of noise in different similar patches during the iterative denoising process. This has motivated us to introduce an improved weighted sparse coding for gray-level image denoising in this paper. On the basis of traditional sparse coding, we introduce a weight matrix to account for the noise variation characteristics of different similar patches, while introduce another weight matrix to make full use of the sparsity priors of natural images. The Maximum A-Posterior estimation (MAP) is used to obtain the closed-form solution of the proposed method. Experimental results demonstrate the competitiveness of the proposed method compared with that of state-of-the-art methods in both the objective and perceptual quality.     

Multiple kernel learning with NOn-conVex group spArsity

As the high-dimensional heterogeneous visual features extracted from images are intrinsically embedded in a non-linear space, some kernel methods such as SVM have been proposed to solve this problem. Since different kinds of heterogeneous features in images have different intrinsic discriminative powers for image understanding, how to enforce grouping sparsity penalty to effectively select out discriminative heterogeneous visual features is critical for image understanding. Most existing approaches are using a convex penalty for feature selection, which easily leads to inconsistent selection. To guarantee a consistent selection for heterogeneous features embedded in a non-linear space, this paper proposes a new approach called MKL-NOVA (Multiple Kernel Learning with NOn-conVex group spArsity). Because MKL-NOVA conducts a non-convex penalty for the selection of groups of features, it achieves the consistent selection. Furthermore, considering the contextual correlation between multi labels, sparse canonical correlation analysis is conducted to boost the image annotation performance by MKL-NOVA. We have demonstrated the superior performance of MKL-NOVA via two experiments in the paper. First, we showed that MKL-NOVA converges to the true underlying model by using a ground-truth-available generative-model simulation. Second, we compare the proposed MKL-NOVA and the state-of-the-art approaches which showed that MKL-NOVA achieved the best performance.     

Multiplicative noise removal via sparse and redundant representations over learned dictionaries and total variation

In this paper, we propose a new three-stage model for multiplicative noise removal. In the first stage, sparse and redundant representation is used to approximate the log-image. The K-SVD algorithm is used to train a redundant dictionary, which can describe the log-image sparsity. Then in the second stage, we use the total variation (TV) method to amend the image obtained. At last, via an exponential function and bias correction, the result is transformed back from the log-domain to the real one. Our method combines the advantages of sparse and redundant representation over trained dictionary and TV method. Experimental results show that the new model is more effective to filter out multiplicative noise than the state-of-the-art models.     

A Novel Sparse Penalty for Singular Value Decomposition

Singular value decomposition (SVD) is a tool widely used in data denoising, matrix approximation, recommendation system, text mining and computer vision. A m a jority of applications prefer sparse singular vectors to capture inherent structures and patterns of the input data so that the results are interpretable. We present a novel penalty for SVD to achieve sparsity. Comparing with the traditional penalties, the proposed penalty is scale, dimen-sional insensitive and bounded between 0 and 1, which are in favor of controlling sparsity. Regulated by the penalty, we provide an efficient algorithm to pro ject a vector onto a given sparse level in O(n) expected time. The efficient pro jection algorithm serve as a drudge for sparse SVD (SSVD). In experiments, SSVD is efficient and could cap-ture the latent structures and patterns of the input data.     

Multi-focus image fusion with Geometrical Sparse Representation

Multi-focus image fusion aims to generate an image with all objects in focus by integrating multiple partially focused images. It is challenging to find an effective focus measure to evaluate the clarity of source images. In this paper, a novel multi-focus image fusion algorithm based on Geometrical Sparse Representation (GSR) over single images is proposed. The main novelty of this work is that it shows the potential of GSR coefficients used for image fusion. Unlike the traditional sparse representation-based (SR) methods, the proposed algorithm does not need to train an overcomplete dictionary and vectorize the signal. In our algorithm, using a single dictionary image, the source images are first represented by geometrical sparse coefficients. Specifically, we employ a weighted GSR model in the sparse coding phase, ensuring the importance of the center pixel. Then, the weighted GSR coefficient is used to measure the activity level of the source image and an average pooling strategy is applied to obtain an initial decision map. Third, the decision map is refined with a simple post-processing. Finally, the fused all-in-focus image is constructed with the refined decision map. Experimental results demonstrate that the proposed method can be competitive with or even superior to the state-of-the-art fusion methods in both subjective and objective comparisons.     

基于低秩分解和改进的非局部平均的SAR图像相干斑抑制

为抑制合成孔径雷达（SAR）图像成像过程中形成的相干斑噪声,提出了一种基于低秩分解和改进的非局部平均的SAR图像相干斑去噪方法。首先将SAR图像进行对数处理,将乘性噪声转换为加性噪声;然后利用低秩稀疏分解将对数图像分解成低秩图像部分和稀疏图像部分;接着对含噪严重的稀疏图像部分分析其结构张量,生成非局部平均滤波所需的衰减因子,进行改进的非局部平均滤波去噪;最后再做图像合成,经指数变换得到去噪后的SAR图像。实验结果表明,该方法经视觉评价、边缘保持指数（EPI）和等效视数（ENL）等方面评测,具有较好的抑制噪声和保持边缘及纹理细节的能力。      

基于非局部相似块低秩的压缩感知图像重建算法

传统的压缩感知重建算法利用信号在某个特征空间下的稀疏性构建目标优化函数,但没有充分考虑信号的局部特性和结构化属性,影响了算法的重建性能和算法的适应性.本文考虑图像的非局部自相似性(NonlocalSelf-Similarity,NLSS),提出一种基于图像相似块低秩的压缩感知图像重建算法,将图像恢复问题转化为聚合的相似块矩阵秩最小问题.算法以最小压缩感知重建误差为约束构建优化模型,并采用加权核范数最小化算法(Weighed Nuclear Norm Minimization,WNNM)求解低秩优化问题,很好地挖掘了图像自身的信息和结构化稀疏特征,保护了图像的结构和纹理细节.多个测试图像、不同采样率下的实验证明了算法的有效性,特别是在低采率下对于纹理较为丰富的图像,提出的算法图像重建质量较明显的优于最新的同类算法.