International Journal of Wavelets, Multiresolution and Information Processing

A bio-inspired two-scale image complementarity evaluation method is proposed. This novel multi-scale method provides a promising alternative for the performance assessment of image fusion algorithms. Moreover, it can also be used to compare and analyze the multi-scale difference of raw images. Two metrics are presented and used to assess the complementarity of fusion images in non-subsampled contourlet transform (NSCT) domains: visual saliency differences (VSDs) at the coarse scales and detail similarities (DSs) at the fine scales. Visual attention mechanism (VAM)-based saliency maps are combined with NSCT low-pass subbands to compute the VSDs, and linear correlation and contrast consistency-based DSs are compared in NSCT band-pass subbands. Five main multi-scale transform (MST)-based fusion algorithms were compared by using 30 groups of raw images that consist of four types of fusion images. Effects of NSCT filters and decomposition levels on evaluation results are discussed in detail. Furthermore, a group of color multi-exposure fusion images were also taken as examples to evaluate the complementarity of raw images. Experimental results demonstrate the effectiveness of the proposed method, especially for MST-based image fusion algorithms.

An outline is presented for construction of wavelet filters with compact support. Our approach does not require any extensive simulations for obtaining the values of design variables like other methods. A unified framework is proposed for designing halfband polynomials with varying vanishing moments. Optimum filter pairs can then be generated by factorization of the halfband polynomial. Although these optimum wavelets have characteristics close to that of CDF 9/7 (Cohen-Daubechies-Feauveau), a compact support may not be guaranteed. Subsequently, we show that by proper choice of design parameters finite wordlength wavelet construction can be achieved. These hardware friendly wavelets are analyzed for their possible applications in image compression and feature extraction. Simulation results show that the designed wavelets give better performances as compared to standard wavelets. Moreover, the designed wavelets can be implemented with significantly reduced hardware as compared to the existing wavelets.

This paper discusses the uniformly strong convergence of multivariate density estimation with moderately ill-posed noise over a bounded set. We provide a convergence rate over Besov spaces by using a compactly supported wavelet. When the model degenerates to one-dimensional noise-free case, the convergence rate coincides with that of Giné and Nickl’s (Ann. Probab., 2009 or Bernoulli, 2010). Our result can also be considered as an extension of Masry’s theorem (Stoch. Process. Appl., 1997) to some extent.

This paper presents a novel destriping method for hyperspectral images. Most of the previous destriping methods regard only the corrupted subimage as an isolated image and fail to consider the high spectral correlation between the subimages in different bands. This may impede their performance of removing striping noises. The proposed method takes advantage of both spectral and spatial information to contribute to the process of striping noise reduction. Firstly, a correntropy-based sparse representation (CSR) model is utilized to learn the high spectral correlation between the subimages in different bands. Then the spatial information of the target subimage with striping noise is incorporated into the CSR model with a unidirectional Huber–Markov random field prior. We devise an Augmented Lagrange Multiplier type of algorithm to efficiently compute the destriped results. The experimental results on two real-world hyperspectral data sets demonstrate the effectiveness of the proposed method.

Nonparametric regression techniques provide a very effective and simple way of finding structure in data sets without the imposition of a parametric regression model. Wavelet theory has the potential to provide statisticians with powerful new techniques for nonparametric inference. In this paper, we consider the wavelet shrinkage kernel estimator of regression function with a common one-dimensional probability density function. We investigate a new nonparametric curve estimator and convergence ratio of given estimator by using cross-validation method to choice of wavelet threshold when the observations are taken on the regular grid. At the end we used simulation study to examine our proposed estimator. We survey the theoretical outcomes with numerical computation by using $R$ software to compare purpose estimator with another estimators.

Hyperspectral unmixing is one of the most important techniques in hyperspectral remote sensing image analysis. During the past decades, many models have been widely used in hyperspectral unmixing, such as nonnegative matrix factorization (NMF) model, sparse regression model, etc. Most recently, a new matrix factorization model, deep matrix, is proposed and shows good performance in face recognition area. In this paper, we introduce the deep matrix factorization (DMF) for hyperspectral unmixing. In this method, the DMF method is applied for hyperspectral unmixing. Compared with the traditional NMF-based unmixing methods, DMF could extract more information with multiple-layer structures. An optimization algorithm is also proposed for DMF with two designed processes. Results on both synthetic and real data have validated the effectiveness of this method, and shown that it has outperformed several state-of-the-art unmixing approaches.

The minimization problem of reconstruction error over large hyperspectral image data is one of the most important problems in unsupervised hyperspectral unmixing. A variety of algorithms based on nonnegative matrix factorization (NMF) have been proposed in the literature to solve this minimization problem. One popular optimization method for NMF is the projected gradient descent (PGD). However, as the algorithm must compute the full gradient on the entire dataset at every iteration, the PGD suffers from high computational cost in the large-scale real hyperspectral image. In this paper, we try to alleviate this problem by introducing a mini-batch gradient descent-based algorithm, which has been widely used in large-scale machine learning. In our method, the endmember can be updated pixel set by pixel set while abundance can be updated band set by band set. Thus, the computational cost is lowered to a certain extent. The performance of the proposed algorithm is quantified in the experiment on synthetic and real data.

Subspace learning (SL) is an important technology to extract the discriminative features for hyperspectral image (HSI) classification. However, in practical applications, some acquired HSIs are contaminated with considerable noise during the imaging process. In this case, most of existing SL methods yield limited performance for subsequent classification procedure. In this paper, we propose a robust subspace learning (RSL) method, which utilizes a local linear regression and a supervised regularization function simultaneously. To effectively incorporate the spatial information, a local linear regression is used to seek the recovered data from the noisy data under a spatial set. The recovered data not only reduce the noise effect but also include the spectral-spatial information. To utilize the label information, a supervised regularization function based on the idea of Fisher criterion is used to learn a discriminative subspace from the recovered data. To optimize RSL, we develop an efficient iterative algorithm. Extensive experimental results demonstrate that RSL greatly outperforms many existing SL methods when the HSI data contain considerable noise.

As a powerful classifier, sparse representation-based classification (SRC) has successfully been applied in various visual recognition problems. However, due to the highly correlated bands and insufficient training samples of hyperspectral image (HSI) data, it still remains a challenging problem to effectively apply SRC in HSI. Considering the rich information of spatial structure of materials in HSI, that means the adjacent pixels belong to the same class with a high probability, in this paper, we propose an efficient superpixel-based sparse representation framework for HSI classification. Each superpixel can be regarded as a small region consisting of a number of pixels with similar spectral characteristics. The proposed framework utilizes superpixel to exploit spatial information which can greatly improve classification accuracy. Specifically, SRC is firstly used to classify the HSI data. Meanwhile, an efficient segmentation algorithm is applied to divide the HSI into many disjoint superpixels. Then, each superpixel is used to fuse the SRC classification results in superpixel level. Experimental results on two real-world HSI data sets have shown that the proposed superpixel-based SRC (SP-SRC) framework has a significant improvement over the pixel-based SRC method.

Hyperspectral image (HSI) classification draws a lot of attentions in the past decades. The classical problem of HSI classification mainly focuses on a single HSI scene. In recent years, cross-scene classification becomes a new problem, which deals with the classification models that can be applied across different but highly related HSI scenes sharing common land cover classes. This paper presents a cross-scene classification framework combining spectral–spatial feature extraction and manifold-constrained feature subspace learning. In this framework, spectral–spatial feature extraction is completed using three-dimensional (3D) wavelet transform while manifold-constrained feature subspace learning is implemented via multitask nonnegative matrix factorization (MTNMF) with manifold regularization. In 3D wavelet transform, we drop some coefficients corresponding to high frequency in order to avoid data noise. In feature subspace learning, a common dictionary (basis) matrix is shared by different scenes during the nonnegative matrix factorization, indicating that the highly related scenes should share than same low-dimensional feature subspace. Furthermore, manifold regularization is applied to force the consistency across the scenes, i.e. all pixels representing the same land cover class should be similar in the low-dimensional feature subspace, though they may be drawn from different scenes. The experimental results show that the proposed method performs well in cross-scene HSI datasets.

Hyperspectral unmixing is one of the most important techniques in the remote sensing image analysis tasks. In recent decades, nonnegative matrix factorization (NMF) has been shown to be effective for hyperspectral unmixing due to the strong discovery of the latent structure. Most NMFs put emphasize on the spectral information, but ignore the spatial information, which is very crucial for analyzing hyperspectral data. In this paper, we propose an improved NMF method, namely NMF with region sparsity learning (RSLNMF), to simultaneously consider both spectral and spatial information. RSLNMF defines a new sparsity learning model based on a small homogeneous region that is obtained via the graph cut algorithm. Thus RSLNMF is able to explore the relationship of spatial neighbor pixels within each region. An efficient optimization scheme is developed for the proposed RSLNMF, and its convergence is theoretically guaranteed. Experiments on both synthetic and real hyperspectral data validate the superiority of the proposed method over several state-of-the-art unmixing approaches.

In this paper, we address the problem of removing striping noise in hyperspectral images (HSI). To this end, we develop a novel destriping method by taking advantage of the spectral and spatial information of the hyperspectral image simultaneously. To obtain satisfactory destriped results, our consideration is two-fold: (1) To model the spectral information of HSI, we utilize low-rank representation to exploit the low-rank property of HSI; (2) To incorporate the spatial information into our method, we adopt the Huber-Markov random field (HMRF) prior model to preserve the edge information of HSI while reducing the striping noise. Finally, we integrate the spectral and spatial model into a unified objective function. In addition, we also devise an effective optimization algorithm to minimize the objective function. The experimental results on real-world HSI data validate the efficacy of the proposed scheme for destriping of HSI.

Band selection plays a key role in the hyperspectral image classification since it helps to reduce the expensive cost of computation and storage. In this paper, we propose a supervised hyperspectral band selection method based on differential weights, which depict the contribution degree of each band for classification. The differential weights are obtained in the training stage by calculating the sum of weight differences between positive and negative classes. Using the effective one-class Support Vector Machine (SVM), the bands corresponding to large differential weights are extracted as discriminative features to make the classification decision. Moreover, label information from training data is further exploited to enhance the classification performance. Finally, experiments on three public datasets, as well as comparison with other popular feature selection methods, are carried out to validate the proposed method.

This paper presents a pork quality evaluation method based on the hyperspectral image datasets of 96 pork samples in the range of 400–1000nm. First, through the K-medoids clustering algorithm based on manifold distance, 30 important wavelengths are selected from 753 wavelengths, and final 8 optimum wavelengths are obtained based on the discriminant value and the spectral resolution. Then, the two-dimensional Gabor wavelet transform is used to extract the eight texture features of the image under the final eight wavelengths respectively, to form a 64-dimensional features of pork quality. Finally, using the fussy C-means (FCM) algorithm based on Isomap dimension reduction, the pork quality evaluation model is constructed. The result of wavelength extraction experiments show that although there is a strong linear correlation between adjacent bands in the hyperspectral image, there is an obvious nonlinear manifold relation in the whole band. Therefore, the K-medoids clustering algorithm based on manifold distance in this paper is more reasonable than the traditional principal component analysis (PCA) in characteristic wavelength selection. According to the experiment of pork quality evaluation, two-dimensional Gabor wavelet transform can extract the texture characteristics of pork better. Compared with the FCM algorithm based on PCA, the FCM algorithm based on Isomap can better solve the high-dimensional clustering problem, and can distinguish fresh chilled meat, frozen-thawed meat and spoiled meat accurately. The study shows that hyperspectral image technology can be used in pork quality evaluation.