Modified LDE for Dimensionality Reduction of Hyperspectral Image

Local Discriminant Embedding (LDE) was recently proposed to overcome some limitations of the global Linear Discriminant Analysis (LDA) method. In the case of a small training data set, however, LDE cannot directly be applied to high-dimensional data. This case is the so-called small-sample-size (SSS) problem. In this paper, we introduce an Exponential Local Discriminant Embedding (ELDE) technique to overcome the SSS problem. The advantages of ELDE are that, compared with Principal Component Analysis (PCA) + LDE, the ELDE method can extract the most discriminant information that was contained in the null space of the locality preserving between-class and within-class scatter matrices. In addition, the proposed ELDE is equivalent to transforming original data into a new space by distance diffusion mapping, and then, LDE is applied in such a new space. As a result of diffusion mapping, the margin between samples belonging to different classes is enlarged, which is helpful in improving classification accuracy. The experiments are conducted on four public face databases, YALE, PIE, Extended Yale and PF01. Experiments conducted on real data show that the performance of ELDE is better than that of LDE and many state-of-the-art discriminant analysis techniques.

Dimensionality reduction is an essential task in hyperspectral image processing. How to preserve the original intrinsic structure information and enhance the discriminant ability is still a challenge in this area. Recently, with the advantage of preserving global intrinsic structure information, low-rank representation has been applied to dimensionality reduction and achieved promising performance. By exploiting the submanifold information of the original data set, multimanifold learning is effective in enhancing the discriminant ability of the processed data set. In addition, due to the ability of preserving the spatial neighborhood structure information, the tensor analysis has become a popular technique for hyperspectral image processing. Motivated by the above-mentioned analysis, a novel tensor-based low-rank graph with multimanifold regularization (T-LGMR) for dimensionality reduction of hyperspectral images is proposed in this paper. In the T-LGMR, a low-rank constraint is employed to preserve the global data structure while multimanifold information is utilized to enhance the discriminant ability, and tensor representation is used to preserve the spatial neighborhood information. Finally, dimensionality reduction is achieved in the graph embedding framework. Experimental results on three real hyperspectral data sets demonstrate the superiority of the proposed method over several state-of-the-art approaches.

A spatial-spectral metric learning (SSML) framework for hyperspectral image (HSI) classification is proposed. SSML learns a metric by considering both the spectral characteristics and spatial features represented as the mean of neighboring pixels. It first performs the local pixel neighborhood preserving embedding (LPNPE) to reduce the dimensionality of HSI and meanwhile to preserve the spatial local similarity structure. Then, it learns a spectral and spatial distance metric, separately. Finally, the combination of the spectral and spatial metrics yields a joint spatial-spectral metric. It is followed by a nearest neighbor (NN) classifier for HSI classification. SSML shows good performance over the spectral and spatial NN and SVM on the benchmark hyperspectral data set of Indian Pines.

Advances in hyper spectral imaging sensors makes it possible to obtain high dimensional and high resolution data which poses challenges for computational cost and time. As the inter-band resolution is high in hyper spectral images, the spectral dimension could be reduced without significant loss of useful information. This requires careful application of dimensionality reduction techniques to reduce the dimension but preserve the original spectral characteristics. It is observed in the literature that filtering techniques can address some of the challenges concerning dimensionality reduction in hyper spectral imaging. In this paper a dimensionality reduction method adopting Discrete Wavelet Transform and Distance Classifier Correlation filter has been proposed for hyper spectral imaging. The experimental results show that the combination of ID-DWT with DCCF outperforms the other methods in dimensionality reduction and classification of given data set.

Extracting discriminative features and reducing the dimensionality of data are two main objectives of manifold learning. Among different techniques, nonlinear manifold learning methods have been proposed in order to extract features from data which are not linearly distributed. Kernel trick is one of the famous nonlinear techniques which helps to project the data without an explicit mapping which can be used in combination with different linear techniques (e.g., Linear discriminant analysis and local discriminant embedding (LDE)). In this paper, we propose a Two Subspace-based Kernel Local Discriminant Embedding (TSKLDE) method which extract features from both non-null and null space of the within-class locality preserving scatter matrix of LDE in the kernel space. We evaluated the proposed algorithm using three publicly available face databases. The obtained results demonstrate that the use of both features in TSKLDE leads to more noise tolerant features compared to other kernel methods and to higher discriminant ability than many existing manifold learning techniques.

In this paper, we proposed a new semi-supervised multi-manifold learning method, called semi- supervised sparse multi-manifold embedding (S3MME), for dimensionality reduction of hyperspectral image data. S3MME exploits both the labeled and unlabeled data to adaptively find neighbors of each sample from the same manifold by using an optimization program based on sparse representation, and naturally gives relative importance to the labeled ones through a graph-based methodology. Then it tries to extract discriminative features on each manifold such that the data points in the same manifold become closer. The effectiveness of the proposed multi-manifold learning algorithm is demonstrated and compared through experiments on a real hyperspectral images.

Hyperspectral imaging has become a significant source of valuable data for astronomers over the past decades. Current instrumental and observing time constraints allow direct acquisition of multispectral images, with high spatial but low spectral resolution, and hyperspectral images, with low spatial but high spectral resolution. To enhance scientific interpretation of the data, we propose a data fusion method which combines the benefits of each image to recover a high spatio-spectral resolution datacube. The proposed inverse problem accounts for the specificities of astronomical instruments, such as spectrally variant blurs. We provide a fast implementation by solving the problem in the frequency domain and in a low-dimensional subspace to efficiently handle the convolution operators as well as the high dimensionality of the data. We conduct experiments on a realistic synthetic dataset of simulated observation of the upcoming James Webb Space Telescope, and we show that our fusion algorithm outperforms state-of-the-art methods commonly used in remote sensing for Earth observation.

The hyperspectral and multispectral image fusion process, commonly known as the multisharpening process (also known as the hypersharpening process), results in the creation of unobservable high spectral and spatial resolution hyperspectral remote sensing data, by combining (or fusing) a hyperspectral image, characterized by a high spectral resolution, with, especially, a high spatial resolution multispectral one. There are several approaches in the literature performing such a process, in particular, those based on the spectral unmixing concept. The latter fusion methods aim to extract pure-material spectra from the high spectral resolution hyperspectral image and combine them with their corresponding proportions extracted from the high spatial resolution multispectral image. However, most of these methods, which mainly consider the standard linear mixing model, do not address the spectral variability phenomenon, precisely due to the considered data mixing model, which does not handle variations in illumination and atmospheric conditions or material composition inducing spectral variability. Neglecting such a phenomenon may lead to errors in the fusion process, thus decreasing the spatial and spectral qualities of sharpened products. In this paper, a new hyperspectral and multispectral data fusion method, based on the linear spectral unmixing concept that deals with spectral variability, is proposed. This approach, based on a multiplicative Nonnegative Matrix Factorization (NMF) technique, substantially extends the multiplicative Coupled NMF (CNMF) algorithm by considering a linear data mixing model that addresses the considered phenomenon. Indeed, the introduced approach minimizes new cost functions involving matrices with specific structures in order to deal with the spectral variability phenomenon. The proposed method is applied to synthetic and real data, and its effectiveness is evaluated with established performance criteria. Experimental results show that the designed algorithm globally yields sharpened hyperspectral data with fine spectral and spatial fidelities. Also, these results demonstrate that the proposed technique globally outperforms the tested literature approaches.

Recent advances and new guidelines on hyperspectral and multispectral image fusion

With the advancement in technology, hyperspectral images have potential applications in the field of remote sensing due to their high spectral resolution. Despite the hyperspectral image providing abundant information, its analysis suffers from the problem of high dimensionality. Hence, Dimensionality Reduction (DR) is an essential task in all hyperspectral image analysis. Band Selection, which is one of the DR techniques, is still a challenging issue even though many algorithms have been developed. To provide remedy for this issue, this paper explores a novel approach for band selection using K-means clustering on statistical feature in hyperspectral images. The proposed method of clustering based band selection for DR is simple and accurate. A reliable estimate of number of bands to be selected is provided by Virtual Dimensionality (VD). Informative bands preserving maximum information are selected based on the statistical feature, the variance using K-means Clustering technique. Further, our proposed work involves the utilization of the effectiveness of Simplex Growing Algorithm (SGA) on endmember extraction in association with clustering based band selection. Using Fully Constrained Least Squares (FCLS) method, abundance fraction is estimated based on endmember signatures, which are derived using Endmember Extraction Algorithm (EEA). The proposed work is investigated and compared with that of N-FINDR and Vertex Component Analysis (VCA) algorithms. The performance of the proposed algorithm is evaluated using Root Mean Square Error (RMSE), Spectral Angle Distance (SAD) and computation time. Experimental results show that the proposed clustering based band selection with SGA endmember extraction algorithm reduces the average SAD by 8 to 10 % and the average RMSE by nearly 1 %, compared to that of N-FINDR and VCA algorithms. In terms of computation time, the proposed band selection based DR with SGA algorithm is seven times faster than conventional transform based DR with SGA algorithm.

For many remote sensing applications it is preferable to have images with both high spectral and spatial resolutions. On this regards, hyperspectral and multispectral images have complementary characteristics in terms of spectral and spatial resolutions. In this paper we propose an approach for the fusion of low spatial resolution hyperspectral images with high spatial resolution multispectral images in order to obtain superresolution (spatial and spectral) hyperspectral images. The proposed approach is based on the assumption that, since both hyperspectral and multispectral images acquired on the same scene, the corresponding endmembers should be the same. On a first step the hyperspectral image is spectrally down-sampled in order to match the multispectral one. Then an endmember extraction algorithm is performed on the down-sampled hyperspectral image and the successive abundance estimation is performed on the multispectral one. Finally, the extracted endmembers are up-sampled back to the original hyperspectral space and then used to reconstruct the superresolution hyperspectral image according to the abundances obtained from the multispectral image.

Matrix exponential based semi-supervised discriminant embedding for image classification

QUasi-Affine TRansformation Evolutionary (QUATRE) algorithm generalized differential evolution (DE) algorithm to matrix form. QUATRE was originally designed for a continuous search space, but many practical applications are binary optimization problems. Therefore, we designed a novel binary version of QUATRE. The proposed binary algorithm is implemented using two different approaches. In the first approach, the new individuals produced by mutation and crossover operation are binarized. In the second approach, binarization is done after mutation, then cross operation with other individuals is performed. Transfer functions are critical to binarization, so four families of transfer functions are introduced for the proposed algorithm. Then, the analysis is performed and an improved transfer function is proposed. Furthermore, in order to balance exploration and exploitation, a new liner increment scale factor is proposed. Experiments on 23 benchmark functions show that the proposed two approaches are superior to state-of-the-art algorithms. Moreover, we applied it for dimensionality reduction of hyperspectral image (HSI) in order to test the ability of the proposed algorithm to solve practical problems. The experimental results on HSI imply that the proposed methods are better than Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA).

Remote sensing technology has undeniable importance in various industrial applications, such as mineral exploration, plant detection, defect detection in aerospace and shipbuilding, and optical gas imaging, to name a few. Remote sensing technology has been continuously evolving, offering a range of image modalities that can facilitate the aforementioned applications. One such modality is Hyperspectral Imaging (HSI). Unlike Multispectral Images (MSI) and natural images, HSI consist of hundreds of bands. Despite their high spectral resolution, HSI suffer from low spatial resolution in comparison to their MSI counterpart, which hinders the utilization of their full potential. Therefore, spatial enhancement, or Super Resolution (SR), of HSI is a classical problem that has been gaining rapid attention over the past two decades. The literature is rich with various SR algorithms that enhance the spatial resolution of HSI while preserving their spectral fidelity. This paper reviews and discusses the most important algorithms relevant to this area of research between 2002-2022, along with the most frequently used datasets, HSI sensors, and quality metrics. Meta-analysis are drawn based on the aforementioned information, which is used as a foundation that summarizes the state of the field in a way that bridges the past and the present, identifies the current gap in it, and recommends possible future directions.

The intent of this study was to develop a technique for weight and ripeness estimation of oil palm (Elaeis guieensis Jacq. var. tenera) bunches from hyperspectral and RGB color images. In the experiments, color and hyperspectral images of the bunch were acquired from four different angles, each differing by 90 degrees. Acquired RGB color images were converted to HSI and L*a*b color space. Gray-scale thresholds were used to identify the area of the bunch and the area of space between the fruits. The total number of pixels in the bunch and the space were counted, respectively. In the hyperspectral images, the total number of pixels in the bunch was also counted from an image composed of three wavelengths (560 nm, 680 nm, and 740 nm), while the total number of pixels of space between fruits was obtained at a wavelength of 910 nm. From these sets of data, weight-estimation equations were determined by linear regression (LR) or multiple linear regression (MLR). As a result, the coefficient of determination (R2) of actual weight and estimated weight were at a level of 0.989 and 0.992 for color and hyperspectral images, respectively. Estimation of oil palm bunch ripeness was also tested. Bunches belonging to 4 classes of ripeness (overripe, ripe, underripe, and unripe) were used for this study. Since ripeness estimation from overall data from a bunch was quite difficult, we focused on the difference in colors or reflectivity of the portion concealed and not-concealed with fronds. Euclidean distances between the test sample and the standard 4 classes of ripeness were calculated, and the test sample was classified into the ripeness class that had the shortest distance from the sample. In the classification based on color image, average RGB values of concealed and not-concealed areas were used, while in hyperspectral images the average intensity values of fruits pixels from the concealed area were used. The results of validation experiments with the developed estimation methods indicated acceptable estimation accuracy, and a possibility for practical use to estimate the ripeness of oil palm bunches.