The regularized alternating least squares (ALS) is a widely used method for computing the CP decomposition of tensors. Existing convergence analyses for the regularized ALS are limited to first-order stationary points. In this work, we study its second-order convergence and prove that, with random initialization, the regularized ALS almost surely avoids strict saddle points. These results provide stronger theoretical guarantees for the effectiveness of regularized ALS in practical tensor approximation tasks.

Recently, principal skewness analysis (PSA) has been introduced into the domain of feature extraction. It is equivalent to the skewness version of Fast independent component analysis (FastICA). Unlike FastICA, PSA does not require all sample points when searching for the projection directions, making it faster. However, for the data of dimension$L$, PSA needs to calculate the eigenvectors of$L$tensors, each of size$L\times L\times L$. When$L$is large, PSA still requires significant computational time to find all projection directions. In this letter, we find that the$(m+1)$th projection direction in PSA can be obtained by calculating the eigenvector of a tensor of size$(L-m)\times (L-m)\times (L-m)$. Furthermore, we propose a fast version of PSA (FastPSA) that is mathematically equivalent to PSA. The experimental results demonstrate that FastPSA has lower computational complexity than PSA.

Vision-language models have demonstrated impressive capabilities in associating images and text by pretraining on extensive image-text paired data. The paradigm of continual pretraining followed by fine-tuning has become prevailing for boosting performance in domain-specific tasks under constrained computation resources. Benefiting from the superior generalization abilities of foundation models, the demands for computational resources and extensive data corpora have been significantly reduced. Nonetheless, it is crucial to tailor the model for the characteristics of downstream tasks to mitigate the misalignment between the pretraining pretext tasks and actual applications of interest. In this study, we utilize a CLIP-based model that has been continually pretrained on the 5 million image-text dataset in the remote sensing field as the foundation model, focusing on cross-modal image-text retrieval tasks. We introduce an efficient framework called remote sensing image-text retrieval fine-grained fine-tuning (RSITR-FFT), which refines the feature space by introducing fine-grained word-region alignment and incorporating consistency constraint regularization terms in the learning objectives. The fine-grained alignment aims for precise word-region correspondence beyond classical global-level image-text matching, while the consistency regularization encourages geometric coherence between the image and text modalities. Remarkably, our method achieves observable performance improvements while requiring far fewer fine-tuning samples—about 10 000, in contrast to the 400 million and 5 million samples used during the CLIP’s initial pretraining and GeoRSCLIP’s continual pretraining stages, respectively. We perform quantitative evaluation on RSICD, NWPU-Captions, and UCM-Captions datasets to demonstrate the effectiveness of RSITR-FFT. We further showcase its realistic application on the high-resolution remote sensing imagery through the qualitative visualization experiments on the FAIR1M-1.0 dataset. The code and models are available athttps://github.com/d1x1u/RSITR-FFT.

Recently, spatio-temporal fusion technologies have been rapidly developed and widely applied, which generally require one or more pairs of coarse- and fine-resolution images as reference data and a coarse-resolution image at the prediction time to produce a fine-resolution image at the forecast time. Consequently, most spatio-temporal fusion methods are phase-based and obtain temporal changing information from the coarse-resolution image pairs. Consequently, they usually have rigid constraints on reference data selection using the temporal interval criterion. However, due to the relatively long revisit cycle and cloud contamination, it is difficult to prepare adequate high-quality reference data with little change, especially for large-scale fusion tasks. Therefore, we propose a spatial-based fusion method, which only requires the coarse images at the prediction time and a fine reference image selected by a spatial-spectral-similarity criterion, named super-resolution based spatial fusion with the generative adversarial network (SRSF-GAN). SRSF-GAN uses a super-resolution (SR) module merely on the coarse images at the prediction time, and then perform a multi-scale fusion with the reference fine image. Moreover, the spatial attention mechanism is adopted to achieve dynamic weight tuning, i.e. assigning more weight to the SR image for changed areas and more weight to the fine reference image for unchanged areas. Comparison experiments based on three datasets show that our model can outperform the state-of-the-art methods, and the changes with different spatial and spectral ranges of variation can be recovered. The code will be uploaded to the following website: https://github.com/Zhaosir996/SRSFGAN.

The hierarchical constrained energy minimization (hCEM) algorithm, published in TGRS, has received more attentions in the field of hyperspectral target detection since publication. Using the classical constrained energy minimization (CEM) detector as the basic unit, it designs a hierarchical structure to gradually suppress the background and to enhance the target detection performance. The authors claimed that the convergence of the hCEM algorithm can be theoretically guaranteed by analyzing the realtionship between different layers of the hierarchical output. However, after some investigations, we found that the key formula presented in the paper is theoretically defective. This implies that the theoretical results do not hold and the convergence of the algorithm cannot be ensured.

Target detection is always an important topic in the field of hyper/multispectral remote sensing image processing. At present, target detection algorithms in this field are generally limited to processing single-temporal remote sensing data, and they cannot obtain satisfactory results when the spectra of target and background are similar to each other. Recently, a target detection algorithm called filter tensor analysis (FTA), which is specially designed for multitemporal remote sensing data, has been reported and has achieved better detection results in many cases than the traditional single-temporal methods. However, FTA can only extract one target of interest at a time, and it cannot work when there are multiple targets of interest in the image. Therefore, considering that the matrix form of the FTA method is similar to that of the constrained energy minimization (CEM) model, it naturally comes to us that we can combine the tensor filter in FTA and the multiple target constraints to detect multiple targets by fully exploiting the time-series information in multitemporal data. To be specific, through: 1) adding the “output to one” constraints to the multiple targets in FTA; 2) applying linear/nonlinear function to the outputs of FTA for the multiple targets; and 3) modifying the autocorrelation matrix in FTA, four multitarget detection algorithms for multitemporal remote sensing data are proposed in this article. Experiments with simulation data and real data both show the effectiveness and superiority of the proposed methods.

Recently, the volume-gradient-based band selection (VGBS) method has attracted more and more attention in the field of band selection. It is a ranking-based unsupervised algorithm which applies the sequential backward selection strategy to successively remove the most abundant band. The key finding of VGBS is that the band redundancy corresponds to the volume gradient matrix with respect to hyperspectral images. However, we have found that VGBS requires to update the gradient matrix after each band removal, which includes the calculation of the matrix inverse, determinant, and multiplication, and thus is time-consuming when the number of bands is large. In this letter, we first find that the norm of the row of the gradient matrix has a one-to-one correspondence to the diagonal element of the covariance matrix of the image. Further, we develop a recursive formula to calculate the inverse of the covariance matrix. The experimental results show the effectiveness of the method, i.e., we can reduce the computational complexity of VGBS with an order of magnitude.

As one of the most important algorithms in target detection, constrained energy minimization (CEM) has been widely used and developed in recent years. However, it is easy to verify that the target detection result of CEM varies with the data origin, which is apparently unreasonable since the distribution of the target of interest is objective and, therefore, unrelated to the selection of data origin. The clever eye (CE) algorithm tries to solve this problem by adding the data origin as a new variable from the perspective of the filter output energy. However, due to the nonconvexity of the objective function, CE can only obtain locally optimal solutions by using the gradient ascent method. In this article, we find a striking conclusion that there exists an analytical solution for CE that corresponds to the solution of a linear equation and further prove that all the solutions of the linear equation are globally optimal.

In[1], the affiliation for the authors was incorrect in the first footnote. It should be as follows.

Non-negative matrix factorization (NMF) has been widely used in mixture analysis for hyperspectral remote sensing. When used for spectral unmixing analysis, however, it has two main shortcomings: (1) since the dimensionality of hyperspectral data is usually very large, NMF tends to suffer from large computational complexity for the popular multiplicative iteration rule; (2) NMF is sensitive to noise (outliers), and thus the corrupted data will make the results of NMF meaningless. Although principal component analysis (PCA) can be used to mitigate these two problems, the transformed data will contain negative numbers, hindering the direct use of the multiplicative iteration rule of NMF. In this paper, we analyze the impact of PCA on NMF, and find that multiplicative NMF can also be applicable to data after principal component transformation. Based on this conclusion, we present a method to perform NMF in the principal component space, named ‘principal component NMF’ (PCNMF). Experimental results show that PCNMF is both accurate and time-saving.

Simplex volume is the most commonly used parameter for endmember extraction. However, when outliers exist in the image, the maximum-volume-criterion (MVC)-based methods tend to extract them as endmembers. Those outlier endmembers could be either physically meaningless or not representative enough for prevalent land covers. This is the biggest bottleneck preventing MVC-based methods from being extended from theoretical analysis to practical applications. This is mainly due to the limitation of the simplex volume formula itself, which is only determined by simplex vertices and completely ignoring the statistics of the data cloud. Usually, the simplex with vertices containing outliers has a larger volume than the one with vertices only containing true endmembers; thus, outliers are more favorably extracted as endmembers. Usually, the outliers are distributed in the direction of low information content. When extracted endmembers contain outliers, the overall information content (OIC) of the data cloud projected onto the endmember subspace will be definitely reduced. Motivated by this fact, we present the concept of statistical volume and develop a new endmember extraction method, which is named statistical volume analysis (SVA). The algorithm simultaneously utilizes the geometrical property of the simplex and the statistical characteristic of the projected data in the endmember subspace. Therefore, SVA not only can find a simplex with a large volume but also can get a large OIC of the projected data. Experiments with both simulated and real data show that SVA can compete with state-of-the-art methods in extracting endmembers of prevalent land covers. Moreover, it is capable of avoiding extracting outliers as endmembers.

Principal skewness analysis (PSA) has been introduced to the remote sensing community recently, which is equivalent to fast independent component analysis (FastICA) when skewness is considered as a non-Gaussian index. However, similar to FastICA, PSA also has the nonconvergence problem in searching for optimal projection directions. In this letter, we propose a new iteration strategy to alleviate PSA's nonconvergence problem, and we name this new version of PSA as momentum PSA (MPSA). MPSA still adopts the same fixed-point algorithm as PSA does. Different from PSA, the (k + 1)th result in the iteration process of MPSA not only depends on the kth iteration result but also is related to the (k - 1)th iteration. Experiments conducted for both simulated data and real-world hyperspectral image demonstrate that MPSA has an obvious advantage over PSA in convergence performance and computational speed.

Band selection (BS) plays an important role in the dimensionality reduction of hyperspectral data. However, as to the existing BS methods, few are specially designed for target detection. In this letter, we combine the target detection and BS process together and put forward a new BS method for target detection, named least absolute shrinkage and selection operator (LASSO)-based BS (LBS). Interestingly, by using a linear regression model with L1 regularization (LASSO model), LBS transforms the discrete BS problem into the continuous optimization problem, which cannot only avoid the complicated subset selection process but also evaluate the importance of all the bands simultaneously. The experiments on real hyperspectral data demonstrate that LBS is a very effective BS method for target detection.

How to find the representative bands is a key issue in band selection for hyperspectral data. Very often, unsupervised band selection is associated with data clustering, and the cluster centers (or exemplars) are considered ideal representatives. However, partitioning the bands into clusters may be very time-consuming and affected by the distribution of the data points. In this letter, we propose a new band selection method, i.e., exemplar component analysis (ECA), aiming at selecting the exemplars of bands. Interestingly, ECA does not involve actual clustering. Instead, it prioritizes the bands according to their exemplar score, which is an easy-to-compute indicator defined in this letter measuring the possibility of bands to be exemplars. As a result, ECA is of high efficiency and immune to distribution structures of the data. The experiments on real hyperspectral data set demonstrate that ECA is an effective and efficient band selection method.

The linear mixture model (LMM) plays a crucial role in the spectral unmixing of hyperspectral data. Under the assumption of LMM, the solution with the minimum reconstruction error is considered to be the ideal endmember. However, for practical hyperspectral data sets, endmembers that enclose all the pixels are physically meaningless due to the effect of noise. Therefore, in many cases, it is not sufficient to consider only the reconstruction error, some constraints (for instance, volume constraint) need to be added to the endmembers. The two terms can be considered as serving two forces: minimizing the reconstruction error forces the endmembers to move outward and thus enlarges the volume of the simplex while the endmember constraint acts in the opposite direction by driving the endmembers to move inward so as to constrain the volume to be smaller. Many existing methods obtain their solution just by balancing the two contradictory forces. The solution acquired in this way can not only minimize the reconstruction error but also be physically meaningful. Interestingly, we find, in this paper, that the two forces are not completely contradictory with each other, and the reconstruction error can be further reduced without changing the volume of the simplex. And more interestingly, our method can further optimize the solution provided by all the endmember extraction methods (both endmember selection methods and endmember generation methods). After optimization, the final endmembers outperform the initial solution in terms of reconstruction error as well as accuracy. The experiments on simulated and real hyperspectral data verify the validation of our method.

In this letter, we present a new feature extraction approach based on third-order statistics (coskewness tensor) called principal skewness analysis (PSA). PSA is the natural extension of principal components analysis from second-order statistics to third-order statistics. The result of PSA is equivalent to that of FastICA when skewness is considered as a non-Gaussian index. Similar to FastICA, PSA also applies the fixed-point method to search the skewness extreme directions. However, when calculating the new projected direction in each iteration, PSA only requires a coskewness tensor, whereas FastICA requires all the pixels to be involved. Therefore, PSA has an advantage over FastICA in speed.

Target detection has recently drawn considerable interest in hyperspectral image processing. People tend to exclude corrupted or badly damaged bands before applying the target detection algorithm to the data for better detection results. In this letter, it is proved that adding any band independent of the original image, even a noisy band, would be always beneficial to the performance of constrained energy minimization in terms of output energy. Finally, several tests are conducted to further justify our viewpoint.

In this paper, a subtle relationship is found between the volume of a subsimplex and the volume gradient of a simplex with respect to hyperspectral images. By using this relationship, we propose an efficient band selection method, namely, the volume-gradient-based band selection (VGBS) method. The VGBS method is an unsupervised method, which tries to remove the most redundant band successively. Interestingly, the VGBS method can find the most redundant band based only on the gradient of volume instead of calculating the volumes of all subsimplexes. Experiments on simulated and real hyperspectral data verify the efficiency of the proposed method.

This letter presents a new endmember generation method, which is called the geometric optimization model (GOM). The algorithm exploits the following fact: anL-dimensional (L-D) simplex can be divided intoL+ 1L-D smaller simplexes by any point within the simplex, and the sum of the volumes of theL+ 1 smaller simplexes is equal to the volume of the simplex. Based on this geometrical property, we propose a new objective function for endmember generation, whose variable only includes the mixing matrix. As a result, all the problems caused by the abundance matrix can be avoided. Experiments using both simulated and real hyperspectral data show that the GOM is effective in searching the optimal solution.

This letter proposes a small target detection method for the hyperspectral image based on higher order statistics. This method first calculates the coskewness tensor of the hyperspectral image, followed by the orthogonal decomposition using higher order singular value decomposition. The obtained singular vectors are then used to perform the orthogonal transform to the centralized image. Compared to the popular blind source separation techniques, the presented method keeps clear of nonconvergence. Experiments with a real hyperspectral image show that the interested small target will be presented in the first few bands (even in the first band) very clearly after the transformation.

Reflectance of typical artificial surfaces, such as road and roof is usually believed to be invariant in a short period of time due to their physical and chemical stability. To examine its variability, reflectance of asphalt, concrete, walkway slab, asphalt roof paper and color plate is measured using dual-beam method. A preprocessing procedure is performed to remove possible errors caused by non-target factors. Measurement results show that reflectance of these targets are relatively stable when sun elevation condition is large and change rapidly when sun elevation is close to 0 °. This result provides useful information about reflectance variation of typical urban surfaces under changing field condition and may benefit reflectance modeling studies on similar targets.