Understanding the spatial distribution of palms in tropical forests is essential for ecological monitoring, conservation strategies, and the sustainable integration of natural forest products into local and global supply chains. However, the analysis of remotely sensed data are challenged by overlapping palm and tree crowns, uneven shading across the canopy surface, and the heterogeneous nature of the forest landscapes, which often affect the performance of palm detection and segmentation algorithms. To overcome these issues, we introduce PalmDSNet, a deep learning framework for efficient detection, segmentation, and counting of canopy palms. To model spatial patterns, we introduce a bimodal reproduction algorithm that simulates palm propagation based on PalmDSNet outputs. We used UAV-captured imagery to create orthomosaics from 21 sites across western Ecuadorian tropical forests, covering a gradient from the everwet Chocó forests near Colombia to the drier forests of southwestern Ecuador. Expert annotations were used to create a comprehensive dataset, including 7,356 bounding boxes on image patches and 7,603 palm centers across five orthomosaics, encompassing a total area of 449 hectares. By integrating detection and spatial modeling, we effectively simulate the spatial distribution of palms in diverse and dense tropical environments, validating its utility for advanced applications in tropical forest monitoring and remote sensing analysis. The dataset can be accessed at 10.5281/zenodo.13822508, and the code to replicate the study is available at github.com/ckn3/palm-ds-sp.

Hyperspectral images (HSIs) provide exceptional spatial and spectral resolution of a scene, crucial for various remote sensing applications. However, the high dimensionality, presence of noise and outliers, and the need for precise labels of HSIs present significant challenges to the analysis of HSIs, motivating the development of performant HSI clustering algorithms. This paper introduces a novel unsupervised HSI clustering algorithm—Superpixel-based and Spatially-regularized Diffusion Learning (S2DL)—which addresses these challenges by incorporating rich spatial information encoded in HSIs into diffusion geometry-based clustering. S2DL employs the Entropy Rate Superpixel (ERS) segmentation technique to partition an image into superpixels, then constructs a spatially-regularized diffusion graph using the most representative high-density pixels. This approach reduces computational burden while preserving accuracy. Cluster modes, serving as exemplars for underlying cluster structure, are identified as the highest-density pixels farthest in diffusion distance from other highest-density pixels. These modes guide the labeling of the remaining representative pixels from ERS superpixels. Finally, majority voting is applied to the labels assigned within each superpixel to propagate labels to the rest of the image. This spatial-spectral approach simultaneously simplifies graph construction, reduces computational cost, and improves clustering performance. S2DL’s performance is illustrated with extensive experiments on four publicly available, real-world HSIs: Indian Pines, Salinas, Salinas A, and WHU-Hi. Additionally, we apply S2DL to landscape-scale, unsupervised mangrove species mapping in the Mai Po Nature Reserve, Hong Kong, using a Gaofen-5 HSI. The success of S2DL in these diverse numerical experiments indicates its efficacy on a wide range of important unsupervised remote sensing analysis tasks.

In this work, a novel algorithm called SVM with Shape-adaptive Reconstruction and Smoothed Total Variation (SaR-SVM-STV) is introduced to classify hyperspectral images, which makes full use of spatial and spectral information. The Shape-adaptive Reconstruction (SaR) is introduced to preprocess each pixel based on the Pearson Correlation be-tween pixels in its shape-adaptive (SA) region. Support Vector Machines (SVMs) are trained to estimate the pixel-wise probability maps of each class. Then the Smoothed Total Variation (STV) model is applied to denoise and generate the final classification map. Experiments show that SaR-SVM-STY outperforms the SVM-STV method with a few training labels, demonstrating the significance of reconstructing hy-perspectral images before classification.

Ash dieback (Hymenoscyphus fraxineus) is an introduced fungal disease that is causing the widespread death of ash trees across Europe. Remote sensing hyperspectral images encode rich structure that has been exploited for the detection of dieback disease in ash trees using supervised machine learning techniques. However, to understand the state of forest health at landscape-scale, accurate unsupervised approaches are needed. This article investigates the use of the unsupervised Diffusion and VCA-Assisted Image Segmentation (D-VIS) clustering algorithm for the detection of ash dieback disease in a forest site near Cambridge, United Kingdom. The unsupervised clustering presented in this work has high overlap with the supervised classification of previous work on this scene (overall accuracy = 71%). Thus, unsupervised learning may be used for the remote detection of ash dieback disease without the need for expert labeling.

Hyperspectral images encode rich structure that can be ex-ploited for material discrimination by machine learning al-gorithms. This article introduces the Active Diffusion and VCA-Assisted Image Segmentation (ADVIS) for active mate-rial discrimination. ADVIS selects high-purity, high-density pixels that are far in diffusion distance (a data-dependent met-ric) from other high-purity, high-density pixels in the hyper-spectral image. The ground truth labels of these pixels are queried and propagated to the rest of the image. The ADVIS active learning algorithm is shown to strongly outperform its fully unsupervised clustering algorithm counterpart, suggesting that the incorporation of a very small number of carefully-selected ground truth labels can result in substantially supe-rior material discrimination in hyperspectral images.

We consider the high-resolution imaging problem of 3-dimensional (3D) point source image recovery from 2-dimensional data using a method based on point spread function (PSF) engineering. The method involves a new technique, recently proposed by Prasad, based on the use of a rotating PSF with a single lobe to obtain depth from defocus. The amount of rotation of the PSF encodes the depth position of the point source. Applications include high-resolution single molecule localization microscopy as well as the problem addressed in this paper on localization of space debris using a space-based telescope. The localization problem is discretized on a cubical lattice where the coordinates of nonzero entries represent the 3D locations and the values of these entries the fluxes of the point sources. Finding the locations and fluxes of the point sources is a large-scale sparse 3D inverse problem. A new non-convex regularization method with a data-fitting term based on Kullback--Leibler (KL) divergence is proposed for 3D localization for the Poisson noise model. In addition, we propose a new scheme of estimation of the source fluxes from the KL data-fitting term. Numerical experiments illustrate the efficiency and stability of the algorithms that are trained on a random subset of image data before being applied to other images. Our 3D localization algorithms can readily be applied to other kinds of depth-encoding PSFs as well.

We present double random projection methods for reconstruction of imaging data. The methods draw upon recent results in the random projection literature, particularly on low-rank matrix approximations, and the reconstruction algorithm has only two simple and noniterative steps, while the reconstruction error is close to the error of the optimal low-rank approximation by the truncated singular-value decomposition. We extend the often-required symmetric distributions of entries in a random-projection matrix to asymmetric distributions, which can be more easily implementable on imaging devices. Experimental results are provided on the subsampling of natural images and hyperspectral images, and on simulated compressible matrices. Comparisons with other random projection methods are also provided.

The main aim of this paper is to study total variation (TV) regularization in deblurring and sparse unmixing of hyperspectral images. In the model, we also incorporate blurring operators for dealing with blurring effects, particularly blurring operators for hyperspectral imaging whose point spread functions are generally system dependent and formed from axial optical aberrations in the acquisition system. An alternating direction method is developed to solve the resulting optimization problem efficiently. According to the structure of the TV regularization and sparse unmixing in the model, the convergence of the alternating direction method can be guaranteed. Experimental results are reported to demonstrate the effectiveness of the TV and sparsity model and the efficiency of the proposed numerical scheme, and the method is compared to the recent Sparse Unmixing via variable Splitting Augmented Lagrangian and TV method by Iordache

In this paper we propose new algorithms for 3D tensor decomposition/factorization with many potential applications, especially in multi-way blind source separation (BSS), multidimensional data analysis, and sparse signal/image representations. We derive and compare three classes of algorithms: multiplicative, fixed-point alternating least squares (FPALS) and alternating interior-point gradient (AIPG) algorithms. Some of the proposed algorithms are characterized by improved robustness, efficiency and convergence rates and can be applied for various distributions of data and additive noise.

This study involves a methodology for the automatic identification of semantic features and document clusters in a heterogeneous text collection. The methodology is based upon encoding the data using low rank non-negative matrix factorization algorithms to preserve natural data non-negativity and thus avoid subtractive basis vector and encoding interactions present in techniques such as principal component analysis. Some existing non-negative matrix factorization techniques are reviewed and some new ones are proposed. Numerical experiments are reported on the use of a hybrid NMF algorithm to produce a parts-based approximation of a sparse term-by-document matrix. The resulting basis vectors and matrix projection can be used to identify underlying semantic features (topics) and document clusters of the corresponding text collection.

Blind image restoration is the process of estimating both the true image and the blur from the degraded image, using only partial information about degradation sources and the imaging system. Our main interest concerns optical image enhancement, where the degradation often involves a convolution process. We provide a method to incorporate truncated eigenvalue and total variation regularization into a nonlinear recursive inverse filter (RIF) blind deconvolution scheme first proposed by Kundar, and by Kundur and Hatzinakos. Tests are reported on simulated and optical imaging problems.

This work involves two-stage approaches to enhancing the quality of images taken through the atmosphere. First, a control problem arising in adaptive-optics is discussed. The problem involves optimal real-time control of very fast-acting deformable mirrors designed to compensate for atmospheric turbulence and other image degradation factors, such as wind-induced telescope vibration (windshake). The surface shapes of the mirrors must change rapidly to correct for time-varying optical distortions. The second stage of compensating for the effects of atmospheric turbulence generally occurs off-line, and consists of the post-processing step of image restoration. Here, the work involves large-scale computations, using either simultaneous image of a natural guide star or a large ensemble of images corresponding to different atmospheric realizations, to deconvolve the blurring effects of atmospheric turbulence.

Removing a linear shift-invariant blur from a signal or image can be accomplished by inverse or Wiener filtering, or by an iterative least-squares deblurring procedure. Because of the ill-posed characteristics of the deconvolution problem, in the presence of noise, filtering methods often yield poor results. On the other hand, iterative methods often suffer from slow convergence at high spatial frequencies. This paper concerns solving deconvolution problems for atmospherically blurred images by the preconditioned conjugate gradient algorithm, where a new approximate inverse preconditioner is used to increase the rate of convergence. Theoretical results are established to show that fast convergence can be expected, and test results are reported for a ground-based astronomical imaging problem.

Numerical properties of the hyperbolic rotation method for windowed RLS filtering are examined. This matrix-oriented approach is important from two standpoints: (1) it provides the LS predictor for a sliding-window block of data, and (2) it is amenable to parallel implementation. It is shown how a hyperbolic rotation matrix may be constructed to update the LS Cholesky factor as a function of the previous Cholesky factor and the data in the sliding window. Finally, it is shown that the hyperbolic rotation method is stable for observation matrices which are not rank-deficient.

An algorithm combining Gaussian elimination with the modified Gram-Schmidt (MGS) procedure is given for solving the linear least squares problem. The method is based on the operational efficiency of Gaussian elimination for LU decompositions and the numerical stability of MGS for unitary decompositions and is designed for slightly overdetermined linear systems.