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Single-image super-resolution (SISR) continues to face difficulties in reconstructing perceptually critical details from degraded low-resolution observations. While conventional Bayesian approaches utilizing Relevance Vector Machines (RVMs) provide probabilistic interpretations, their reliance on fixed blur kernel definitions and homogeneous pixel dependency models often yields artifacts in complex scenarios. To resolve these issues, this study introduces a hierarchical Bayesian architecture enhanced by an adaptive Laplacian prior, which extends the sparse Bayesian learning (SBL) paradigm. Diverging from traditional Gaussian-based frameworks, our method employs sparsity-inducing regularization to selectively prioritize structurally salient regions (e.g., edge discontinuities, texture boundaries), while dynamically quantifying reconstruction uncertainty through pixel-wise variance analysis. Additionally, a spatially adaptive optimization mechanism is designed to streamline computational workflows without compromising restoration fidelity. Evaluations across multiple benchmarks confirm the framework’s advantages: it surpasses existing state-of-the-art techniques in both quantitative metrics (PSNR, SSIM) and qualitative assessments, demonstrating superior artifact suppression in high-frequency domains. Comparative analyses against recent state-of-the-art models further validate its capability to harmonize sparse representation with structural coherence.

Spectral unmixing is important in analyzing and processing hyperspectral images (HSIs). With the availability of large spectral signature libraries, the main task of spectral unmixing is to estimate corresponding proportions called abundances of pure spectral signatures called endmembers in mixed pixels. In this vein, only a few endmembers participate in the formation of mixed pixels in the scene and so we call them active endmembers. A plethora of sparse unmixing algorithms exploit spectral and spatial information in HSIs to enhance abundance estimation results. Many algorithms, however, treat the abundances corresponding to active and nonactive endmembers in the scene equivalently. In this article, we propose a framework named mixing support detection (MSD) for the spectral unmixing problem. The main idea is first to detect the active and nonactive endmembers at each iteration and then to treat the corresponding abundances differently. It follows that we only focus on the estimation of active abundances with the assumption of zero abundances corresponding to nonactive endmembers. It can be expected to reduce the computational cost, avoid the perturbations in nonactive abundances, and enhance the sparsity of the abundances. We embed the MSD framework in classic alternating direction method of multipliers (ADMM) updates and obtain an ADMM-MSD algorithm. In particular, five ADMM-MSD-based unmixing algorithms are provided. The residual and objective convergence results of the proposed algorithm are given under certain assumptions. Both simulated and real-data experiments demonstrate the efficacy and superiority of the proposed algorithm compared with some state-of-the-art algorithms.

A joint radar-communication (JRC) system utilizes the integrated transmit waveform and a single platform to perform radar and communication functions simultaneously. Admittedly, the multibeam waveform design approach could transmit the assigned waveforms in different beams with the aid of spatial and temporal degrees of freedom. However, a high sidelobe level (SLL) in the beampattern reduces energy efficiency and expands exposure probability. In this study, we propose a novel spatial–temporal joint waveform design method based on the beamforming algorithm to form a low SLL beampattern. Waveform synthesis constraints are considered to synthesize desired radar and communication waveforms at designated directions. Furthermore, we impose the constant modulus constraint to lessen the impact of the high peak-to-average ratio (PAPR). The optimization process of the whole model can be summarized as two stages. First, the covariance matrix is created by convex optimization with respect to the minimum SLL. Second, the integrated transmit waveform is tuned through an alternating projection algorithm. Based on the simulation findings, we demonstrate that the proposed method outperforms the traditional methods in terms of low SLL and waveform synthesis. Meanwhile, we validate the effectiveness of the proposed method using semi-physical experiment results.

We propose a novel two-stage method for the classification of hyperspectral images. Pixel-wise classifiers, such as the classical support vector machine (SVM), consider spectral information only. As spatial information is not utilized, the classification results are not optimal and the classified image may appear noisy. Many existing methods, such as morphological profiles, superpixel segmentation, and composite kernels, exploit the spatial information. In this paper, we propose a two-stage approach inspired by image denoising and segmentation to incorporate the spatial information. In the first stage, SVMs are used to estimate the class probability for each pixel. In the second stage, a convex variant of the Mumford–Shah model is applied to each probability map to denoise and segment the image into different classes. Our proposed method effectively utilizes both spectral and spatial information of the data sets and is fast as only convex minimization is needed in addition to the SVMs. Experimental results on three widely utilized real hyperspectral data sets indicate that our method is very competitive in accuracy, timing, and the number of parameters when compared with current state-of-the-art methods, especially when the inter-class spectra are similar or the percentage of training pixels is reasonably high.

Spectral unmixing of hyperspectral images is an important issue in the fields of remote sensing. Jointly exploring the spectral and spatial information embedded in the data is helpful to enhance the consistency between mixing/unmixing models and real scenarios. This paper proposes a graph regularized nonlinear unmixing method based on the recent multilinear mixing model (MLM). The MLM takes account of all orders of interactions between endmembers, and indicates the pixel-wise nonlinearity with a single probability parameter. By incorporating the Laplacian graph regularizers, the proposed method exploits the underlying manifold structure of the pixels’ spectra, in order to augment the estimations of both abundances and nonlinear probability parameters. Besides the spectrum-based regularizations, the sparsity of abundances is also incorporated for the proposed model. The resulting optimization problem is addressed by using the alternating direction method of multipliers (ADMM), yielding the so-called graph regularized MLM (G-MLM) algorithm. To implement the proposed method on large hypersepectral images in real world, we propose to utilize a superpixel construction approach before unmixing, and then apply G-MLM on each superpixel. The proposed methods achieve superior unmixing performances to state-of-the-art strategies in terms of both abundances and probability parameters, on both synthetic and real datasets.

Synthetic aperture radar (SAR) automatic target recognition (ATR) underpins various remote sensing tasks, such as defense surveillance, environmental monitoring, and disaster management. However, the scarcity of annotated SAR data significantly limits the performance of conventional data-driven methods. To address this challenge, we propose a novel few-shot learning (FSL) framework: the alternating direction method of multipliers–graph convolutional network (ADMM-GCN) framework. ADMM-GCN integrates a GCN with ADMM to enhance SAR ATR under limited data conditions, effectively capturing both global and local structural information from SAR samples. Additionally, it leverages a mixed regularized loss to mitigate overfitting and employs an ADMM-based optimization strategy to improve training efficiency and model stability. Extensive experiments conducted on the Moving and Stationary Target Acquisition and Recognition (MSTAR) dataset demonstrate the superiority of ADMM-GCN, achieving an impressive accuracy of 92.18% on the challenging three-way 10-shot task and outperforming the benchmarks by 3.25%. Beyond SAR ATR, the proposed approach also advances FSL for real-world applications in remote sensing and geospatial analysis, where learning from scarce data is essential.

In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at p locations and n time points with the possibility that p > n. While principal component analysis (PCA) is commonly applied to find the dominant patterns, the eigenimages produced from PCA may exhibit patterns that are too noisy to be physically meaningful when p is large relative to n. To obtain more precise estimates of eigenimages, we propose a regularization approach incorporating smoothness and sparseness of eigenimages, while accounting for their orthogonality. Our method allows data taken at irregularly spaced or sparse locations. In addition, the resulting optimization problem can be solved using the alternating direction method of multipliers, which is easy to implement, and applicable to a large spatial dataset. Furthermore, the estimated eigenfunctions provide a natural basis for representing the underlying spatial process in a spatial random-effects model, from which spatial covariance function estimation and spatial prediction can be efficiently performed using a regularized fixed-rank kriging method. Finally, the effectiveness of the proposed method is demonstrated by several numerical examples.

We consider an energy production network with zones of production and transfer links. Each zone representing an energy market (a country, part of a country or a set of countries) has to satisfy the local demand using its hydro and thermal units and possibly importing and exporting using links connecting the zones. Assuming that we have the appropriate tools to solve a single zonal problem (approximate dynamic programming, dual dynamic programming, etc.), the proposed algorithm allows us to coordinate the productions of all zones. We propose two reformulations of the dynamic model which lead to different decomposition strategies. Both algorithms are adaptations of known monotone operator splitting methods, namely the alternating direction method of multipliers and the proximal decomposition algorithm which have been proved to be useful to solve convex separable optimization problems. Both algorithms present similar performance in theory but our numerical experimentation on real-size dynamic models have shown that proximal decomposition is better suited to the coordination of the zonal subproblems, becoming a natural choice to solve the dynamic optimization of the European electricity market.

Deep neural networks have shown great potential in various low-level vision tasks, leading to several state-of-the-art image denoising techniques. Training a deep neural network in a supervised fashion usually requires the collection of a great number of examples and the consumption of a significant amount of time. However, the collection of training samples is very difficult for some application scenarios, such as the full-sampled data of magnetic resonance imaging and the data of satellite remote sensing imaging. In this paper, we overcome the problem of a lack of training data by using an unsupervised deep-learning-based method. Specifically, we propose a deep-learning-based method based on the deep image prior (DIP) method, which only requires a noisy image as training data, without any clean data. It infers the natural images with random inputs and the corrupted observation with the help of performing correction via a convolutional network. We improve the original DIP method as follows: Firstly, the original optimization objective function is modified by adding nonlocal regularizers, consisting of a spatial filter and a frequency domain filter, to promote the gradient sparsity of the solution. Secondly, we solve the optimization problem with the alternating direction method of multipliers (ADMM) framework, resulting in two separate optimization problems, including a symmetric U-Net training step and a plug-and-play proximal denoising step. As such, the proposed method exploits the powerful denoising ability of both deep neural networks and nonlocal regularizations. Experiments validate the effectiveness of leveraging a combination of DIP and nonlocal regularizers, and demonstrate the superior performance of the proposed method both quantitatively and visually compared with the original DIP method.

In a previous study, a thin In-Ga-Zn-oxide light addressable potentiometric sensor (IGZO LAPS) was indicated to have the advantages of low interference from ambient light, a high photocurrent and transfer efficiency, and a low cost. However, illumination optimization to obtain two-dimensional (2D) chemical images with better spatial resolutions has not been fully investigated. The trigger current and AC-modulated frequency of a 405-nm laser used to illuminate the fabricated IGZO LAPS were modified to check the photocurrent of the sensing area and SU8–2005 masking area, obtaining spatial resolution-related functions for the first time. The trigger current of illumination was adjusted from 0.020 to 0.030 A to compromise between an acceptable photocurrent and the integrity of the SU8–2005 masking layer. The photocurrent (PC) and differential photocurrent (DPC) versus scanning length (SL) controlled by an X-Y stage were used to check the resolved critical dimensions (CDs). The difference between resolved CD and optically measured CD (e.g., delta CD) measured at an AC frequency of 500 Hz revealed overall smaller values, supporting precise measurement in 2D imaging. The signal-to-noise ratio (SNR) has an optimized range of 2.0 to 2.15 for a better resolution for step spacings of both 10 and 2 μm in the scanning procedure to construct static 2D images. Under illumination conditions with a trigger current of 0.025 A and at an AC frequency of 500 Hz, the spatial resolution can be reduced to 10 μm from the pattern width of 6 μm. This developed methodology provides a quantitative evaluation with further optimization in spatial resolution without an extra cost for applications requiring a high spatial resolution, such as single-cell activity.