To date, transformer-based frameworks have demonstrated impressive results in single-image super-resolution (SISR). However, under practical lightweight scenarios, the complex interaction of deep image feature extraction and similarity modeling limits the performance of these methods, since they require simultaneous layer-specific optimization of both two tasks. In this work, we introduce a novel Unified Projection Sharing algorithm(UPS) to decouple the feature extraction and similarity modeling, achieving notable performance. To do this, we establish a unified projection space defined by a learnable projection matrix, for similarity calculation across all self-attention layers. As a result, deep image feature extraction remains a per-layer optimization manner, while similarity modeling is carried out by projecting these image features onto the shared projection space. Extensive experiments demonstrate that our proposed UPS achieves state-of-the-art performance relative to leading lightweight SISR methods, as verified by various popular benchmarks. Moreover, our unified optimized projection space exhibits encouraging robustness performance for unseen data (degraded and depth images). Finally, UPS also demonstrates promising results across various image restoration tasks, including real-world and classic SISR, image denoising, and image deblocking.

Shapley values, a gold standard for feature attribution in Explainable AI, face two primary challenges. First, the canonical Shapley framework assumes that the worth function is additive, yet real-world payoff constructions--driven by non-Gaussian distributions, heavy tails, feature dependence, or domain-specific loss scales--often violate this assumption, leading to distorted attributions. Secondly, achieving sparse explanations in high dimensions by computing dense Shapley values and then applying ad hoc thresholding is prohibitively costly and risks inconsistency. We introduce Sparse Isotonic Shapley Regression (SISR), a unified nonlinear explanation framework. SISR simultaneously learns a monotonic transformation to restore additivity--obviating the need for a closed-form specification--and enforces an L0 sparsity constraint on the Shapley vector, enhancing computational efficiency in large feature spaces. Its optimization algorithm leverages Pool-Adjacent-Violators for efficient isotonic regression and normalized hard-thresholding for support selection, yielding implementation ease and global convergence guarantees. Analysis shows that SISR recovers the true transformation in a wide range of scenarios and achieves strong support recovery even in high noise. Moreover, we are the first to demonstrate that irrelevant features and inter-feature dependencies can induce a true payoff transformation that deviates substantially from linearity. Experiments in regression, logistic regression, and tree ensembles demonstrate that SISR stabilizes attributions across payoff schemes, correctly filters irrelevant features while standard Shapley values suffer severe rank and sign distortions. By unifying nonlinear transformation estimation with sparsity pursuit, SISR advances the frontier of nonlinear explainability, providing a theoretically grounded and practical attribution framework.

Self-induced stochastic resonance (SISR) is the emergence of coherent oscillations in slow-fast excitable systems driven solely by noise, without external periodic forcing or proximity to a bifurcation. This work presents a physics-informed machine learning framework for modeling and predicting SISR in the stochastic FitzHugh-Nagumo neuron. We embed the governing stochastic differential equations and SISR-asymptotic timescale-matching constraints directly into a Physics-Informed Neural Network (PINN) based on a Noise-Augmented State Predictor architecture. The composite loss integrates data fidelity, dynamical residuals, and barrier-based physical constraints derived from Kramers' escape theory. The trained PINN accurately predicts the dependence of spike-train coherence on noise intensity, excitability, and timescale separation, matching results from direct stochastic simulations with substantial improvements in accuracy and generalization compared with purely data-driven methods, while requiring significantly less computation. The framework provides a data-efficient and interpretable surrogate model for simulating and analyzing noise-induced coherence in multiscale stochastic systems.

How to achieve such spatial adaptation in a principled manner has been an open problem in both traditional model-based and modern learning-based approaches toward SISR. In this paper, we propose a new adaptive weighted loss for SISR to train deep networks focusing on challenging situations such as textured and edge pixels with high uncertainty.

To date, transformer-based frameworks have demonstrated impressive results in single-image super-resolution (SISR). However, under practical lightweight scenarios, the complex interaction of deep image feature extraction and similarity modeling limits the performance of these methods, since they require simultaneous layer-specific optimization of both two tasks. In this work, we introduce a novel Unified Projection Sharing algorithm(UPS) to decouple the feature extraction and similarity modeling, achieving notable performance. To do this, we establish a unified projection space defined by a learnable projection matrix, for similarity calculation across all self-attention layers. As a result, deep image feature extraction remains a per-layer optimization manner, while similarity modeling is carried out by projecting these image features onto the shared projection space.

Learning-based methods for blind single image super resolution (SISR) conduct the restoration by a learned mapping between high-resolution (HR) images and their low-resolution (LR) counterparts degraded with arbitrary blur kernels. However, these methods mostly require an independent step to estimate the blur kernel, leading to error accumulation between steps. We propose an end-to-end learning framework for the blind SISR problem, which enables image restoration within a unified Bayesian framework with either full- or semi-supervision. The proposed method, namely SREMN, integrates learning techniques into the generalized expectation-maximization (GEM) algorithm and infers HR images from the maximum likelihood estimation (MLE). Extensive experiments show the superiority of the proposed method with comparison to existing work and novelty in semi-supervised learning.

This paper proposes a quantum computing-based algorithm to solve the single image super-resolution (SISR) problem. One of the well-known classical approaches for SISR relies on the well-established patch-wise sparse modeling of the problem. Yet, this field's current state of affairs is that deep neural networks (DNNs) have demonstrated far superior results than traditional approaches. Nevertheless, quantum computing is expected to become increasingly prominent for machine learning problems soon. As a result, in this work, we take the privilege to perform an early exploration of applying a quantum computing algorithm to this important image enhancement problem, i.e., SISR. Among the two paradigms of quantum computing, namely universal gate quantum computing and adiabatic quantum computing (AQC), the latter has been successfully applied to practical computer vision problems, in which quantum parallelism has been exploited to solve combinatorial optimization efficiently. This work demonstrates formulating quantum SISR as a sparse coding optimization problem, which is solved using quantum annealers accessed via the D-Wave Leap platform. The proposed AQC-based algorithm is demonstrated to achieve improved speed-up over a classical analog while maintaining comparable SISR accuracy.

Here we present Symplectically Integrated Symbolic Regression (SISR), a novel technique for learning physical governing equations from data. SISR employs a deep symbolic regression approach, using a multi-layer LSTM-RNN with mutation to probabilistically sample Hamiltonian symbolic expressions. Using symplectic neural networks, we develop a model-agnostic approach for extracting meaningful physical priors from the data that can be imposed on-the-fly into the RNN output, limiting its search space. Hamiltonians generated by the RNN are optimized and assessed using a fourth-order symplectic integration scheme; prediction performance is used to train the LSTM-RNN to generate increasingly better functions via a risk-seeking policy gradients approach. Employing these techniques, we extract correct governing equations from oscillator, pendulum, two-body, and three-body gravitational systems with noisy and extremely small datasets.

Taking advantage of GANs enables to reconstruct SR images with high-frequency details and high perceptual quality. GAN based approach usually consists of Single Image Super Resolution (SISR) is a generator and a discriminator. Discriminator try to a very active research field. This paper identify HR or SR image whereas generator try to fool addresses SISR by using GAN-based approach discriminator to classify its generated SR image as with dual discriminators and incorporate HR image. SRGAN [3] employs an adversarial loss with attention mechanism. The experimental term to increase visually pleasing quality. SRFeat [7] results show that GDCA can used two discriminators and adopts the adversarial generate sharper and high pleasing images loss terms in both image and feature domains, resulting compare to other conventional methods.