In this article, we propose a novel solution for nonconvex problems of multiple variables, especially for those typically solved by an alternating minimization (AM) strategy that splits the original optimization problem into a set of subproblems corresponding to each variable and then iteratively optimizes each subproblem using a fixed updating rule. However, due to the intrinsic nonconvexity of the original optimization problem, the optimization can be trapped into a spurious local minimum even when each subproblem can be optimally solved at each iteration. Meanwhile, learning-based approaches, such as deep unfolding algorithms, have gained popularity for nonconvex optimization; however, they are highly limited by the availability of labeled data and insufficient explainability. To tackle these issues, we propose a meta-learning based alternating minimization (MLAM) method that aims to minimize a part of the global losses over iterations instead of carrying minimization on each subproblem, and it tends to learn an adaptive strategy to replace the handcrafted counterpart resulting in advance on superior performance. The proposed MLAM maintains the original algorithmic principle, providing certain interpretability. We evaluate the proposed method on two representative problems, namely, bilinear inverse problem: matrix completion and nonlinear problem: Gaussian mixture models. The experimental results validate the proposed approach outperforms AM-based methods.

Learning based approaches have witnessed great successes in blind single image super-resolution (SISR) tasks, however, handcrafted kernel priors and learning based kernel priors are typically required. In this paper, we propose a meta-learning and Markov Chain Monte Carlo (MCMC) based SISR approach to learn kernel priors from organized randomness. In concrete, a lightweight network is adopted as kernel generator, and is optimized via learning from the MCMC simulation on random Gaussian distributions. This procedure provides an approximation for the rational blur kernel, and introduces a network-level Langevin dynamics into SISR optimization processes, which contributes to preventing bad local optimal solutions for kernel estimation. Meanwhile, a meta-learning based alternating optimization procedure is proposed to optimize the kernel generator and image restorer, respectively. In contrast to the conventional alternating minimization strategy, a meta-learning based framework is applied to learn an adaptive optimization strategy, which is less-greedy and results in better convergence performance. These two procedures are iteratively processed in a plug-and-play fashion, for the first time, realizing a learning-based but plug-and-play blind SISR solution in unsupervised inference. Extensive simulations demonstrate the superior performance and generalization ability of the proposed approach when compared with the Start-of-the-Art solutions on synthesis and real-world datasets.

This paper focuses on generating Inverse Synthetic Aperture Radar (ISAR) images from optical images, in particular, for orbit space targets. ISAR images are widely applied in space target observation and classification tasks, whereas, limited to the expensive cost of ISAR sample collection, training deep learning-based ISAR image classifiers with insufficient samples and generating ISAR samples from emulation optical images via image translation techniques have attracted increasing attention. Image translation has highlighted significant success and popularity in computer vision, remote sensing and data generation societies. However, most of the existing methods are implemented under the discipline of extracting the explicit pixel-level features and do not perform effectively while entailing translation to domains with specific implicit features, such as ISAR image does. We propose a meta-learning based domain prior to implicit feature modelling and apply it to CycleGAN and UNIT models to realize effective translations between the ISAR and optical domains. Two representative implicit features, ISAR scattering distribution feature from the physical domain and the classification identifying feature from the task domain, are elaborately formulated with explicit modelling in statistic form. A meta-learning based training scheme is introduced to leverage the mutual knowledge of domain priors across different samples, and thus allows few-shot learning capacity with dramatically reduced training samples. Extensive simulations validate that the obtained ISAR images have better visible-authenticity and training-effectiveness than the existing image translation approaches on various synthetic datasets. Source codes are available at.

This letter proposes a learning aided gradient descent (LAGD) algorithm to solve the weighted sum rate (WSR) maximization problem for multiple-input single-output (MISO) beamforming. The proposed LAGD algorithm directly optimizes the transmit precoder through implicit gradient descent based iterations, at each of which the optimization strategy is determined by a neural network, and thus, is dynamic and adaptive. At each instance of the problem, this network is initialized randomly, and updated throughout the iterative solution process. Therefore, the LAGD algorithm can be implemented at any signal-to-noise ratio (SNR) and for arbitrary antenna/user numbers, does not require labelled data or training prior to deployment. Numerical results show that the LAGD algorithm can outperform of the well-known WMMSE algorithm as well as other learning-based solutions with a modest computational complexity. Our code is available at https://github.com/XiaGroup/LAGD .

Hyperspectral image super-resolution (HSI-SR) is fundamentally more difficult than RGB image SR, since its ultrahigh spectral dimensionality. Existing supervised methods rely on labeled training data to obtain data prior, which incurs prohibitive collection costs and limits generalization. Unsupervised methods individually preset the band and kernel with handcrafted priors, whereas this decoupling modeling artificially creates a complexity-performance trade-off in the selected band number. To address these issues, we propose BKX-HMM, a unified statistical framework for blind HSI-SR, which uniformly models the band selection, kernel estimation, and HSI restoration through the state transition of a hidden Markov model (HMM). BKX-HMM redefines the trade-off as a distributional fitting problem: each Markov transition progressively learns optimal parameters of a full-band distribution via limited spectral observations. Based on BKX-HMM, we propose BKSR, the first unsupervised blind HSI-SR method, which consists of three synergistic modules: Gibbs sampling-based band selection (GBS), test-time-training kernel estimation (TKE), and robust HSI restoration (RHR). These modules form a closed-loop optimization cycle: i) In GBS, the dynamic ergodicity of Gibbs sampling provides a global spectral view for kernel estimation and HSI restoration while maintaining local spectral computations; ii) In TKE, the GBS-sampled bands guide the kernel estimator update, achieving a learnable sampling-based mechanism, which refines kernel estimation to regularize RHR's diffusion trajectory; iii) In RHR, a spectral hyper-Laplacian prior is integrated into the reverse process of an off-the-shelf diffusion model, which achieves non-i.i.d. noise robust HSI restoration, feedback reweights band and kernel importance for subsequent GBS and TKE iterations. Extensive experiments on both synthetic and real HSI datasets demonstrate our BKSR's superiority over baseline methods across diverse scenarios (e.g., unknown Gaussian/motion kernel, non-i.i.d. noise) while maintaining comparable computational costs to the classic band selection methods. The code is available at https://github.com/XYLGroup/BKSR https://github.com/XYLGroup/BKSR.