With the rapid advancement of artificial intelligence and the widespread availability of multi-source data, high-dimensional data have become ubiquitous in modern scientific and engineering applications, including image and signal processing, medical imaging, industrial inspection, financial econometrics, text and semantic analysis, and remote sensing. While high-dimensional representations enable richer information modeling, they also introduce fundamental challenges to traditional mathematical methodologies, statistical inference techniques, and learning-based models.

Key issues such as effective dimensionality reduction, feature extraction, structural modeling, robust estimation, and scalable inference in high-dimensional settings remain at the forefront of applied mathematics and statistics. Addressing these challenges requires not only algorithmic innovation but also solid theoretical foundations that bridge optimization, statistical modeling, and modern machine learning.

This Special Issue aims to bring together recent theoretical advances, methodological developments, and representative applications in high-dimensional data processing. By fostering cross-fertilization among optimization theory, statistical learning, and deep models, the issue seeks to advance new mathematical frameworks, computational paradigms, and theoretical insights for analyzing and processing high-dimensional data.

We welcome original research articles, review papers, and methodological contributions on topics including, but not limited to, the following areas:

1. Mathematical Foundations of High-Dimensional Data
- High-dimensional statistical theory and sparse representation
- Tensor analysis and multimodal data theory
- Convex and nonconvex optimization in high-dimensional settings
- Variational analysis, functional analysis, and random matrix theory

2. Optimization-Based Methods for High-Dimensional Data Processing
- Sparse coding, low-rank matrix recovery, and tensor decomposition
- Variational models, graph-based optimization, and multiscale methods
- Efficient representation and recovery of images, videos, and 3D point clouds
- Robust estimation under complex noise and data corruption

3. Deep Learning for High-Dimensional Data
- Deep architectures for high-dimensional signals and images (CNNs, Transformers, diffusion models)
- Generative models for data reconstruction, completion, and denoising
- Deep feature extraction and nonlinear dimensionality reduction
- Interpretability, robustness, and stability analysis of deep models

4. Fusion of Optimization Theory and Deep Models
- Optimization-inspired and model-driven deep learning
- Deep unfolding and algorithm unrolling methods
- Differentiable optimization and learnable iterative schemes
- Learning algorithms with theoretical guarantees (convergence, consistency, generalization)

5. Applications of High-Dimensional Data Processing
- Medical image reconstruction and computer-aided diagnosis
- Remote sensing imaging, super-resolution, and change detection
- Industrial nondestructive testing and quality control
- Bioinformatics, genomics, and high-dimensional biological data analysis
- Financial time-series modeling and risk management
- Representation learning for text, semantic, and graph-structured data

Impact

Frontiers in Applied Mathematics and Statistics

Optimization

Mathematics of Computation and Data Science