ABsinNonlinear

ABsinNonlinear is a computational framework and algorithm designed for solving nonlinear inverse problems in scientific and engineering applications. Inverse problems involve determining unknown parameters or functions from observed data, often in the presence of noise or incomplete measurements. The ABsinNonlinear method builds upon the Alternating Direction Method of Multipliers (ADMM) framework, integrating it with nonlinear regularization techniques to improve stability and accuracy in reconstruction tasks.

The algorithm is particularly useful in fields such as medical imaging, materials science, and geophysics, where traditional linear inversion methods may fail due to the inherent nonlinearity of the underlying physical processes. By iteratively decomposing the problem into simpler subproblems, ABsinNonlinear efficiently balances data fidelity and regularization constraints, reducing computational complexity while maintaining robustness.

Key features of ABsinNonlinear include its ability to handle large-scale problems, adaptability to various nonlinear models, and convergence guarantees under mild conditions. The method employs a split-Bregman formulation, which enhances numerical stability and allows for parallelizable implementations. This makes it suitable for high-performance computing environments, where efficiency is critical.

Researchers have applied ABsinNonlinear to tasks such as phase retrieval, microscopy, and tomographic reconstruction, demonstrating its effectiveness in recovering high-quality solutions from noisy or sparse data. The algorithm’s flexibility also extends to hybrid models, combining linear and nonlinear components for more complex scenarios. While its performance depends on problem-specific tuning, ABsinNonlinear provides a versatile tool for advancing inverse problem solvers in both theoretical and applied contexts.