Tikhonov Regularization

Tikhonov regularization is a widely used technique for solving ill-posed inverse problems, aiming to stabilize solutions by incorporating prior knowledge through a penalty term. Current research focuses on extending its application to complex problems like robot localization, seismic impedance inversion, and medical imaging (e.g., Magnetic Particle Imaging), often integrating it with deep learning or other advanced methods to improve accuracy and efficiency. This approach is particularly valuable in scenarios with noisy or incomplete data, where traditional methods struggle, and ongoing work explores optimal regularization parameter selection and the development of more sophisticated penalty functions to enhance performance and theoretical understanding.