This comprehensive volume develops deep learning methods for image reconstruction within the rigorous mathematical framework of regularization theory. The central thesis is that the principal deep learning approaches — data-consistent networks, learned regularization, and implicit non-variational regularization — are all convergent regularization methods: they produce stable reconstructions that converge to the exact solution as the noise level tends to zero. Each method is treated with full proofs and quantitative convergence rates. The theory covers both exact and approximate data consistency, including networks that learn corrections beyond the null space under regularization control. Numerical experiments on computed tomography, photoacoustic tomography, and inpainting illustrate the methods in full and limited data regimes.The book is aimed at master students, doctoral researchers, and scientists in inverse problems, medical imaging, and mathematical image reconstruction seeking a solid mathematical foundation.
