This book is devoted to the study of variational methods in imaging. The presentation is mathematically rigorous and covers a detailed treatment of the approach from an inverse problems point of view.Key Features: (1) Introduces variational methods with motivation from the deterministic, geometric, and stochastic point of view. (2) Bridges the gap between regularization theory in image analysis and in inverse problems. (3) Presents case examples in imaging to illustrate the use of variational methods e.g. denoising, thermoacoustics, computerized tomography. (4) Discusses link between non-convex calculus of variations, morphological analysis, and level set methods. (5) Analyses variational methods containing classical analysis of variational methods, modern analysis such as G-norm properties, and non-convex calculus of variations. (6) Uses numerical examples to enhance the theory.This book is geared towards graduate students and researchers in applied mathematics. It can serve as a main text for graduate courses in image processing and inverse problems or as a supplemental text for courses on regularization. Researchers and computer scientists in the area of imaging science will also find this book useful.