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Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2003. This book contains a detailed mathematical analysis of the variational approach to image restoration based on the minimization of the total variation submitted to the constraints given by the image acquisition model. This model, initially introduced by Rudin, Osher, and Fatemi, had a strong influence in the development of variational methods for image denoising and restoration, and pioneered the use of the BV model in image processing. After a full analysis of the model, the minimizing total variation flow is studied under different boundary conditions, and its main qualitative properties are exhibited. In particular, several explicit solutions of the denoising problem are computed. Front Matter Total Variation Based Image Restoration The Neumann Problem for the Total Variation Flow The Total Variation Flow in ℝ N Asymptotic Behaviour and Qualitative Properties of Solutions The Dirichlet Problem for the Total Variation Flow Parabolic Equations Minimizing Linear Growth Functionals: L 2 -Theory Parabolic Equations Minimizing Linear Growth Functionals: L 1 -Theory Back Matter