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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.

Differential equations, Nonlinear. --- Differential equations, Parabolic. --- Finite differences. --- Image processing --- Nonlinear operators. --- Mathematics. --- Differential equations, Parabolic --- Differential equations, Nonlinear --- Nonlinear operators --- Finite differences --- Mathematics --- Partial differential equations. --- Approximation theory. --- Functional analysis. --- Visualization. --- Calculus of variations. --- Partial Differential Equations. --- Approximations and Expansions. --- Functional Analysis. --- Calculus of Variations and Optimal Control; Optimization. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Visualisation --- Imagination --- Visual perception --- Imagery (Psychology) --- Math --- Science --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Partial differential equations --- Image processing - Mathematics