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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: - Introduces variational methods with motivation from the deterministic, geometric, and stochastic point of view - Bridges the gap between regularization theory in image analysis and in inverse problems - Presents case examples in imaging to illustrate the use of variational methods e.g. denoising, thermoacoustics, computerized tomography - Discusses link between non-convex calculus of variations, morphological analysis, and level set methods - Analyses variational methods containing classical analysis of variational methods, modern analysis such as G-norm properties, and non-convex calculus of variations - 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.

Imaging systems. --- Variational principles. --- Extremum principles --- Minimal principles --- Variation principles --- Mathematics. --- Radiology. --- Image processing. --- Numerical analysis. --- Calculus of variations. --- Calculus of Variations and Optimal Control; Optimization. --- Image Processing and Computer Vision. --- Signal, Image and Speech Processing. --- Numerical Analysis. --- Imaging / Radiology. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Mathematical analysis --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Radiological physics --- Physics --- Radiation --- Math --- Science --- Calculus of variations --- Radar --- Remote sensing --- Television --- Scanning systems --- Equipment and supplies --- Mathematical optimization. --- Computer vision. --- Radiology, Medical. --- Clinical radiology --- Radiology, Medical --- Radiology (Medicine) --- Medical physics --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Operations research --- Simulation methods --- System analysis --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Variational principles --- Optical data processing. --- Signal processing. --- Speech processing systems. --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Optical equipment

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Numerical methods of optimisation --- Numerical analysis --- Physical methods for diagnosis --- Computer. Automation --- beeldverwerking --- radiologie --- medische beeldvorming --- kansrekening --- numerieke analyse --- signaalverwerking --- optimalisatie