Introduction to Variational Calculus

This textbook introduces variational calculus and regularization methods forinverse problems, seamlessly blending classical concepts with contemporary computationalapplications, particularly in the field of image processing. The classical perspective draws upon foundational topics explored by pioneers such as Euler andLagrange, establishing a solid theoretical groundwork. In recent decades, the advent of disciplinessuch as computer vision has expanded the horizons of variational calculus, showcasing its effectivenessin addressing complex problems that necessitate computational solutions. Consequently, this bookplaces a strong emphasis on the synergy between mathematical theory, practical applications, andalgorithmic development. To ensure the text is comprehensive and accessible, essential principles offunctional analysis and Fourier analysis are incorporated, facilitating a deeper and more nuanced understanding ofthe applications presented.Covering both classic and more recent aspects of variationalcalculus, this book suggests thatmany topics of modern technology such as computer vision, robotics and especiallydigital image processing can be formulated in terms of variational problems.