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This textbook introduces variational calculus and regularization methods for inverse problems, seamlessly blending classical concepts with contemporary computational applications, particularly in the field of image processing.
The classical perspective draws upon foundational topics explored by pioneers such as Euler and Lagrange, establishing a solid theoretical groundwork. In recent decades, the advent of disciplines such as computer vision has expanded the horizons of variational calculus, showcasing its effectiveness in addressing complex problems that necessitate computational solutions. Consequently, this book places a strong emphasis on the synergy between mathematical theory, practical applications, and algorithmic development.
To ensure the text is comprehensive and accessible, essential principles of functional analysis and Fourier analysis are incorporated, facilitating a deeper and more nuanced understanding of the applications presented. Covering both classic and more recent aspects of variational calculus, this book suggests that many topics of modern technology such as computer vision, robotics and especially digital image processing can be formulated in terms of variational problems.
List of contents
Introduction.- Mathematical Preliminaries.- Linear Operators and Functionals.- Minimization of Functionals.- Inverse Problems and Variational Regularization.- Variational Curve and Surface Interpolation.- Further Models and Applications.
About the author
Hebert Montegranario is an applied mathematician and computational scientist, currently serving as a professor at the Antioquia University, Medellín, Colombia. He holds a Ph.D. in Engineering from Universidad Nacional de Colombia, with a research focus on image processing, computer vision, and machine learning. Dr. Montegranario has extensive expertise in numerical analysis, scientific computing, and software design. He has authored several academic papers and a book on variational regularization of 3D data, showcasing his contributions to the field.
