Inverse problems

Inverse problems occur in natural sciences and engineering, where non-directly observable physical quantities are to be inferred from measurable effects they produce. For example, one might attempt to deduce information about rock layers in the Earth's interior from measurements of gravitational force, or to assess the elasticity of tissue by comparing ultrasound images of tissues compressed to varying degrees. A common challenge is that even the smallest measurement inaccuracies can lead to significant impacts in the calculated solution. This solution is only meaningful if a supplementary measure is taken in the solution process, known as regularization. This book aims to provide a quick and mathematically grounded introduction to the technique of regularized solutions for inverse problems, without requiring more mathematical knowledge than what is typically covered in a bachelor's degree program.