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Nowadays inverse problems and applications in science and engineering represent an extremely active research field. The subjects are related to mathematics, physics, geophysics, geochemistry, oceanography, geography and remote sensing, astronomy, biomedicine, and other areas of applications. This monograph reports recent advances of inversion theory and recent developments with practical applications in frontiers of sciences, especially inverse design and novel computational methods for inverse problems. The practical applications include inverse scattering, chemistry, molecular spectra data processing, quantitative remote sensing inversion, seismic imaging, oceanography, and astronomical imaging. The book serves as a reference book and readers who do research in applied mathematics, engineering, geophysics, biomedicine, image processing, remote sensing, and environmental science will benefit from the contents since the book incorporates a background of using statistical and non-statistical methods, e.g., regularization and optimization techniques for solving practical inverse problems.
Inverse Problems are found in many areas of engineering mechanics
and there are many successful applications e.g. in non-destructive
testing and characterization of material properties by ultrasonic
or X-ray techniques, thermography, etc. Generally speaking, inverse
problems are concerned with the determination of the input and the
characteristics of a system, given certain aspects of its output.
Mathematically, such problems are ill-posed and have to be overcome
through development of new computational schemes, regularization
techniques, objective functionals, and experimental procedures.
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