Inverse Problems
An inverse problem is a general framework that is used to convert observed measurements into information about a physical object or system that we are interested in. For example, if we have measurements of the Earth's gravity field, then we might ask the question: "given the data that we have available, what can we say about the density distribution of the Earth in that area?" The solution to this problem (i.e. the density distribution that best matches the data) is useful because it generally tells us something about a physical parameter that we cannot directly observe. Thus, inverse problems are some of the most important and well-studied mathematical problems in science and mathematics. Inverse problems arise in many branches of science and mathematics, including computer vision, natural language processing, machine learning, statistics, statistical inference, geophysics, medical imaging (such as computed axial tomography and EEG/ERP), remote sensing, ocean acoustic tomography, nondestructive testing, astronomy, physics and many other fields.
Read more about Inverse Problems: History, Conceptual Understanding, General Statement of The Problem, Linear Inverse Problems, Non-linear Inverse Problems, Mathematical Considerations, Inverse Problems Societies
Famous quotes containing the words inverse and/or problems:
“The quality of moral behaviour varies in inverse ratio to the number of human beings involved.”
—Aldous Huxley (1894–1963)
“We are all adult learners. Most of us have learned a good deal more out of school than in it. We have learned from our families, our work, our friends. We have learned from problems resolved and tasks achieved but also from mistakes confronted and illusions unmasked. . . . Some of what we have learned is trivial: some has changed our lives forever.”
—Laurent A. Daloz (20th century)