Abstract
An understanding of forward and inverse problems [12, 301] lies at the heart of any large estimation problem. Abstractly, most physical systems can be defined or parametrized in terms of a set of attributes, or unknowns, from which other attributes, or measurements, can be inferred. In other words, the quantities \(\underline{m}\) which we measure are some mathematical function
of other, more basic, underlying quantities \(\underline{z},\) where f may be deterministic or stochastic. In the special case when f is linear, a case of considerable interest to us, then (2.1) may be expressed as
for the deterministic or stochastic cases, respectively. Normally \(\underline{z},\) is an ideal, complete representation of the system: detailed, noise-free, and regularly structured (e.g.,pixellated), whereas the measurements \(\underline{m},\) are incomplete and approximate: possibly noise-corrupted, irregularly structured, limited in number, or somehow limited by the physics of the measuring device.
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© 2011 Springer New York
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Fieguth, P. (2011). Inverse Problems. In: Statistical Image Processing and Multidimensional Modeling. Information Science and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7294-1_2
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DOI: https://doi.org/10.1007/978-1-4419-7294-1_2
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