Nonlinear inverse problems

Nonlinear inverse problems involve determining the original cause or input from observed outcomes when the relationship between them is not straightforward or directly proportional. Unlike simple (linear) problems where outputs change proportionally with inputs, nonlinear problems have more complex, often curving relationships. Solving these problems requires working backwards from the results to infer the initial conditions or inputs, which can be challenging due to the complexity and potential ambiguity of the solutions. They are common in fields like medical imaging, geophysics, and engineering, where understanding the hidden sources behind observable data is essential.