Abstract
Inverse problems can best be characterized through their counterparts, namely direct or forward problems. A classical forward problem is to find a unique effect of a given cause using an appropriate physical or mathematical model. Forward problems are usually well-posed, i.e., they have a unique solution which is insensitive to small changes of the initial values. Inverse problems are the opposite to forward problems, meaning that one is given the effect and the task is to recover the cause. Inverse problems do not necessarily have unique and stable solutions, i.e., they are often ill-posed in the sense of Hadamard [7].
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To keep the notation slim, we omitted all the units in this example.
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The area under study is a managed boreal forest in Eastern Finland (lat. 62∘31′N, lon. 30∘10′E). ALS data were collected on June 26, 2009 using an Optech ALTM Gemini laser scanning system from approximately 720 m above ground level, with a field of view of 26∘. A more detailed description is given by Packalén et al. in [14].
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Vauhkonen, M., Tarvainen, T., Lähivaara, T. (2016). Inverse Problems. In: Pohjolainen, S. (eds) Mathematical Modelling. Springer, Cham. https://doi.org/10.1007/978-3-319-27836-0_12
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