Inverse problem

Definition: In the framework of the forward problem (y = Ax, where y is the simulated or measurement data, A is the sensitivity matrix, and x is the changes in optical properties), the goal of an inverse problem would be to reconstruct or infer the characteristics of the original signal source (e.g, changes in hemodynamic activity in the brain) based on the measured signal (e.g., changes in optical intensity). This model is often expressed as an inverse operator or transform, which maps the unknowns to the observed data. However, due to the possibilities of multiple solutions or uncertainties, inverse problems often tend to be ill-posed. Definition: In the framework of the forward problem (y = Ax, where y is the simulated or measurement data, A is the sensitivity matrix, and x is the changes in optical properties), the goal of an inverse problem would be to reconstruct or infer the characteristics of the original signal source (e.g, changes in hemodynamic activity in the brain) based on the measured signal (e.g., changes in optical intensity). This model is often expressed as an inverse operator or transform, which maps the unknowns to the observed data. However, due to the possibilities of multiple solutions or uncertainties, inverse problems often tend to be ill-posed.

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References: https://doi.org/10.34133/2022/9850248

Related terms: Forward model, Forward problem, Inverse problem, Image Reconstruction

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