| 21. | Typically, the models and mathematical methods Kaasalainen has developed with his colleagues are connected with inverse problems.
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| 22. | But solving an inverse problem is often time-consuming because it involves the computation of an inverse matrix.
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| 23. | To do so, we define a goal, also known as an objective function, for the inverse problem.
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| 24. | It is called an inverse problem because it starts with the results and then calculates the causes.
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| 25. | Inverse problems seek to identify features of the geometry from information about the eigenvalues of the Laplacian.
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| 26. | It combines theoretical, experimental and mathematical papers on inverse problems with numerical and practical approaches to their solution.
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| 27. | This explains the necessity of highly sophisticated mathematical algorithms that will address the inverse problem and its ill-posedness.
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| 28. | Because we cannot directly invert the observation matrix, we use methods from optimization to solve the inverse problem.
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| 29. | Inverse problems and tomography are key signal processing tasks where state of the art techniques have high potential impact.
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| 30. | He is a founding member of the Finnish Inverse Problems Society, the world's first scientific society for inverse problems.
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