To do this, we also use the definition of the logarithm ( as the inverse operator of exponentiation ) that
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In multiple dimensions, however, the deconvolution process is iterative due to the difficulty of defining an inverse operator.
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The important concepts directly related to operators between finite-dimensional vector spaces are the ones of rank, determinant, inverse operator, and eigenspace.
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This page from Dr . Math makes some great points about what inverse operators actually are . risk 19 : 29, 7 November 2007 ( UTC)
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For the first time defined the conditions for the solvability and spent the classification of the resonant cases a wide class of nonlinear boundary value problems for systems of ordinary differential and difference equations, delay equations, equations with impulsive and singularly perturbed equations for which the proposed use of the apparatus of generalized inverse operators.
6.
However, in most cases of practical use, it may be extremely difficult to implement the inverse distortion operator D ^ {-1 } [ \ cdot ] or the such an inverse distortion operator may not exist and even in situations where the distortion operator D [ \ cdot ] is known and its inverse can be approximately implemented, the resultant reconstructed signal \ tilde x ( n _ 1, n _ 2, . . . ., n _ m ) can have very reconstruction errors due to the inaccuracies present in the estimation of the inverse operator D ^ {-1 } [ \ cdot ].
7.
However, in most cases of practical use, it may be extremely difficult to implement the inverse distortion operator D ^ {-1 } [ \ cdot ] or the such an inverse distortion operator may not exist and even in situations where the distortion operator D [ \ cdot ] is known and its inverse can be approximately implemented, the resultant reconstructed signal \ tilde x ( n _ 1, n _ 2, . . . ., n _ m ) can have very large reconstruction errors due to the inaccuracies present in the estimation of the inverse operator D ^ {-1 } [ \ cdot ].
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