Definition: Moore-Penrose Pseudoinverse, or simply the Moore-Penrose inverse, is a mathematical operation that produces an inverse of a matrix that may not have a conventional inverse. For a square matrix A, the inverse
exists if and only if the determinant of A is non-zero. However, many matrices encountered in practice are not invertible. The pseudoinverse is a generalization of the inverse that can be used for any matrix, regardless of its invertibility (not a square or a full rank matrix).In image reconstruction, to recover the optical properties of the voxels, the computation of the Moore-Penrose Pseudoinverse
is required.Since fNIRS measurements contain different types of noise,
is formulated including Tikhonov regularization to aid in smoothing the noise, as follows: ,
where
is the regularization parameter and
is the identity matrix.
It should be noted that Moore-Penrose’s is not the only pseudo inverse.
Alternative definition:
Synonym:
References: https://doi.org/10.1017/S0305004100030401
https://doi.org/10.1063/5.0015512
https://doi.org/10.1117%2F1.JBO.26.5.056001
Related terms: Image reconstruction
