Highly Nonlinear Approximations for Sparse Signal Representation
Let and be vectors spaces. A mapping is a linear operator if
The adjoint of an operator is the unique operator satisfying that
An operator has an inverse if there exists such that
andwhere and denote the identity operators in and , respectively. By a generalised inverse we shall mean an operator satisfying the following conditions
The unique generalized inverse satisfying
is known as the Moore Penrose pseudoinverse.