where is the observed data which is regularly or irregularly sampled, is the unknown data we want to reconstruct and is the sampling matrix. The sampling operator has a diagonal structure, which is composed by zero and identity matrix:

Each in equation 2 corresponds to sampling a trace, and each corresponds to missing a trace.

As equation 1 is under-determined, additional constraint is required in order to solve the equation. By applying a regularization term, we get a least-squares minimization solution for solving equation 1:

where is a regularization operator and denotes the square of norm.

2020-02-28