The least squares method is a common approach to the solution of problems that can be reduced that of approximating one variable by some combination of others. It is based upon well grounded statistical notions. For a number of reasons, the least squares approach does not always lead to the most useful solution of this problem. Two common reasons are sensitivity to errors in the data (called ill-conditioning or ill-posedness) and the assumption that all errors in the data are concentrated in one variable.

The first difficulty is corrected using regularization, a method to obtain a better conditioned solution. The second difficulty leads to the total least squares problem, an approach that assumes errors in all of the variables.

In this talk, least squares, total least squares, and the related computational approaches are discussed. The notion of structured total least squares solution is also introduced and is applied to a problem in high resolution image reconstruction.