An Alternating Least Squares Algorithm with Application to Image Processing

Least Squares (LS) estimation is a classical problem, often arising in practice. When the dimension of the problem is large, the solution may be difficult to obtain, due to complexity reasons. A general way to reduce the complexity is that of breaking the problem in smaller sub-problems. Following this approach, in the paper we introduce an Alternating Least Squares (ALS) algorithm that finds the LS estimate by iteratively solving two sub-problems. The algorithm can speed up the solution of any LS problem, but it is especially well suited for applications where the partition arises naturally so that the sub-problems have a structure and are simple to solve. To illustrate this fact, we discuss the application of the ALS to an image formation system affected by noise and drift, describing an efficient implementation and showing that the ALS is an effective image formation method. Key–Words: Least Squares, Image Formation