  The image deblurring problem consists of reconstructing images from blur and
noise contaminated available data. In this AMS Notices article, we provide an
overview of some well known numerical linear algebra techniques that are use
for solving this problem. In particular, we start by carefully describing how
to represent images, the process of blurring an image and modeling different
kind of added noise. Then, we present regularization methods such as Tikhonov
(on the standard and general form), Total Variation and other variations with
sparse and edge preserving properties. Additionally, we briefly overview some
of the main matrix structures for the blurring operator and finalize presenting
multilevel methods that preserve such structures. Numerical examples are used
to illustrate the techniques described.
