1. Two examples of inversion

1.1 Image restoration

As the problem of restoring an image degraded by an observation process is frequently encountered in engineering, we have chosen it as our first guideline to illustrate the various concepts that will be introduced later.

An image is generally defined as a scalar function of two variables belonging to a given region of space. Although this medium is often continuous, it is usually sampled on a rectangular grid. This defines a set of pixels, and the image is represented by a two-dimensional signal x _{n, m} of the pixel intensity values, where indices n and m are those of their coordinates.

In all the image processing problems mentioned in the introduction