Review

Convolution and deconvolution: two mathematical tools to help performing tests in research and industry

¹ Electricity & Magnetism, LNE, Paris, France
² ECAM-EPMI, Cergy-Pontoise, France

^* Corresponding author: jean-pierre.fanton@wanadoo.fr

Received: 26 June 2020
Accepted: 10 February 2021

Abstract

The concepts of convolution and deconvolution are well known in the field of physical measurement. In particular, they are of interest in the field of metrology, since they can positively influence the performance of the measurement. Numerous mathematical models and computer developments dedicated to convolution and deconvolution have emerged, enabling a more efficient use of experimental data; this in sectors as different as biology, astronomy, manufacturing and energy industries. The subject finds today a new topicality because it has been made accessible to a large public for applications such as processing photographic images. The purpose of this paper is to take into account some recent evolutions such as the introduction of convolution methods in international test standards. Thus, its first part delivers a few reminders of some associated definitions. They concern linear systems properties, and integral transforms. If convolution, in most cases, does not create major calculation problems, deconvolution on the contrary is an inverse problem, and as such needs more attention. The principles of some of the methods available today are exposed. In the third part, illustrations are given on recent examples of applications, belonging to the domain of electrical energy networks and photographic enhancement.