The iTWIST workshop series aim at fostering collaboration between international scientific teams for developing new theories, applications and generalizations of low-complexity models. These events emphasize dissemination of ideas through both specific oral and poster presentations, as well as free discussions. For this fourth edition, iTWIST'18 gathered in CIRM, Marseille, France, 74 international participants and featured 7 invited talks, 16 oral presentations, and 21 posters. From iTWIST'18, the scientific committee has decided that the workshop proceedings will adopt the episcience.org philosophy, combined with arXiv.org: in a nutshell, "the proceedings are equivalent to an overlay page, built above arXiv.org; they add value to these archives by attaching a scientific caution to the validated papers." This means that all papers listed in the HTML page of this arxiv publication (see the menu on the right) have been thoroughly evaluated and approved by two independent reviewers, and authors have revised their work according to the comments provided by these reviewers.