Whilst the diffusion and evaluation of healthcare innovations receive a lot of attention, the early design stages are less studied and potential innovators lack methods to identify where new innovations are necessary and to propose concepts relevant to users. To change this, we propose a structured methodology, Radical Innovation Design ® (RID), which supports designers who want to work on the unstated needs of potential end-users in order to create superior value. In this article, the first part of RID is introduced with its two sub-processes: Problem Design and Knowledge Design. In this first period, RID guides innovators to systematically explore users' problems and evaluate which ones are most pressing in terms of innovation, taking into account existing solutions. The result is an ambition perimeter, composed of a set of value buckets, i.e. important usage situations where major problems are experienced and the current solutions provide little or no relief. The methodology then moves on to Solution Design and Business Design (which are not detailed in this paper) to address the value buckets identified. With its emphasis on problem exploration, RID differs from methods based on early prototyping. The RID methodology has been validated in various industrial sectors, and is well-adapted for healthcare innovation. To exemplify the methodology, we present a case study in dental imagery performed by ten students in 8 weeks. This example demonstrates how RID favors efficiency in Problem Design and allows designers to explore unaddressed and sometimes undeclared user needs.