Data Assimilation is a methodological framework used in environmental sciences to perform forecasts with complex systems such as meteorological, oceanographic and air quality models. Data Assimilation requires the resolution of a system with three components: one describing the temporal evolution of the state vector, one coupling the observations and the state vector, and one defining the initial condition. In this article we use this mathematical framework to study a class of ill-posed Image Processing problems, which are usually solved using regularization techniques. To this end, the ill-posed problem is formulated according to the three-component system of the Data Assimilation framework. To illustrate the method, an application for computing optical flow is described.