V4-ICARUS is a scientific research project that intends to develop the next generation of mathematical signal processing and data analysis methods for the new era of big data. The innovative paradigm of V4-ICARUS will move well beyond the state-of-the art in both signal processing and machine learning, wherein instrument-specific methods are considered for monolithic tasks, such as classification and clustering. Within our project, modern signal processing (e.g. sparse representations, tensor completion), machine learning (e.g. deep learning), and distributed computing (e.g. in-memory analytics) techniques will be intertwined and evolve to encompass the complex Big Sensor Data characteristics (e.g. non-linearity, high-dimensionality, noisy artifacts, spatio-temporal evolving behaviors). The envisaged models will yield a mathematically rigid framework for selectively combining data from diverse, and possibly inhomogeneous, data streams.