The aim of this Innovative Training Network is to train a new generation of creative, entrepreneurial and innovative early-stage researchers (ESRs) in the research area of measurement and estimation of signals using knowledge or data about the underlying structure. With its combination of ideas from machine learning and sensing, we refer to this research topic as “Machine Sensing”. We will train all ESRs in research skills needed to obtain an internationally-recognized PhD; to experience applying their research a non-Academic sector; and to gain transferrable skills such as entrepreneurship and communication skills. We will further encourage an open “reproducible research” approach to research, through open publication of research papers, data and software, and foster an entrepreneurial and innovation-oriented attitude through exposure to SME and spin-out Partners in the network. In the research we undertake, we will go beyond the current, and hugely popular, sparse representation and compressed sensing approaches, to develop new signal models and sensing paradigms. These will include those based on new structures, nonlinear models, and physical models, while at the same time finding computationally efficient methods to perform this processing. We will develop new robust and efficient Machine Sensing theory and algorithms, together methods for a wide range of signals, including: advanced brain imaging; inverse imaging problems; audio and music signals; and non-traditional signals such as signals on graphs. We will apply these methods to real-world problems, through work with non-Academic partners, and disseminate the results of this research to a wide range of academic and non-academic audiences, including through publications, data, software and public engagement events.