In sensor array imaging the objective is to probe an unknown medium with waves, and this can be done in two steps. In the data acquisition step, waves are emitted by a source array, they propagate through the medium being probed, and they are recorded by a receiver array. In the data processing step, this data set is used to extract information about the medium, such as the location of reflectors embedded in it. Recent developments in imaging in complex media and on passive, ambient noise imaging have had a profound impact in many different applied fields. It is these developments that have motivated us to write this book.

Research in wave propagation in complex, scattering media has been active for a long time. It is relevant in many imaging applications in which one wants to probe a medium such as the Earth's lithosphere in seismic imaging, concrete structures in non-destructive testing, the human body in medical imaging, the turbulent atmosphere in optical imaging, or shallow water environments in acoustic imaging. These media are quite complex, while we often want to image only some particular features in them. It turns out that the established imaging methods, which we also describe in this book, may fail when the ambient medium is scattering. It is only recently that wave propagation in complex media, modeled by random media, has been formulated and analyzed in a way that makes it possible to develop new imaging techniques that can mitigate the effects of random scattering.

Array imaging has also been analyzed and used in many applications for a long time. The recent trend to deploy large sensor arrays is due to improved sensor technology, reduced cost in data storage, and increased computational capabilities. In particular, passive sensor array imaging has recently become an area of intense research activity because of the potential impact of its applications. Passive means here that only receiver arrays are used, instead of active source/receiver arrays, and the illumination is provided by unknown, uncontrolled, asynchronous, or opportunistic sources. Imaging with ambient noise sources is one of the main topics of this book. Of course, the structure of the array data is quite different from that of active sensor arrays, and this requires the development of new imaging techniques.