Ultrasonic imaging is a widely used tool for detection, localisation and characterisation of material inhomogeneities with important applications in many fields. This task is particularly challenging when imaging in a complex medium, where the ultrasonic wave is scattered by the material microstructure, preventing detection and characterisation of weak targets. Fundamentally, the maximum information that can be experimentally obtained from each material region consists of a set of reflected signals for different incident waves. However, these data are not directly accessible from the raw measurements, which represent a superposition of reflections from all scatterers in the medium. Here we show, that a complete set of transmitter-receiver data encodes sufficient information in order to achieve full spatio-temporal separation of transmitter-receiver data, corresponding to different local scattering areas. We show that access to the local scattering data can provide valuable benefits for many applications. More importantly, this technique enables fundamentally new approaches, exploiting the angular distribution of the scattering amplitude and phase of each local scattering region. Here we demonstrate how the local scattering directivity can be used to build the local scattering image, releasing the full potential and richness of the transmit-receive data. As a proof of concept, we demonstrate the detection of small inclusions in various highly scattering materials using numerical and experimental examples. The described principles are very general and can be applied to any research field where the phased array technology is employed.