Ultrasonic probes for non-destructive inspection of materials have now reached a sufficient maturity level to allow their regular deployment in industrial applications, a process known as Structural Health Inspection (SHM). In general, to detect defects on metal plates, one can simply measure the time of traversal of the ultrasonic signal between the two sides of the plate, or excite a through-thickness standing wave, to get a precise estimate of the metal thickness. This information can then be used to detect thickness-affecting alterations such as corrosion or damages due to impacts. A promising and more sophisticated technique for such envisioned inspection is the use of Ultrasonic Guided Waves (UGW), in particular shear horizontal and Lamb waves. These waves propagate through the entire material thickness while following a direction parallel to the material surface. In the appropriate conditions, and based on the physical effect of acoustic mode conversion, the properties of the propagated spectrum can be used to infer the material state and in particular to detect cracks, corrosion or holes. This requires measuring the transmitted spectrum at multiple points precisely spaced along the wave propagation direction in order to build a space-time spectrum and analyze its variations. The complexity of the analysis of the transmitted signal in practical cases makes the detection and characterization of defects a challenging problem for signal processing and a promising application domain for machine learning techniques such as deep convolutional neural networks (CNN).