## 1 Introduction  
Fiber reinforced polymer composites are becoming increasingly important in modern industries due to their high specific strength-weight ratio, anti-corrosion properties, and recyclability. They are manufactured using different processes such as resin transfer molding, extrusion, and automated tape placement, according to different property requirements. Recently, additive manufacturing, combined with various reinforcement control methods (e.g., standing-wave field [1], magnetic field [2], rotational deposition [3]), has come to be considered a cost-efficient method for composite design and manufacturing. During these processes, defects such as voids, cracks, and delaminations may be introduced into the part and lead to structure failure in service. Defect localization and characterization are critical in modern lightweight structures made of fiber reinforced composites. The early detection of these defects is beneficial to the structural integrity and maintenance. Different methods have been exploited in recent years, including pulse-thermography [4], ultrasonic [5], X ray, acoustic emission [6; 7], and electric resistance variation [8; 9]. Among all these methods, ultrasonic testing is considered to be promising for in-situ or online inspection. Localization sensitivity can be improved through a higher ultrasonic frequency, but with regards heterogeneous materials such as concretes, biology tissues, and fiber reinforced composites, wave propagation becomes more complicated with increasing frequency. A full understanding of such process and proper signal processing methods is required to overcome or even benefit from scattering and attenuation phenomena. The complex internal fiber distribution results in multiple scattering in the fiber reinforced composite. In such mediums, the whole waveform can be separated into the direct (ballistic, the first arrival) wave part and the diffuse wave part [10]. The direct wave is often strongly attenuated and only exists for a short distance that corresponds to the transport mean free path [11]. Subsequently, the energy of the direct waves rapidly converts into late-arriving diffuse waves [12]. The conventional ultrasonic inspection methods tend to lower the frequency to prevent the difficulties brought by attenuation and scattering. They often rely on the information from the direct wave part including the C scan method [13] and the Lamb wave inspection method [5]. The former has been widely accepted in aerospace industry to check defect existence in composite structures with considerable capital cost, and the latter is suitable for thin plate structures and can improve inspection efficiency. Nevertheless, careful interpretation of different propagation modes and boundary reflections/refractions are required [14]. By contrast, the diffuse wave is repeatable and independent of the direct wave path [15], and it can also be applied to structure inspection. Being treated as ambient noise [16] for a long time, the diffuse wave is found to contain valuable information, especially in seismology and civil engineering. [PERSON] and [PERSON] [17] showed that the cross-correlation of two diffuse wave fields from the same excitation is equal to the direct response of one transducer to an impulse applied to the other. More recently, there has been a growing interest in using [PERSON]'s function recovery technique to study the temperature effect on subsurface velocity variation in the lunar environment [18], to improve the near-surface ultrasonic array imaging resolution [19], etc. By comparing diffuse waves before and after external perturbations, time-lapse monitoring such as stress change [20], temperature variation [21], and progressive damage [22] can be achieved locally from only one fixed transmitter-receiver pair.