# Tree Internal Defected Imaging Using Model-Driven Deep Learning Network
## 1 Introduction  
As a renewable resource, wood is widely used in construction, decoration, energy, and other fields [1]. When defects, such as voids and decay, occur in the trunk due to various natural factors, and its characteristics, not only will the quality of the wood products not meet standards, but the tree may even collapse in severe cases [2]. The detection of living trees can prevent the influence of various unfavorable factors in time, reduce unnecessary waste and make full use of forest resources [3, 4, 5].  
For the detection of internal defects of living trees, the current mainstream methods include the stress wave method, ultrasound method, and computer tomography (CT) scan [6, 7, 8]. However, most methods have their corresponding shortcomings [9, 10]. For example, the stress wave method must drive nails into each measurement point on the trunk due to its detection characteristics; tree needle detection also requires probes to be drilled into the trunk [11]. Both detection methods will cause damage to the tree and cannot be defined as non-destructive testing. The ultrasonic detection process is susceptible to interference from the external environment, and the use of coupling agents may cause environmental pollution [12]. The cost of CT equipment is relatively expensive, and it is easy to cause radiation hazards to researchers in terms of safety [13, 14]. Compared withother non-destructive testing technologies applied in the forestry field, electromagnetic waves have received great attention because of their fast, high-efficiency, easy-to-operate, non-susceptible external interference, and the ability to achieve non-intrusive and non-destructive testing [15; 16; 17]. With the substantial improvement of computer performance, some researchers have developed progressive algorithms to identify defects in common wood by means of a BP neural network and a convolution neural network, which improves the detection accuracy and efficiency [18].  
In this article, we analyzed the contrast source inversion (CSI) and the neural network algorithm and proposed a model-driven deep learning network inversion algorithm to conduct simulation experiments on the detection of internal defects in trees. The CSI, BP neural network algorithm and the model-driven deep learning network inversion algorithm are compared and analyzed. The results show that the model-driven deep learning network inversion algorithm improves the defect inversion imaging rate and image quality. The main work of this paper is as follows:  
1. The objective function of the comparison source inversion is obtained by using the Lippmann-Schwinger equation and the equivalent current source radiation process of the scattering field. The models of comparison; source inversion algorithm, BP neural network inversion algorithm, and model-driven inversion algorithm based on deep learning networks, are established;
2. Determine the simulated imaging evaluation metrics; on the basis of building simulation environment and training database, the inversion imaging of single defect, homogeneous double defect and heterogeneous multi-defect is realized, and the algorithm iterative stability is analyzed.  
The main physical variables involved in this article and their meanings are shown in Table 1.