# Active Sonar Target Classification Method Based on Fisher's Dictionary Learning
## 2 Related Work  
The main concept of spare representation classification [5; 6] is to use the sparseness of the original signal and a set of over-complete dictionaries to linearly express the original signal to obtain a set of sparse coefficients with the essential characteristics of the original signal, and finally to combine the sparse coefficient and redundant dictionary to distinguish the category through the reconstruction error of the signal. [PERSON] et al. [7] were the first to apply sparse representation classification (SRC) to facial recognition, and proposed sparse representation-based classification. This algorithm directly uses the training sample set to construct a redundant dictionary, and limits the sparsity of the sparse coefficient through the 1-norm minimization method. Subsequently, [PERSON] et al. [8] proposed SRC based on dictionary learning, and [PERSON] applied it to the facial recognition [9]. This algorithm no longer uses the training signal directly as a dictionary, but performs adaptive learning based on the input original signal to obtain a discriminating dictionary, and finally, according to the testing data and sparse coefficient, reconstructs the error to complete the classification. [PERSON] et al. [10] presented discriminative K-singular value decomposition (D-KSVD), which adds a linear classifier penalty function related to the category label information of the objective function. [PERSON] et al. [11] proposed a label-consistent K-SVD (LC-KSVD), which introduced the \"recognition sparse coefficient error\" item based on dictionary learning. This item assigns \"label consistency\" to the sparse coefficient obtained in the final training. [PERSON] et al. [12] proposed the Fisher discriminant dictionary learning (FDDL) model, which introduces Fisher recognition criteria to learn a structured dictionary, and achieves relatively better results; it has achieved excellent results in fields such as facial recognition [13; 14] and image denoising [15; 16].  
However, compared with the abovementioned fields, active sonar work in a complex marine environment, as well as its interference, includes not only noise but also reverberation generated by the sea surface, seabed, and other interference targets [17]. The problem of reverberation suppression has always been a key issue in active sonar research [18]. As a frequency sweeper, FRFT [19] can obtain the characteristics of the target signal in the time, frequency, and multi-order domains through angle transformation. The characteristic domain of the target signal has a strong energy concentration at an optimal angle. Therefore, for the active sonar target classification problem in a complex ocean environment, FRFT can determine the characteristic amplitude of the target signal under the optimal order, and can filter the reverberation of the random signal to a certain extent in order to suppress the reverberation [20; 21]. Thus, this paper proposes an active sonar target classification method based on [PERSON]'s dictionary learning to realize the classification of active sonar targets in a low-signal-reverberation ratio. The paper's contributions are to suppress the reverberation using the optimal-order domain features of the fractional Fourier transform, and to increase the separability between the similarity objects by limiting the sparse coefficient based on the Fisher criterion.