# Signal Separation Based on Knowledge Representation
## 5 Conclusions  
This study introduces a novel framework for knowledge representation specifically designed to tackle the diverse scenarios encountered in signal separation. The framework is flexible enough to handle variations in the quantity of data samples and the complexity of knowledge representations. Its versatility allows it to be applied across a wide range of domains, from seismic signal separation to the segregation of mixed handwritten digits. Through rigorous numerical simulations, this approach has been shown to be effective, demonstrating adaptability and robustness across different signal types and scenarios. The proposed framework addresses three main types of knowledge representation: observed knowledge representation, physical knowledge representation, and data-driven knowledge representation. Each type is tailored to the specific nature of the signal and the available information, allowing for a nuanced and precise separation process. Observed knowledge representation leverages experiential knowledge derived from observed mixed signals. Physical knowledge representation utilizes the underlying physical mechanisms and satisfies certain physical partial differential equations. Data-driven knowledge representation takes advantage of abundant data samples related to the target signal, enabling a data-driven approach to knowledge representation. To validate the effectiveness of these knowledge representations, we selected datasets that align closely with the characteristics of each scenario. For observed knowledge representation, we employed a geological model with a flat-layer structure, which generates significant up- and downgoing wavefield signals. In the physical knowledge representation scenario, the Marmousi-II complex model was utilized, as it includes diverse geological structures and produces extensive P-wave and S-wavefield signal data, making it a widely used benchmark in seismic exploration. For data-driven knowledge representation, we  
Figure 13: MNIST handwritten digit dataset mixed handwriting separation results. adopted the MNIST dataset, which is commonly used in handwritten digit recognition tasks. These datasets were chosen for their strong relevance to our research focus and our familiarity with them, which enables effective validation of the proposed framework. While other datasets could be explored, their selection requires deeper analysis of their characteristics. This aspect will be further addressed in future research work. Moreover, the framework provides valuable insights into the underlying principles governing signal separation, highlighting the intricate interplay between data and knowledge representations. By integrating knowledge representation with neural networks, the framework improves the interpretability of the separation process and reduces the dependency on extensive data samples. This integration results in more accurate and reliable signal separation outcomes. This framework has the ability to represent knowledge according to specific application scenarios, offering not only a more generalizable approach but also paving the way for further exploration and development in this field. Researchers can now apply this framework to various types of signals and scenarios, expanding the scope and possibilities of signal separation. Conceptualization, C.L., J.Z. and X.Z. ; methodology, C.L. ; software, X.Z. ; validation, X.Z., J.Z. and C.L. ; formal analysis, C.L. ; investigation, C.L. ; resources, X.Z. ; data curation, X.Z. ; writing--original draft preparation, X.Z. ; writing--review and editing, C.L. ; visualization, C.L. and X.Z. ; supervision, C.L and J.Z. ; project administration, C.L. ; funding acquisition, C.L. All authors have read and agreed to the published version of the manuscript. This research was supported by the National Natural Science Foundation of China under Grant 42474171, 41974147 and 42104130. Not applicable. Data Availability Statement: Data are contained within the article. We are grateful to the reviewers for their valuable comments.