Abstract: This article first proposes that several linear structures (which can be regarded as local plane waves) float in local high-dimensional data volume with different probability distribution characteristics, which is the core conceptual mode of seismic signal processing.It is believed that modeling and optimal prediction of linear structures in local high-dimensional data volumes, in order to solve the problems such as denoising, data regularization, and deblending, are the very basic steps in seismic data processing.It is considered that the optimal modeling and prediction of linear signals include model-driven and data-driven methoel.The former represents the signals contained in the local high-dimensional data volume by the linear superposition of pre-selected local plane wave basis functions.The latter uses the data matrix (tensor) decomposition method to infer the linear structure contained in the local high-dimensional data volume.Then, the basic theories of high-dimensional Wiener filtering method, autocorrelation matrix and Hankel matrix orthogonal decomposition method (SSA method), high-dimensional linear Radon transform method (high-dimensional Beamforming method), and tensor decomposition method in the frequency space domain were comprehensively analyzed, and a theoretical foundation for linear signal prediction and various applications in local high-dimensional data volume is built.Finally, it is pointed out that the coherent noise and incoherent noise in the real data of the piedmont zone and other complex surface exploration areas often seriously deviate from the theoretical assumptions of linear signal modeling and prediction, developing nonlinear denoising methods is also inevitable.