Inpainting of Historical Seismograms Using Sparse Representation Method

wang, lifu ; sun, yi ; cai, xiaogang;

This paper presents a method of in painting historical seismograms recorded by a pen and paper drum-typeseismograph. In these is mogram, some portions of the wave may belost or distorted owing to time marks or violent shaking. In this study, the seismic waveform is divided into several frames of equal length, and the lost or distorted portions are restored frame by frame. Because a seismogram contains several repetitive patterns in the entire waveform, each frame can be sparsely represented on the basis of these patterns. Therefore, the sparse representation model is employed to represent historical seismograms. In addition, an inpainting model that employs sparsity as a prior is formulated, and it is used to restore the lost portions by solving a L0-norm minimization problem. However, this minimization problem may be ill posed and result in an incorrect outcome if the missing interval duration of the wave is very large. Therefore, to solve this ill-posed problem, a prior based on the Fourier spectrum of the waveform is added to the inpainting method. Simulation results prove that the proposed inpainting method can restore the missing wave well.