Complex structure reconstruction using segmented random sampling and combined dictionary

Abstract

The reconstruction of data is a critical preliminary work in the seismic data processing. Compressed sensing (CS) has been well applied in the field of reconstruction. The key point of CS is random sampling, which converts the mutual interference alias caused by regular undersampling into lower-amplitude outside noise. But traditional sampling methods lack constraints on sampling points, emerging too much alias. Segmented random sampling (SRS) effectively controls the distance between sampling points. On the other hand, a single mathematical transformation will lead to incomplete sparse expression and bad restoration effects. Morphological component analysis (MCA) decomposes a signal into several components with outstanding morphological features to approximate the complex internal structure of data. In this paper, we found a new dictionary combination (shearlet + DCT) under the MCA framework and used the block coordinate relaxation algorithm to get the optimal solution to obtain reconstruction results. Tests of 2D data and 3D data have proved that the proposed method can get a better effect when reconstructing the SRS data.