Irregular Seismic Data Reconstruction Via Low-rank Constraints

In the process of realistic seismic data acquisition, due to the economic orgeographical limitations, there are data missing phenomenon for the obtainedseismic data. Reconstruction and interpolation of missing traces in seismic recordsis a critical element of the data processing chain, which is very important forsubsequent processing steps including improvement of spatial resolution, migration,multiple suppression, and amplitude analysis. Moreover, the seismic data in asuitable domain is low rank while missing traces increases the rank of the data, thusthe rank-reduced methods can be applied for seismic interpolation.In this thesis, we use an orthogonal matrix pursuit with the texture-patchtransformation for reconstruction of randomly missing traces via matrix completion.The key idea is to extend orthogonal matching pursuit method form vector case tomatrix case. In each iteration, updated basis is obtained by using the residual, thenminimum of difference between data and observed data gives coefficient of updatedbasis. Finally, reconstruction data is computed by linear combination of thesecoefficient and basis. However, SVD method is needed in each iteration, whichincreases computational cost. Thus the FOR1MP algorithm is not suitable for largedata problems. In contrast, orthogonal rank-one matrix pursuit method (OR1MP),using the Power method to replace the SVD method, improves computational cost.But the OR1MP algorithm has to track all pursued bases and to save them in thememory, which needs a large storage space. To adapt our algorithm to large scaleproblems with a large approximation rank, we simplify the orthogonal projectionstep by only tracking the estimated matrix and the rank-one update matrix in thisiteration.At last, we compare the EOR1MP algorithm with the OR1MP algorithm onrealistic data sets. Numerical results show that the EOR1MP algorithm is moreefficient than the OR1MP algorithm.