Abstract:

Compressive sensing(CS) is a new kind of theory which breaks the limitation of  the conventional Nyquist-Shannon sampling theorem and recovers the complete signal from few data by using the sparse or compressed characteristics of the signal. With the theory of CS, a seismic data recovery model is built in this paper. Based on the measure matrix which is incoherent with the sparsifying basis,a kind of restrained matrix is proposed as to achieve the effects of seismic missing data with gaussian random distribution or nearly gaussian random distribution and hence the sparsifying coefficient of the aliasing seismic data will contain many random noises which is uncorrelated with the effective signal. The full data can be reconstructed from a new adaptive iterative threshold solution and an inverse sparse transform. From the test of the synthetic seismic data and Marmousi 2  model, we verified the availability and feasibility of our method.

Key words: compressive sensing, sparse transform, measurement matrix, recovery algorithm, aliasing seismic data