Seismic Data Reconstruction, Bayesian Compressive Sensing, (BCS), l1-MAGIC, StOMP CFAR, Wavelets, Kustosis, Entropy, Sparsity.
Seismic Data Reconstruction, Bayesian Compressive Sensing, (BCS), l1-MAGIC, StOMP CFAR, Wavelets, Kustosis, Entropy, Sparsity.
The Compressive Sensing (CS) is a data and efficient processing technique for recovering signals from a lower sampling that required by Shannon-Nyquist theorem. This technique allows a great reduction in data and computational cost for signs that can be represented sparsely. The Wavelet Transform has been used to compress and represent many natural signals including seismic, in a sparse way. There are several signals reconstruction algorithms that use the CS, for example, MAGIC l1, Fast Bayesian Compressive Sensing (Fast BCS) and Stagewise Orthogonal Matching Pursuit (stomp CFAR). This thesis compares the recovery of seismic traces in a statistical perspective using different methods of CS, wavelet transforms and sampling rates. We did a study of the correlation between the recovery rate by CS and the coefficient of variation, skewness, kurtosis and entropy of the original signal. There seems to be a correlation between the kurtosis and entropy with the recovery rate by CS. Also analyzed the distribution of the recovery rate: the l1-MAGIC had better results for sample rates up to 40%. Moreover, the distribution of the recovery rate is more normal, symmetrical and mesokurtic that for the Fast BCS. However, to above 50% sample rates Fast BCS showed a better performance than the average recovery rate. Our analysis showed that the STOMP CFAR was the worst method in all aspects studied.