Curvelet-based Seismic Data Denoise

The idea and method that wavelet as a multiresolution analysis in numerical and digital signal processing, it has very successful application in many fields, which is attributed to its efficient one-dimensional sub-continuous signal for analysis. Ridgelet Transform inherited a wavelet good local time-frequency analysis capabilities and a strong orientation selectivity and identification capability. Ridge-line that can effectively the singular nature of the singularity of a straight line with the multi-variable function of a good approximation, but the image of the edge of the description of their approximate equivalent of only wavelet transform, do not have the best non-line Approximation error of attenuation bands of singularity is still a curve, rather than a point, the singularity of the wavelet that will not be sparse, so it's not a factor Ridgelet said sparse.In order to find the better way, In 1999 ,Candes and Donoho put forward the curvelet transform, and the formed structure of the Curvelet framework, which provided a stable, efficient and near-optimal express for a smooth curve singularity of the objective function.Wavelet is the development of Fourier transform. It is an important branch in mathematics developed gradually from the mid-1980s. As one of the fundamental methods wavelet transform image processing had many advantgages, such as computing speed, flexibility and so on. So it was widely used in the field of image processing . Ridgelet transform and Curvelet transform were developed on the basis of the wavelet transform, Radon transform. Compared with the wavelet transform, Ridgelet transformation is more suitable to describe the straight-line image features, and it is more suitable for Curvelet transform to show the details of performance characteristics of the image. The second generation of Curvelet (Fast Curvelet) also makes it easier to understand and realize this theory.After the introduction of the Curvelet, the researchers put forward some new algorithm on the application of Curvelet. The general transformation is now divided into discrete Curvelet USFFT algorithm and Wrap algorithm. Geophysicists have begun a series tests of successful examples. Now these new algorithms are all based on the original Curvelet structure. The pretreatment step of the structure is a special division, It means that, in the space domain and frequency domain, using Ridgelet transforma to localize the data.Curvelet as a new multiscale analysis is more suitable than wavelet in the analysis for two-dimensional image of the curve or straight-edge features, and it has a higher precision in approximation and a better sparse expression. The creation of the second generation curvelet theory also makes it easier to understand and realize. Currently, the study on the second generation curvelet has just started. There are still a lot of work to do on how to use it in the actual seismic data processing.This paper will talk about the usage of curvelet in processing seismic data, it will get a very good denoising effect through the appropriate threshold selection and provide more information for the interpretation of seismic data. This paper introduced the curvelet transform and Ridgelet transform,which were related to the Curvelet, then described the basic principles of Curvelet in details. Discussed its algorithm. It introduced the second-generation Curvelet into the seismic data processing, By choosing threshold appropriately, it does a Curvelet transform in the seimic datat. It also calculted the simulation data of curvelet transformation. And it makes a comparison of different results of the denosing effects under the different noise ratio. And the result of the actual denoising seismic data processing was relatively ideal through the Curvelet transformation.It also introduces a more complex L1-optimization problem on the base of the Curvelet transformation. Under the ideal circumstances, this method can be achieved a desired effect on the seismic data processing by selecting the appropriate coefficients.