Lifting dual tree complex wavelets transform

We describe the lifting dual tree complex wavelet transform (LDTCWT), a type of lifting wavelets remodeling that produce complex coefficients by employing a dual tree of lifting wavelets filters to get its real part and imaginary part. Permits the remodel to produce approximate shift invariance, directionally selective filters and reduces the computation time (properties lacking within the classical wavelets transform). We describe a way to estimate the accuracy of this approximation and style appropriate filters to attain this. These benefits are often exploited among applications like denoising, segmentation, image fusion and compression. The results of applications shrinkage denoising demonstrate objective and subjective enhancements over the dual tree complex wavelet transform (DTCWT). The results of the shrinkage denoising example application indicate empirical and subjective enhancements over the DTCWT. The new transform with the DTCWT provide a trade-off between denoising computational competence of performance, and memory necessities. We tend to use the PSNR (peak signal to noise ratio) alongside the structural similarity index measure (SSIM) and the SSIM map to estimate denoised image quality.

Missing trace reconstruction for 2D land seismic data with randomized sparse sampling

Acquisition of high-quality land seismic data requires (expensive) dense source and receiver geometries to avoid aliasing-related problems. Alternatively, acquisition using the concept of compressive sensing (CS) allows for similarly high quality land seismic data using fewer measurements provided that the designed geometry and sparse recovery strategy are well matched. We propose a complex wavelet-based sparsity-promoting wavefield reconstruction strategy to overcome challenges in land seismic data interpolation using the CS framework. Despite having lower angular sensitivity than curvelets, complex wavelets improve the reconstruction of sparsely acquired land data while being faster and requiring less storage. Unlike the Fourier transform, the complex wavelet transform localizes aliasing-related artifacts likely to be present in field data, and yields reconstructions with fewer artifacts and higher signal-to-noise ratios. We demonstrate that the data recovery success depends on both the number and the geometry of the missing traces as revealed by analyzing reconstructions from multiple realizations of trace geometry and data decimation ratios. Using half the number of traces required by the regular sampling rules and thus reducing the acquisition costs, we show that data are appropriately reconstructed provided that there are no big gaps in the strategic places.