High-Resolution Seismic Data Deconvolution by A0 Algorithm

Abstract

Sparse spikes deconvolution is one of the oldest inverse problems, which is a stylized version of recovery in seismic imaging. The goal of sparse spike deconvolution is to recover an approximation of a given noisy measurement T = W ∗ r + W 0 . Since the convolution destroys many low and high frequencies, this requires some prior information to regularize the inverse problem. In this paper, the authors continue to study the problem of searching for positions and amplitudes of the reflection coefficients of the medium (SP&ARCM). In previous research, the authors proposed a practical algorithm for solving the inverse problem of obtaining geological information from the seismic trace, which was named A 0 . In the current paper, the authors improved the method of the A 0 algorithm and applied it to the real (non-synthetic) data. Firstly, the authors considered the matrix approach and Differential Evolution approach to the SP&ARCM problem and showed that their efficiency is limited in the case. Secondly, the authors showed that the course to improve the A 0 lays in the direction of optimization with sequential regularization. The authors presented calculations for the accuracy of the A 0 for that case and experimental results of the convergence. The authors also considered different initialization parameters of the optimization process from the point of the acceleration of the convergence. Finally, the authors carried out successful approbation of the algorithm A 0 on synthetic and real data. Further practical development of the algorithm A 0 will be aimed at increasing the robustness of its operation, as well as in application in more complex models of real seismic data. The practical value of the research is to increase the resolving power of the wave field by reducing the contribution of interference, which gives new information for seismic-geological modeling.

Through-Wall UWB Radar Based on Sparse Deconvolution with Arctangent Regularization for Locating Human Subjects

“…The sparse deconvolution with arctangent regularization is so efficient in extracting the sparse signal from the noisy reflected signal (raw data) that lowpass, bandpass, and smooth filters are no longer required [ 16 , 17 , 18 , 19 , 20 , 21 , 22 ]. Figure 6 illustrates the steps for extracting the sparse signal for through-wall UWB radars.…”

“…Given the limitation of L2 norm regularization and the noisy characteristic of received signal y , we can easily estimate x to be a sparse signal (spike) from y by minimizing Equation (10) with a convex regularization term of the L1 norm [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ], . where is called L1 norm regularization (convex regularization) represented by the sum of absolute values of vector x , .…”

“…However, in real-world applications, the output signal ( y ) is noisy and distorted by inhomogeneous media, such as ground-penetrating radar (GPR) [ 1 , 2 ], seismicity [ 3 , 4 ], radars [ 5 , 6 , 7 , 8 ], astronomy [ 9 ], speech recognition [ 10 , 11 ], and image reconstruction [ 12 , 13 , 14 , 15 ]. Nowadays, sparse deconvolution plays an important role in extracting the original data from the noisy received signal; it has been widely used in denoising, interpolation, super-resolution, and declipping [ 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 ]. Whereas linear time-invariant (LTI) filters, such as low-pass, band-pass and high pass, have amplitude distortions on the original signal resolution [ 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 ].…”