Reference-free single-pass EPI Nyquist ghost correction using annihilating filter-based low rank Hankel matrix (ALOHA)

2016 ◽  
Vol 76 (6) ◽  
pp. 1775-1789 ◽  
Author(s):  
Juyoung Lee ◽  
Kyong Hwan Jin ◽  
Jong Chul Ye
Keyword(s):  
Hankel Matrix ◽  
Low Rank ◽  
Single Pass

Enhanced low-rank matrix estimation for simultaneous denoising and reconstruction of five-dimensional seismic data

Geophysics ◽  
2021 ◽  
pp. 1-96
Author(s):  
Yapo Abolé Serge Innocent Oboué ◽  
Yangkang Chen
Keyword(s):  
Seismic Data ◽  
Hankel Matrix ◽  
Low Rank ◽  
The Novel ◽  
Proximity Function ◽  
Rank Reduction ◽  
Matrix Estimation ◽  
Useful Signal ◽  
Truncated Svd ◽  
Noisy Observation

Noise and missing traces usually influence the quality of multidimensional seismic data. It is, therefore, necessary to e stimate the useful signal from its noisy observation. The damped rank-reduction (DRR) method has emerged as an effective method to reconstruct the useful signal matrix from its noisy observation. However, the higher the noise level and the ratio of missing traces, the weaker the DRR operator becomes. Consequently, the estimated low-rank signal matrix includes a unignorable amount of residual noise that influences the next processing steps. This paper focuses on the problem of estimating a low-rank signal matrix from its noisy observation. To elaborate on the novel algorithm, we formulate an improved proximity function by mixing the moving-average filter and the arctangent penalty function. We first apply the proximity function to the level-4 block Hankel matrix before the singular value decomposition (SVD), and then, to singular values, during the damped truncated SVD process. The relationship between the novel proximity function and the DRR framework leads to an optimization problem, which results in better recovery performance. The proposed algorithm aims at producing an enhanced rank-reduction operator to estimate the useful signal matrix with a higher quality. Experiments are conducted on synthetic and real 5-D seismic data to compare the effectiveness of our approach to the DRR approach. The proposed approach is shown to obtain better performance since the estimated low-rank signal matrix is cleaner and contains less amount of artifacts compared to the DRR algorithm.

scholarly journals A sporadic decomposition of Hankel structured matrix in logarithmic and wavelet domain for impulse noise removal

2018 ◽  
Vol 7 (4) ◽  
pp. 2309
Author(s):  
Baby Victoria.L ◽  
Sathappan S
Keyword(s):  
Impulse Noise ◽  
Hankel Matrix ◽  
Noise Removal ◽  
Noise Model ◽  
Low Rank ◽  
Impulse Noise Removal ◽  
Structured Matrix ◽  
Filter Methods ◽  
Patch Image ◽  
Transform Domains

Noise removal from the color images is the most significant and challenging task in image processing. Among different conventional filter methods, a robust Annihilating filter-based Low-rank Hankel matrix (r-ALOHA) approach was proposed as an impulse noise removal algorithm that uses the sparse and low-rank decomposition of a Hankel structured matrix to decompose the sparse impulse noise components from an original image. However, in this algorithm, the patch image was considered as it was sparse in the Fourier domain only. It requires an analysis of noise removal performance by considering the other transform domains. Hence in this article, the r-ALOHA can be extended into other transform domains such as log and exponential. In the log and exponential domain, the logarithmic and exponential functions are used for modeling the multiplicative noise model. But, this model is used only for positive outcomes. Therefore, wavelet transform domain is applied to the noise model that localizes an image pixel in both frequency and time domain simultaneously. Moreover, it separates the most vital information in a given image. Thus, it is feasible for obtaining a better approximation of the considered function using few coefficients. Finally, the experimental results show the performance effectiveness of the proposed algorithm.  

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