scholarly journals Quantitative susceptibility map reconstruction using annihilating filter‐based low‐rank Hankel matrix approach

2019 ◽  
Vol 83 (3) ◽  
pp. 858-871 ◽  
Author(s):  
Hyun‐Seo Ahn ◽  
Sung‐Hong Park ◽  
Jong Chul Ye
Keyword(s):  
Hankel Matrix ◽  
Low Rank ◽  
Susceptibility Map ◽  
Matrix Approach

scholarly journals Fast live cell imaging at nanometer scale using annihilating filter-based low-rank Hankel matrix approach

2015 ◽  
Author(s):  
Junhong Min ◽  
Lina Carlini ◽  
Michael Unser ◽  
Suliana Manley ◽  
Jong Chul Ye
Keyword(s):  
Live Cell Imaging ◽  
Cell Imaging ◽  
Hankel Matrix ◽  
Live Cell ◽  
Low Rank ◽  
Nanometer Scale ◽  
Matrix Approach

Patch-based image despeckling using low-rank Hankel matrix approach with speckle level estimation

2019 ◽  
Vol 2019 (11) ◽  
pp. 252-1-252-5
Author(s):  
Hansol Kim ◽  
Paul Oh ◽  
Sangyoon Lee ◽  
Moon Gi Kang
Keyword(s):  
Hankel Matrix ◽  
Low Rank ◽  
Matrix Approach ◽  
Image Despeckling

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.

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