Compressed sensing with log-sum heuristic recover for seismic denoising
Bibliographic record
Abstract
The compressed sensing (CS) method, commonly utilized for restructuring sparse signals, has been extensively used to attenuate the random noise in seismic data. An important basis of CS-based methods is the sparsity of sparse coefficients. In this method, the sparse coefficient vector is acquired by minimizing the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mrow><mml:msub><mml:mi mathvariant="bold">l</mml:mi><mml:mn mathvariant="bold">1</mml:mn></mml:msub></mml:mrow></mml:math> norm as a substitute for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:mrow><mml:msub><mml:mi mathvariant="bold">l</mml:mi><mml:mn mathvariant="bold">0</mml:mn></mml:msub></mml:mrow></mml:math> norm. Many efforts have been made to minimize the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"><mml:mrow><mml:msub><mml:mi mathvariant="bold">l</mml:mi><mml:mi mathvariant="bold">p</mml:mi></mml:msub></mml:mrow></mml:math> norm (0 &lt; p &lt; 1) to obtain a more desirable sparse coefficient representation. Despite the improved performance that is achieved by minimizing the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m4"><mml:mrow><mml:msub><mml:mi mathvariant="bold">l</mml:mi><mml:mi mathvariant="bold">p</mml:mi></mml:msub></mml:mrow></mml:math> norm with 0 &lt; p &lt; 1, the related sparse coefficient vector is still suboptimal since the parameter p is greater than 0 rather than infinitely approaching 0 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m5"><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi mathvariant="bold">p</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mn mathvariant="bold">0</mml:mn><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:mfenced></mml:mrow></mml:math> . Therefore, the CS method with the limit <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m6"><mml:mrow><mml:mi mathvariant="bold">p</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mn mathvariant="bold">0</mml:mn><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math> is proposed to enhance the sparse performance and thus generate better denoised results in this paper. Our proposed method is referred to as the CS-LHR method because the solving process for minimizing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m7"><mml:mrow><mml:mi mathvariant="bold">p</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mn mathvariant="bold">0</mml:mn><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math> is the log-sum heuristic recovery (LHR). Furthermore, to improve the computational efficiency, we incorporate the majorization-minimization (MM) algorithm in this CS-LHR method. Experimental results of synthetic and real seismic records demonstrate the remarkable performance of CS-LHR in random noise suppression.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".