RECORD
Basis Pursuit Denoise with Nonsmooth Constraints
Optimization and Control · Submitted 28 Nov 2018
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The new methods are particularly promising for seismic applications, where the amplitude in the data varies significantly, and measurement noise in low-amplitude regions can wreak havoc for standard Gaussian error models.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
Level-set optimization formulations with data-driven constraints minimize a regularization functional subject to matching observations to a given error level. These formulations are widely used, particularly for matrix completion and sparsity promotion in data interpolation and denoising. The misfit level is typically measured in the l2 norm, or other smooth metrics. In this paper, we present a new flexible algorithmic framework that targets nonsmooth level-set constraints, including L1, Linf, and even L0 norms. These constraints give greater flexibility for modeling deviations in observation and denoising, and have significant impact on the solution. Measuring error in the L1 and L0 norms makes the result more robust to large outliers, while matching many observations exactly. We demonstrate the approach for basis pursuit denoise (BPDN) problems as well as for extensions of BPDN to matrix factorization, with applications to interpolation and denoising of 5D seismic data. The new methods are particularly promising for seismic applications, where the amplitude in the data varies significantly, and measurement noise in low-amplitude regions can wreak havoc for standard Gaussian error models.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Level-set optimization formulations with data-driven constraints minimize a regularization functional subject to matching observations to a given error level. | background 1.00 | 0.05 | 0.04 | asserted 1.00 |
| s1 | These formulations are widely used, particularly for matrix completion and sparsity promotion in data interpolation and denoising. | background 1.00 | 0.04 | 0.03 | asserted 1.00 |
| s2 | The misfit level is typically measured in the l2 norm, or other smooth metrics. | background 0.98 | 0.04 | 0.02 | asserted 0.96 |
| s3 | In this paper, we present a new flexible algorithmic framework that targets nonsmooth level-set constraints, including L1, Linf, and even L0 norms. | contribution 1.00 | 0.88 | 0.18 | asserted 1.00 |
| s4 | These constraints give greater flexibility for modeling deviations in observation and denoising, and have significant impact on the solution. | interpretation 0.71 | 0.23 | 0.18 | asserted 1.00 |
| s5 | Measuring error in the L1 and L0 norms makes the result more robust to large outliers, while matching many observations exactly. | interpretation 0.74 | 0.23 | 0.18 | asserted 1.00 |
| s6 | We demonstrate the approach for basis pursuit denoise (BPDN) problems as well as for extensions of BPDN to matrix factorization, with applications to interpolation and denoising of 5D seismic data. | contribution 0.91 | 0.92 | 0.16 | asserted 1.00 |
| s7 | The new methods are particularly promising for seismic applications, where the amplitude in the data varies significantly, and measurement noise in low-amplitude regions can wreak havoc for standard Gaussian error models. | interpretation 0.89 | 0.26 | 0.25 | hedged possibility 0.54 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
Level-set optimization formulations with data-driven constraints minimize a regularization functional subject to matching observations to a given error level. These formulations are widely used, particularly for matrix completion and sparsity promotion in data interpolation and denoising. The misfit level is typically measured in the l2 norm, or other smooth metrics. In this paper, we present a new flexible algorithmic framework that targets nonsmooth level-set constraints, including L1, Linf, and even L0 norms. These constraints give greater flexibility for modeling deviations in observation and denoising, and have significant impact on the solution. Measuring error in the L1 and L0 norms makes the result more robust to large outliers, while matching many observations exactly. We demonstrate the approach for basis pursuit denoise (BPDN) problems as well as for extensions of BPDN to matrix factorization, with applications to interpolation and denoising of 5D seismic data. The new methods are particularly promising for seismic applications, where the amplitude in the data varies significantly, and measurement noise in low-amplitude regions can wreak havoc for standard Gaussian error models.
Human review
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.