A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems

Beck, Amir; Teboulle, Marc

doi:10.1137/080716542

Cited by 9,938 publications

(9,795 citation statements)

References 17 publications

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“…In order to reduce the required computational time, a fast iterative soft-thresholding algorithm (Beck & Teboulle 2009) is used to solve the cost function. Fig.…”

Section: R E F E R E N C E S a P P E N D I X : T H E O Ry O F C O M Pmentioning

confidence: 99%

Quantitative evaluation of thin-layer thickness and CO₂mass utilizing seismic complex decomposition at the Ketzin CO₂storage site, Germany

Huang

Juhlin

Han³

et al. 2016

Geophys. J. Int.

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S U M M A R YDetermining thin layer thickness is very important for reservoir characterization and CO 2 quantification. Given its high time-frequency resolution and robustness, the complex spectral decomposition method was applied on time-lapse 3-D seismic data from the Ketzin pilot site for CO 2 storage to evaluate the frequency-dependent characteristics of thin layers at the injection level. Higher temporal resolution and more stratigraphic details are seen in the all-frequency and monochromatic reflectivity amplitude sections obtained by complex spectral decomposition compared to the stacked sections. The mapped geologic discontinuities within the reservoir are consistent with the preferred orientation of CO 2 propagation. Tuning frequency mapping shows the thicknesses of the reservoir sandstone and gaseous CO 2 is consistent with the measured thickness of the sandstone unit from well logging. An attempt to discriminate between pressure effects and CO 2 saturation using the extracted tuning frequency indicates that CO 2 saturation is the main contributor to the amplitude anomaly at the Ketzin site. On the basis of determined thickness of gaseous CO 2 in the reservoir, quantitative analysis of the amount of CO 2 was performed and shows a discrepancy between the injected and calculated CO 2 mass. This may be explained by several uncertainties, like structural reservoir heterogeneity, a limited understanding of the complex subsurface conditions, error of determined tuning frequency, the presence of ambient noise and ongoing CO 2 dissolution.

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“…In order to reduce the required computational time, a fast iterative soft-thresholding algorithm (Beck & Teboulle 2009) is used to solve the cost function. Fig.…”

Section: R E F E R E N C E S a P P E N D I X : T H E O Ry O F C O M Pmentioning

confidence: 99%

Quantitative evaluation of thin-layer thickness and CO₂mass utilizing seismic complex decomposition at the Ketzin CO₂storage site, Germany

Huang

Juhlin

Han³

et al. 2016

Geophys. J. Int.

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“…In this section, ECRC, CRC and SRC with fast l 1 minimization methods, including L1LS [6], FISTA [7] and Homotopy [8] are compared on the AR and Extended Yale B databases. The parameter λ is set as 0.05.…”

Section: Resultsmentioning

confidence: 99%

Extended CRC: Face Recognition with a Single Training Image per Person via Intraclass Variant Dictionary

Lin

Xie

Mao

2013

IEICE Trans. Inf. & Syst.

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SUMMARYFor face recognition with a single training image per person, Collaborative Representation based Classification (CRC) has significantly less complexity than Extended Sparse Representation based Classification (ESRC). However, CRC gets lower recognition rates than ESRC. In order to combine the advantages of CRC and ESRC, we propose Extended Collaborative Representation based Classification (ECRC) for face recognition with a single training image per person. ECRC constructs an auxiliary intraclass variant dictionary to represent the possible variation between the testing and training images. Experimental results show that ECRC outperforms the compared methods in terms of both high recognition rates and low computation complexity.

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“…The cost function for updating x is as below: (13) With the presence of the regularization term l 1 /l 2 , Equation (13) can be solved by a minimization algorithm. We chose ISTA, the iterative shrinkage-thresholding algorithm by Beck [24]. ISTA can be considered an inverse transform, which estimates a sharp image from a blurry image and kernel.…”

Section: ) Sharp Image X-updatementioning

confidence: 99%

Fast Patch-based De-blurring with Directional-oriented Kernel Estimation

Min¹,

Chong²

2017

Journal of IKEEE

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This paper proposes a fast patch-based de-blurring algorithm including kernel estimation based on the angle between the edge and the blur direction. For de-blurring, image patches from the most informative edges in the blurry image are used to estimate a kernel with low computational cost. Moreover, the kernels of each patch are estimated based on the correlation between the edge direction and the blur direction. This makes the final kernel more reliable and creates an accurate latent image from the blurry image. The combination of directionally oriented kernel estimation and patch-based de-blurring is faster and more accurate than existing state-of-the art methods. Experimental results using various test images show that the proposed method achieves its objectives: speed and accuracy. key words: de-blurring, edge direction, image restoration, kernel estimation, motion blur.

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A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems

Cited by 9,938 publications

References 17 publications

Quantitative evaluation of thin-layer thickness and CO₂mass utilizing seismic complex decomposition at the Ketzin CO₂storage site, Germany

Quantitative evaluation of thin-layer thickness and CO₂mass utilizing seismic complex decomposition at the Ketzin CO₂storage site, Germany

Extended CRC: Face Recognition with a Single Training Image per Person via Intraclass Variant Dictionary

Fast Patch-based De-blurring with Directional-oriented Kernel Estimation

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A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems

Cited by 9,938 publications

References 17 publications

Quantitative evaluation of thin-layer thickness and CO2mass utilizing seismic complex decomposition at the Ketzin CO2storage site, Germany

Quantitative evaluation of thin-layer thickness and CO2mass utilizing seismic complex decomposition at the Ketzin CO2storage site, Germany

Extended CRC: Face Recognition with a Single Training Image per Person via Intraclass Variant Dictionary

Fast Patch-based De-blurring with Directional-oriented Kernel Estimation

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Product

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About

Quantitative evaluation of thin-layer thickness and CO₂mass utilizing seismic complex decomposition at the Ketzin CO₂storage site, Germany

Quantitative evaluation of thin-layer thickness and CO₂mass utilizing seismic complex decomposition at the Ketzin CO₂storage site, Germany