An Edge Driven Wavelet Frame Model for Image Restoration

Bin Dong; Jae Kyu Choi; Xiaoqun Zhang

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An Edge Driven Wavelet Frame Model for Image Restoration

Jae Kyu Choi, Bin Dong, Xiaoqun Zhang

Numerical Analysis · Submitted 25 Jan 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Finally, numerical results on image inpainting and deblurring show that the proposed model is compared favorably against several popular image restoration models.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,863 input tokens.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.09 · human participants 0.02 · controlled comparison 0.51 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.93 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Wavelet frame systems are known to be effective in capturing singularities from noisy and degraded images. In this paper, we introduce a new edge driven wavelet frame model for image restoration by approximating images as piecewise smooth functions. With an implicit representation of image singularities sets, the proposed model inflicts different strength of regularization on smooth and singular image regions and edges. The proposed edge driven model is robust to both image approximation and singularity estimation. The implicit formulation also enables an asymptotic analysis of the proposed models and a rigorous connection between the discrete model and a general continuous variational model. Finally, numerical results on image inpainting and deblurring show that the proposed model is compared favorably against several popular image restoration models.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Wavelet frame systems are known to be effective in capturing singularities from noisy and degraded images.	background 1.00	0.04	0.02	asserted 0.95
s1	In this paper, we introduce a new edge driven wavelet frame model for image restoration by approximating images as piecewise smooth functions.	contribution 0.98	0.93	0.10	asserted 1.00
s2	With an implicit representation of image singularities sets, the proposed model inflicts different strength of regularization on smooth and singular image regions and edges.	method 0.96	0.81	0.10	asserted 1.00
s3	The proposed edge driven model is robust to both image approximation and singularity estimation.	result 0.74	0.79	0.19	asserted 1.00
s4	The implicit formulation also enables an asymptotic analysis of the proposed models and a rigorous connection between the discrete model and a general continuous variational model.	contribution 0.83	0.87	0.07	asserted 0.99
s5	Finally, numerical results on image inpainting and deblurring show that the proposed model is compared favorably against several popular image restoration models.	result 1.00	0.95	0.71	asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.95.

What was examined, and what was not

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arXiv listing abstract v1

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full text
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references and citing sentences
relations to other papers

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P abstract

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S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

Wavelet frame systems are known to be effective in capturing singularities from noisy and degraded images. In this paper, we introduce a new edge driven wavelet frame model for image restoration by approximating images as piecewise smooth functions. With an implicit representation of image singularities sets, the proposed model inflicts different strength of regularization on smooth and singular image regions and edges. The proposed edge driven model is robust to both image approximation and singularity estimation. The implicit formulation also enables an asymptotic analysis of the proposed models and a rigorous connection between the discrete model and a general continuous variational model. Finally, numerical results on image inpainting and deblurring show that the proposed model is compared favorably against several popular image restoration models.

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How the literature uses it

2 arXiv papers cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 1 sentence without a confident label

Compares with it 1 paper

In Section [ref], we perform the comparison on the simulation of image debluring with our model, the $l_o$-WF model and the EDWF [ref] model.

A wavelet frame coefficient total variational model for image restoration · Experimental results · 1.00

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