Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems

Beck, Amir; Teboulle, Marc

doi:10.1109/tip.2009.2028250

Cited by 1,751 publications

(1,621 citation statements)

References 20 publications

(44 reference statements)

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“…This can be realized in different ways, e.g., by the simple gradient descent reprojection algorithm in [15] or by faster multistep algorithms [6,50,63].…”

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confidence: 99%

Removing Multiplicative Noise by Douglas-Rachford Splitting Methods

2009

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In this paper, we consider a variational restoration model consisting of the I-divergence as data fitting term and the total variation semi-norm or nonlocal means as regularizer for removing multiplicative Gamma noise. Although the I-divergence is the typical data fitting term when dealing with Poisson noise we substantiate why it is also appropriate for cleaning Gamma noise. We propose to compute the minimizers of our restoration functionals by applying Douglas-Rachford splitting techniques, resp. alternating direction methods of multipliers. For a particular splitting, we present a semi-implicit scheme to solve the involved nonlinear systems of equations and prove its Q-linear convergence. Finally, we demonstrate the performance of our methods by numerical examples.

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“…This can be realized in different ways, e.g., by the simple gradient descent reprojection algorithm in [15] or by faster multistep algorithms [6,50,63].…”

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confidence: 99%

Removing Multiplicative Noise by Douglas-Rachford Splitting Methods

2009

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“…In the future work, we will address the issue of motion blur in two perspectives: 1) integrate deblurring techniques [43, 44] into our system; 2) provide a simple training process to familiarize blind users with the device to reduce motion blur. Our future work will also focus on evaluating the proposed system to recognize banknotes of different countries and transferring the method to mobile phones.…”

Section: Discussionmentioning

confidence: 99%

Robust and Effective Component-Based Banknote Recognition for the Blind

Hasanuzzaman

Yang

Tian

2012

IEEE Trans. Syst., Man, Cybern. C

103

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We develop a novel camera-based computer vision technology to automatically recognize banknotes for assisting visually impaired people. Our banknote recognition system is robust and effective with the following features: 1) high accuracy: high true recognition rate and low false recognition rate, 2) robustness: handles a variety of currency designs and bills in various conditions, 3) high efficiency: recognizes banknotes quickly, and 4) ease of use: helps blind users to aim the target for image capture. To make the system robust to a variety of conditions including occlusion, rotation, scaling, cluttered background, illumination change, viewpoint variation, and worn or wrinkled bills, we propose a component-based framework by using Speeded Up Robust Features (SURF). Furthermore, we employ the spatial relationship of matched SURF features to detect if there is a bill in the camera view. This process largely alleviates false recognition and can guide the user to correctly aim at the bill to be recognized. The robustness and generalizability of the proposed system is evaluated on a dataset including both positive images (with U.S. banknotes) and negative images (no U.S. banknotes) collected under a variety of conditions. The proposed algorithm, achieves 100% true recognition rate and 0% false recognition rate. Our banknote recognition system is also tested by blind users.

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“…In this work, Eq. (7) is solved by the gradient-based recovery method [30,31], whose iteration form is given by…”

Section: A Conventional Landweber Iteration L1 Regularization and Tmentioning

confidence: 99%

An Image Reconstruction Algorithm for Electrical Impedance Tomography Using Adaptive Group Sparsity Constraint

Yang

Jia

2017

IEEE Trans. Instrum. Meas.

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Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems

Cited by 1,751 publications

References 20 publications

Removing Multiplicative Noise by Douglas-Rachford Splitting Methods

Removing Multiplicative Noise by Douglas-Rachford Splitting Methods

Robust and Effective Component-Based Banknote Recognition for the Blind

An Image Reconstruction Algorithm for Electrical Impedance Tomography Using Adaptive Group Sparsity Constraint

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