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A Fast algorithm for Deconvolution and Poisson Noise Removal

JOURNAL OF SCIENTIFIC COMPUTING 2018年第3期75卷 1535-1554页

作者： Zhang, Xiongjun Ng, Michael K. Bai, Minru Cent China Normal Univ Sch Math & Stat Wuhan 430079 Hubei Peoples R China Hong Kong Baptist Univ Ctr Math Imaging & Vis Kowloon Tong Hong Kong Peoples R China Hong Kong Baptist Univ Dept Math Kowloon Tong Hong Kong Peoples R China Hunan Univ Coll Math & Econometr Changsha 410082 Hunan Peoples R China

Poisson noise removal problems have attracted much attention in recent years. The main aim of this paper is to study and propose an alternating minimization algorithm for Poisson noise removal with nonnegative constraint. The algorithm minimizes the sum of a Kullback-Leibler divergence term and a total variation term. We derive the algorithm by utilizing the quadratic penalty function technique. Moreover, the convergence of the proposed algorithm is also established under very mild conditions. Numerical comparisons between our approach and several state-of-the-art algorithms are presented to demonstrate the efficiency of our proposed algorithm.

关键词： Poisson noise alternating minimization algorithm Total variation Kullback-Leibler divergence

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A Retinex modulated piecewise constant variational model for image segmentation and bias correction

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APPLIED MATHEMATICAL MODELLING 2018年 54卷 697-709页

作者： Wu, Yongfei Li, Meng Zhang, Qifeng Liu, Yang Taiyuan Univ Technol Coll Data Sci Taiyuan 030024 Shanxi Peoples R China Chongqing Technol & Business Univ Coll Math & Stat Chongqing 400067 Peoples R China Chongqing Univ Coll Math & Stat Chongqing 401331 Peoples R China

In this paper, we propose a novel Retinex induced piecewise constant variational model for simultaneous segmentation of images with intensity inhomogeneity and bias correction. Firstly, we obtain an additive model by decomposing the original image into a smooth bias component and a structure part based on the Retinex theory. Secondly, the structure part can be modeled by the piecewise constant variational model and thus deduced a new data fidelity term. Finally, we formulate a new energy functional by incorporating the data fidelity term into the level set framework and introducing a GL-regularizer to the level set function and a smooth regularizer to model the bias component. Based on the alternating minimization algorithm and the operator splitting method, we present a numerical scheme to solve the minimization problem efficiently. Experimental results on images from diverse modalities demonstrate the competitive performances of the proposed model and algorithm over other representative methods in term of efficiency and robustness. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Image segmentation Variational model Bias correction alternating minimization algorithm

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A sparse regularization approach to inverse heat source identification

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2019年 142卷 118430-000页

作者： Lu, Zhong-Rong Pan, Tiancheng Wang, Li Sun Yat Sen Univ Sch Aeronaut & Astronaut Guangzhou Guangdong Peoples R China

This paper proposes a new sparse regularization approach for both steady-state and transient heat source identification within the finite element (FE) framework. The whole work is mainly twofold. On the one hand, the sparse regularization is introduced to formulate heat source identification with the sparsity constraint that the heat sources are often spatially sparse and thereof, the FE heat source vector is a sparse vector. On the other hand, the alternating minimization algorithm is developed to get the solution. Particular attention is paid to the choice of the regularization parameter which controls the sparsity of the heat sources and to this end, an efficient threshold setting method is presented. Three numerical examples concerning one-dimensional steady-state, two- and three-dimensional transient heat source identification are studied to testify the feasibility, performance and robustness of the proposed approach for steady-state or transient, single or multiple heat source identification. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Heat source identification Sparse regularization alternating minimization algorithm Threshold setting method

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Path planning for mobile-anchor based wireless sensor network localization: Static and dynamic schemes

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AD HOC NETWORKS 2018年 77卷 1-10页

作者： Erdemir, Ecenaz Tuncer, T. Engin Imperial Coll London Dept Elect & Elect Engn London England Middle East Tech Univ Dept Elect & Elect Engn Ankara Turkey

In wireless sensor networks, node locations are required for many applications. Usually, anchors with known positions are employed for localization. Sensor positions can be estimated more efficiently by using mobile anchors (MAs). Finding the best MA trajectory is an important problem in this context. Various path planning algorithms are proposed to localize as many sensors as possible by following the shortest path with minimum number of anchors. In this paper, path planning algorithms for MA assisted localization are proposed for both static and dynamic schemes. These approaches use MAs by stopping at minimum number of nodes to cover the monitoring area with shortest path length. A novel node localization algorithm based on alternating minimization is proposed. The performances of the proposed path planning algorithms are compared with previous approaches through simulations. The results show that more sensors are localized with less anchors in a shorter path and time for both schemes. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Wireless sensor network localization Mobile anchor Path planning alternating minimization algorithm

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Signal Recovery From Unlabeled Samples

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2018年第5期66卷 1242-1257页

作者： Haghighatshoar, Saeid Caire, Giuseppe Tech Univ Berlin Commun & Informat Theory Grp D-10623 Berlin Germany

In this paper, we study the recovery of a signal from a set of noisy linear projections (measurements), when such projections are unlabeled, that is, the correspondence between the measurements and the set of projection vectors (i.e., the rows of the measurement matrix) is not known a priori. We consider a special case of unlabeled sensing referred to as unlabeled ordered sampling (UOS) where the ordering of the measurements is preserved. We identify a natural duality between this problem and classical compressed sensing (CS), where we show that the unknown support (location of nonzero elements) of a sparse signal in CS corresponds to the unknown indices of the measurements in UOS. While in CS, it is possible to recover a sparse signal from an underdetermined set of linear equations (less equations than the signal dimension), successful recovery in UOS requires taking more samples than the dimension of the signal. Motivated by this duality, we develop a restricted isometry property (RIP) similar to that in CS. We also design a low-complexity alternating minimization algorithm that achieves a stable signal recovery under the established RIP. We analyze our proposed algorithm for different signal dimensions and number of measurements theoretically and investigate its performance empirically via numerical simulations. The results are reminiscent of a phase transition occurring in CS.

关键词： Unlabeled sensing compressed sensing alternating minimization algorithm

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A NOVEL FLUORESCENCE MICROSCOPY IMAGE DECONVOLUTION APPROACH 15

A NOVEL FLUORESCENCE MICROSCOPY IMAGE DECONVOLUTION APPROACH

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15th IEEE International Symposium on Biomedical Imaging (ISBI)

作者： Qin, Jing Yi, Xiyu Weiss, Shimon Montana State Univ Dept Math Sci Bozeman MT 59717 USA Univ Calif Los Angeles Dept Chem & Biochem Los Angeles CA 90095 USA

ISBN: (纸本)9781538636367

Superresolution optical fluctuation imaging (SOFI) is an attractive and affordable alternative to more established superresolution imaging methods. It provides moderate resolution enhancement and an efficient estimation of the optical point spread function (PSF). Moreover, further resolution enhancement could be achieved by deconvolution of the SOFI image. In this paper, we propose a novel image deconvolution approach based on the shearlet transform and the fractional-order total variation (FOTV) to further improve SOFI images. Since SOFI PSF estimation is imperfect in practice, we also propose a prior-guided semi-blind deconvolution method. Numerical experiments on simulated images with microtubule-like structures have shown that our proposed algorithms can recover filamentous features with high accuracy and outperforms other state-of-the-art deconvolution methods.

关键词： Image deconvolution SOFI shearlet transform fractional-order total variation alternating direction method of multipliers alternating minimization algorithm

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Implementation and Evaluation of a Penalized alternating minimization algorithm for Computational DIC Microscopy

Implementation and Evaluation of a Penalized Alternating Min...

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Conference on Computational Imaging VIII

作者： Preza, Chrysanthe O'Sullivan, Joseph A. Univ Memphis Dept Elect & Comp Engn Memphis TN 38152 USA Washington Univ Dept Elect & Syst Engn St Louis MO 63130 USA

ISBN: (纸本)9780819479266

We present the implementation and evaluation of a penalized alternating minimization (AM) method(1) for the computation of a specimen's complex transmittance function (magnitude and phase) from images captured with Differential Interference Contrast (DIC) microscopy. The magnitude of the transmittance function is constrained to be less than 1. The penalty is on the roughness of the complex transmittance function. Without the penalty, we show via simulation that the difference between the true and estimated transmittance function takes values in the null space of the DIC point-spread function, thereby characterizing the ill-posed nature of this inverse problem. The penalty effectively attenuates larger spatial frequencies that are in this null space. The algorithm is implemented on yeast cell images after proper normalization of the measured data. Preliminary results are promising.

关键词： alternating minimization algorithm complex function estimation regularization penalties phase estimation computational DIC (Nomarski) microscopy

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Coverage Control on Multi-Agent System 6

Coverage Control on Multi-Agent System

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6th International Annual Engineering Seminar (InAES)

作者： Ananto, Pramudya Saifussalam, Muhammad Inovan, Reka Iswanto Cahyadi, Adha Imam Gadjah Mada Univ Elect Engn & Informat Technol Dept Bulaksumur Yogyakarta Indonesia

ISBN: (纸本)9781509007417

The problem of maximizing the coverage of a Mobile Sensor Network under an unknown interest function through distributed means is discussed in this paper. The distributed version of the Voronoi locational optimization method is used to maximize the coverage. The stability results of the method is discussed. Numerical experiment is conducted to study the effect of network topology and interest function. The distributed Recursive Least Square method based on alternating minimization algorithm Framework is used to estimate the interest function. The correctness and effectiveness of the method is proved through numerical simulation. Some modification to the RLS algorithm introduced to alleviate the problem of the lack of excitation. The combined algorithm is then simulated to show its effectiveness. The result of this work shows that the modified method perform slightly worse compared with the case of centralized locational optimization with known interest field due to the lack of excitation.

关键词： Locational Optimization Voronoi based optimization Distributed Estimation Recursive Least Square alternating minimization algorithm Consensus building

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Adaptive Regularized Multichannel Blind Deconvolution Using alternating minimization 5

Adaptive Regularized Multichannel Blind Deconvolution Using ...

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IEEE International Advance Computing Conference (IACC 2015)

作者： James, Soniya Maik, Vivek Paik, Joonki Oxford Coll Engn Dept Elect & Commun Bangalore Karnataka India Chung Ang Univ Image Proc & Intelligent Syst Lab Seoul South Korea

ISBN: (纸本)9781479980475

Multichannel blind deconvolution is an ill posed problem where regularizers plays an important role. Adaptive regularization is used to obtain better quality restored image. This adds penalty weighted term along with image regularizer. The Isotropic TV image regularizers have chosen along with directional priors which preserves the over smoothing of the edges when compare to horizontal and vertical priors, thereby improving the Peak Signal to Noise Ratio(PSNR) of the reconstructed image. The Blind deconvolution problem can be solved using alternating minimization algorithm as it is best suited for two unknown variables. The formulation of blind deconvolution can be l(1) regularized optimization and geometry can be l(2). It results in hard optimization problem. The minimization step alternates between two sub optimization problems and this can be solve efficiently using Augmented Lagrangian method(ALM), where each iteration undergoes Bregman variable splitting or iterative method. This converted unconstrained problem in to constrained. This method can be applicable to medical images such as X Ray in order to reduce the amount of rays penetrating in to the body and to observe more details.

关键词： Bregman Iterative method alternating minimization algorithm Isotropic TV model l(p) norm Isotropic TV model l(2) norm Directional priors Adaptive regularization

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Efficient algorithms for hybrid regularizers based image denoising and deblurring

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2015年第7期69卷 675-687页

作者： Liu, Xinwu Hunan Univ Sci & Technol Sch Math & Computat Sci Xiangtan 411201 Hunan Peoples R China

To better eliminate the staircase effect and simultaneously preserve edge details, this paper investigates a hybrid regularizers model for image denoising and deblurring. This technique closely incorporates the advantages of the classical total variation (TV) filter and the fourth-order filter. Computationally, we develop an extremely efficient relaxation scheme and alternating minimization algorithm, and give the rigorous convergence analyses there in detail. Provided experimental results distinctly illustrate the high efficiency of the addressed numerical algorithms. Also, in comparison with the recovered results by the stateof-the-art models, simulations manifestly demonstrate the competitive performance of our proposed scheme in reducing the blocky images and sharply maintaining the edge features. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Image denoising Image deblurring Hybrid regularizers Relaxation method alternating minimization algorithm

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