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Conference on Computational Imaging VI

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

ISBN: (纸本)9780819469861

A new iterative algorithm for quantitative image reconstruction for differential-interference contrast (DIC) microscopy is presented, along with simulations demonstrating key properties of the algorithm. The algorithm is an alternating minimization (AM) algorithm based on a diffraction imaging model for DIC images. The algorithm computes a specimen's complex transmittance function (magnitude and phase) from the DIC images. This new method extends the rotational diversity (RD) method developed by Preza that is based on the assumption that the specimen does not absorb light (or that its magnitude is constant and can be ignored) and thus only the specimen's phase function is computed from rotationally-diverse DIC images. The AM approach lifts the optimization problem to a higher dimensional space that is intimately tied to the underlying physics. The variables that are introduced in this lifting process are the unknown, immeasurable phases on the data. The AM algorithm iterates between estimating the image given the phase of the data and estimating the phase given the image. The framework allows constraints and penalties on the magnitude and phase estimates to be incorporated in a principled manner. The performance of the AM method is evaluated using simulated noiseless data. Simulation results compare specimen magnitude (absorption) and phase estimated with the AM method to the true specimen parameters showing good quantitative agreement using the mean square error and difference images. The estimated phase is a significant improvement over the phase estimated with the RD method from the same DIC images as shown in a comparison between the two methods. The AM method provides a novel approach in extracting quantitative phase and amplitude information of the same field of view from a single microscope mode.

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

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A Unified Bregman alternating minimization algorithm for Generalized DC Programs with Application to Imaging

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JOURNAL OF SCIENTIFIC COMPUTING 2024年第3期101卷 76页

作者： He, Hongjin Zhang, Zhiyuan Ningbo Univ Sch Math & Stat Ningbo 315211 Peoples R China Southern Methodist Univ Dept Operat Res & Engn Management Dallas TX 75205 USA

In this paper, we consider a class of nonconvex (not necessarily differentiable) optimization problems called generalized Difference-of-Convex functions (DC) programs, which is minimizing the sum of two separable DC parts and one two-block-variable coupling function. To circumvent the nonconvexity and nonseparability of the problem under consideration, we accordingly introduce a unified Bregman alternating minimization algorithm by maximally exploiting the favorable DC structure of the objective. Specifically, we first follow the spirit of alternating minimization to update each block variable in a sequential order, which can efficiently tackle the nonseparablitity caused by the coupling function. Then, we employ the Fenchel-Young inequality to approximate the second DC components (i.e., concave parts) so that each subproblem reduces to a convex optimization problem, thereby alleviating the computational burden of the nonconvex DC parts. Moreover, each subproblem absorbs a Bregman proximal regularization term, which is usually beneficial for inducing closed-form solutions of subproblems for many cases via choosing appropriate Bregman kernel functions. It is remarkable that our algorithm not only provides an algorithmic framework to understand the iterative schemes of some recently proposed algorithms, but also enjoys implementable schemes with easier subproblems than some state-of-the-art first-order algorithms developed for generic nonconvex and nonsmooth optimization problems. Theoretically, we prove that the sequence generated by our algorithm globally converges to a critical point under the Kurdyka-& Lstrok;ojasiewicz (K & Lstrok;) condition. Besides, we estimate the local convergence rates of our algorithm when we further know the prior information of the K & Lstrok;exponent. A series of numerical experiments on imaging data demonstrate the reliability and efficiency of the proposed algorithmic framework.

关键词： DC programs Nonconvex optimization Bregman distance alternating minimization algorithm First-order methods Kurdyka-& Lstrok ojasiewicz property Image processing

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Low dose CT reconstruction via L1 norm dictionary learning using alternating minimization algorithm and balancing principle

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JOURNAL OF X-RAY SCIENCE AND TECHNOLOGY 2018年第4期26卷 603-622页

作者： Wu, Junfeng Dai, Fang Hu, Gang Mou, Xuanqin Xian Univ Technol Coll Sci Xian 710048 Shaanxi Peoples R China Southeast Univ Key Lab Comp Network & Informat Integrat Minist Educ Nanjing Jiangsu Peoples R China Xi An Jiao Tong Univ Inst Image Proc & Pattern Recognit Xian Shaanxi Peoples R China

Excessive radiation exposure in computed tomography (CT) scans increases the chance of developing cancer and has become a major clinical concern. Recently, statistical iterative reconstruction (SIR) with l(0)-norm dictionary learning regularization has been developed to reconstructCTimages from the lowdose and few-viewdataset in order to reduce radiation dose. Nonetheless, the sparse regularization term adopted in this approach is l(0)-norm, which cannot guarantee the global convergence of the proposed algorithm. To address this problem, in this study we introduced the l(1)norm dictionary learning penalty into SIR framework for low dose CT image reconstruction, and developed an alternating minimization algorithm to minimize the associated objective function, which transforms CT image reconstruction problem into a sparse coding subproblem and an image updating subproblem. During the image updating process, an efficient model function approach based on balancing principle is applied to choose the regularization parameters. The proposed alternating minimization algorithm was evaluated first using real projection data of a sheep lung CT perfusion and then using numerical simulation based on sheep lung CT image and chest image. Both visual assessment and quantitative comparison using terms of root mean square error (RMSE) and structural similarity (SSIM) index demonstrated that the new image reconstruction algorithm yielded similar performance with l(0)-norm dictionary learning penalty and outperformed the conventional filtered backprojection (FBP) and total variation (TV) minimization algorithms.

关键词： L-1 norm dictionary learning alternating minimization algorithm balancing principle low dose CT reconstruction

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Line Integral alternating minimization algorithm for Dual-Energy X-Ray CT Image Reconstruction

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IEEE TRANSACTIONS ON MEDICAL IMAGING 2016年第2期35卷 685-698页

作者： Chen, Yaqi O'Sullivan, Joseph A. Politte, David G. Evans, Joshua D. Han, Dong Whiting, Bruce R. Williamson, Jeffrey F. Washington Univ Dept Elect & Syst Engn St Louis MO 63130 USA Washington Univ Sch Med Mallinckrodt Inst Radiol Elect Radiol Lab St Louis MO 63110 USA Virginia Commonwealth Univ Dept Radiat Oncol Richmond VA 23220 USA Univ Pittsburgh Dept Radiol Pittsburgh PA 15213 USA

We propose a new algorithm, called line integral alternating minimization (LIAM), for dual-energy X-ray CT image reconstruction. Instead of obtaining component images by minimizing the discrepancy between the data and the mean estimates, LIAM allows for a tunable discrepancy between the basis material projections and the basis sinograms. A parameter is introduced that controls the size of this discrepancy, and with this parameter the new algorithm can continuously go from a two-step approach to the joint estimation approach. LIAM alternates between iteratively updating the line integrals of the component images and reconstruction of the component images using an image iterative deblurring algorithm. An edge-preserving penalty function can be incorporated in the iterative deblurring step to decrease the roughness in component images. Images from both simulated and experimentally acquired sinograms from a clinical scanner were reconstructed by LIAM while varying the regularization parameters to identify good choices. The results from the dual-energy alternating minimization algorithm applied to the same data were used for comparison. Using a small fraction of the computation time of dual-energy alternating minimization, LIAM achieves better accuracy of the component images in the presence of Poisson noise for simulated data reconstruction and achieves the same level of accuracy for real data reconstruction.

关键词： alternating minimization algorithm dual-energy iterative deblurring algorithm line integral X-ray CT

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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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A new alternating minimization algorithm for image segmentation

A new alternating minimization algorithm for image segmentat...

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6th International Conference on Wireless, Mobile and Multi-Media (ICWMMN 2015)

作者： Zeyang Dou Bin Zhang Xinyan Yu Department of Applied Mathematics Communication University of China Beijing China

ISBN: (纸本)9781510822030

A new alternating minimization algorithm for image segmentation is proposed. Based on the similarities between Ambrosio-Tortorelli model and Perona-Malik model, a new explicit alternating minimization algorithm is developed. The Euler-Lagrange equations of Ambrosio-Tortorelli model is modified to produce sharper edges. The effect of parameters is studied. Numerical results are presented to illustrate the effectiveness of the proposed model.

关键词： Image segmentation Ambrosio -Tortorelli model Perona-Malik model alternating minimization algorithm Explicit scheme image segmentation algorithms

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alternating minimization differential privacy protection algorithm for the novel dual-mode learning tasks model

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 259卷

作者： Zhao, Pengfei Zhang, Kaili Zhang, Haibin Chen, Haibin Beijing Univ Civil Engn & Architecture Sch Civil & Transportat Engn Beijing 102616 Peoples R China Beijing 2 Middle Sch Beijing 100010 Peoples R China Chinese Acad Sci Acad Math & Syst Sci Beijing 100190 Peoples R China Beijing Univ Technol Dept Operat Res & Informat Engn Beijing 100124 Peoples R China Qufu Normal Univ Sch Management Sci Rizhao 276800 Shandong Peoples R China Ctr Intelligent Multidimens Data Anal Shatin Hong Kong Sci Pk Hong Kong Peoples R China

The privacy-protected algorithm (PPA) is pivotal in the realm of machine learning, especially for handling sensitive data types, such as medical and financial records. PPA enables two distinct operations: data publishing and data analysis, each capable of functioning independently. However, the field lacks a unified framework or an efficient algorithm to synergize these operations. This deficiency inspires our current research endeavor. In this paper, we introduce a novel dual-mode empirical risk minimization (D-ERM) model, specifically designed for integrated learning tasks. We also develop an alternating minimization differential privacy protection algorithm (AMDPPA) for implementing the D-ERM model. Our theoretical analysis confirms the differential privacy and accuracy of AMDPPA. We validate the algorithm's efficacy through numerical experiments using real-world datasets, demonstrating its ability to effectively balance privacy with learning efficiency.

关键词： Differential privacy protection Dual-mode learning Dual-mode empirical risk minimization model alternating minimization algorithm

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On the convergence of adaptive first order methods: proximal gradient and alternating minimization algorithms 6

On the convergence of adaptive first order methods: proximal...

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6th Annual Learning for Dynamics and Control Conference

作者： Latafat, Puya Themelis, Andreas Patrinos, Panagiotis Katholieke Univ Leuven Dept Elect Engn ESAT STADIUS Kasteelpark Arenberg 10 B-3001 Leuven Belgium Kyushu Univ Fac Informat Sci & Elect Engn ISEE 744 MotookaNishi-Ku Fukuoka 8190395 Japan

Building upon recent works on linesearch-free adaptive proximal gradient methods, this paper proposes AdaPG(q,r), a framework that unifies and extends existing results by providing larger stepsize policies and improved lower bounds. Different choices of the parameters q and r are discussed and the efficacy of the resulting methods is demonstrated through numerical simulations. In an attempt to better understand the underlying theory, its convergence is established in a more general setting that allows for time-varying parameters. Finally, an adaptive alternating minimization algorithm is presented by exploring the dual setting. This algorithm not only incorporates additional adaptivity, but also expands its applicability beyond standard strongly convex settings.

关键词： Convex minimization proximal gradient method alternating minimization algorithm locally Lipschitz gradient linesearch-free adaptive stepsizes

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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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minimization of multi-penalty functionals by alternating iterative thresholding and optimal parameter choices

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INVERSE PROBLEMS 2014年第12期30卷 125003-125003页

作者： Naumova, Valeriya Peter, Steffen Simula Res Lab NO-1364 Fornebu Norway Tech Univ Munich Fac Math D-85748 Garching Germany

Inspired by several recent developments in regularization theory, optimization, and signal processing, we present and analyze a numerical approach to multi-penalty regularization in spaces of sparsely represented functions. The sparsity prior is motivated by the largely expected geometrical/structured features of high-dimensional data, which may not be well-represented in the framework of typically more isotropic Hilbert spaces. In this paper, we are particularly interested in regularizers which are able to correctly model and separate the multiple components of additively mixed signals. This situation is rather common as pure signals may be corrupted by additive noise. To this end, we consider a regularization functional composed by a data-fidelity term, where signal and noise are additively mixed, a non-smooth and non-convex sparsity promoting term, and a penalty term to model the noise. We propose and analyze the convergence of an iterative alternating algorithm based on simple iterative thresholding steps to perform the minimization of the functional. By means of this algorithm, we explore the effect of choosing different regularization parameters and penalization norms in terms of the quality of recovering the pure signal and separating it from additive noise. For a given fixed noise level numerical experiments confirm a significant improvement in performance compared to standard one-parameter regularization methods. By using high-dimensional data analysis methods such as principal component analysis, we are able to show the correct geometrical clustering of regularized solutions around the expected solution. Eventually, for the compressive sensing problems considered in our experiments we provide a guideline for a choice of regularization norms and parameters.

关键词： multi-penalty regularization compressed sensing support identification non-convex constraints iterative thresholding alternating minimization algorithm

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