1
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Kalligeris EN, Karagrigoriou A, Parpoula C. On stochastic dynamic modeling of incidence data. Int J Biostat 2024; 20:201-215. [PMID: 37118931 DOI: 10.1515/ijb-2021-0134] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2021] [Accepted: 03/07/2023] [Indexed: 04/30/2023]
Abstract
In this paper, a Markov Regime Switching Model of Conditional Mean with covariates, is proposed and investigated for the analysis of incidence rate data. The components of the model are selected by both penalized likelihood techniques in conjunction with the Expectation Maximization algorithm, with the goal of achieving a high level of robustness regarding the modeling of dynamic behaviors of epidemiological data. In addition to statistical inference, Changepoint Detection Analysis is performed for the selection of the number of regimes, which reduces the complexity associated with Likelihood Ratio Tests. Within this framework, a three-phase procedure for modeling incidence data is proposed and tested via real and simulated data.
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Affiliation(s)
- Emmanouil-Nektarios Kalligeris
- Laboratory of Mathematics Raphaël Salem, University of Rouen Normandy, Avenue de l'Université, BP. 12, 76801 Saint Étienne du Rouvray, Rouen, France
- Lab of Statistics and Data Analysis, University of the Aegean, 83200 Karlovasi, Samos, Greece
| | - Alex Karagrigoriou
- Lab of Statistics and Data Analysis, University of the Aegean, 83200 Karlovasi, Samos, Greece
- Graphic Era Deemed to be University, Dehradun, India
| | - Christina Parpoula
- Department of Psychology, Panteion University of Social and Political Sciences, 17671, Athens, Greece
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2
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Xie D, Dong W, Zheng J, Tian C. Spatially-variant image deconvolution for photoacoustic tomography. OPTICS EXPRESS 2023; 31:21641-21657. [PMID: 37381257 DOI: 10.1364/oe.486846] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2023] [Accepted: 05/25/2023] [Indexed: 06/30/2023]
Abstract
Photoacoustic tomography (PAT) system can reconstruct images of biological tissues with high resolution and contrast. However, in practice, the PAT images are usually degraded by spatially variant blur and streak artifacts due to the non-ideal imaging conditions and chosen reconstruction algorithms. Therefore, in this paper, we propose a two-phase restoration method to progressively improve the image quality. In the first phase, we design a precise device and measuring method to obtain spatially variant point spread function samples at preset positions of the PAT system in image domain, then we adopt principal component analysis and radial basis function interpolation to model the entire spatially variant point spread function. Afterwards, we propose a sparse logarithmic gradient regularized Richardson-Lucy (SLG-RL) algorithm to deblur the reconstructed PAT images. In the second phase, we present a novel method called deringing which is also based on SLG-RL to remove the streak artifacts. Finally, we evaluate our method with simulation, phantom and in vivo experiments, respectively. All the results show that our method can significantly improve the quality of PAT images.
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3
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Kong W, Hui HWH, Peng H, Goh WWB. Dealing with missing values in proteomics data. Proteomics 2022; 22:e2200092. [PMID: 36349819 DOI: 10.1002/pmic.202200092] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2022] [Revised: 09/15/2022] [Accepted: 10/11/2022] [Indexed: 11/10/2022]
Abstract
Proteomics data are often plagued with missingness issues. These missing values (MVs) threaten the integrity of subsequent statistical analyses by reduction of statistical power, introduction of bias, and failure to represent the true sample. Over the years, several categories of missing value imputation (MVI) methods have been developed and adapted for proteomics data. These MVI methods perform their tasks based on different prior assumptions (e.g., data is normally or independently distributed) and operating principles (e.g., the algorithm is built to address random missingness only), resulting in varying levels of performance even when dealing with the same dataset. Thus, to achieve a satisfactory outcome, a suitable MVI method must be selected. To guide decision making on suitable MVI method, we provide a decision chart which facilitates strategic considerations on datasets presenting different characteristics. We also bring attention to other issues that can impact proper MVI such as the presence of confounders (e.g., batch effects) which can influence MVI performance. Thus, these too, should be considered during or before MVI.
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Affiliation(s)
- Weijia Kong
- Lee Kong Chian School of Medicine, Nanyang Technological University, Singapore, Singapore.,School of Biological Sciences, Nanyang Technological University, Singapore, Singapore
| | - Harvard Wai Hann Hui
- Lee Kong Chian School of Medicine, Nanyang Technological University, Singapore, Singapore.,School of Biological Sciences, Nanyang Technological University, Singapore, Singapore
| | - Hui Peng
- Lee Kong Chian School of Medicine, Nanyang Technological University, Singapore, Singapore.,School of Biological Sciences, Nanyang Technological University, Singapore, Singapore
| | - Wilson Wen Bin Goh
- Lee Kong Chian School of Medicine, Nanyang Technological University, Singapore, Singapore.,School of Biological Sciences, Nanyang Technological University, Singapore, Singapore.,Centre for Biomedical Informatics, Nanyang Technological University, Singapore, Singapore
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4
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da Silva Ferreira C, Montoril MH, Paula GA. Partially linear models with p-order autoregressive skew-normal errors. BRAZ J PROBAB STAT 2022. [DOI: 10.1214/22-bjps556] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
| | - Michel H. Montoril
- Department of Statistics, Federal University of São Carlos, São Carlos, SP, Brazil
| | - Gilberto A. Paula
- Institute of Mathematics and Statistics, University of São Paulo, São Paulo, SP, Brazil
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5
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Millardet M, Moussaoui S, Idier J, Mateus D, Conti M, Bailly C, Stute S, Carlier T. A Multiobjective Comparative Analysis of Reconstruction Algorithms in the Context of Low-Statistics 90Y-PET Imaging. IEEE TRANSACTIONS ON RADIATION AND PLASMA MEDICAL SCIENCES 2022. [DOI: 10.1109/trpms.2021.3126951] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Mael Millardet
- LS2N, CNRS UMR 6004, École centrale de Nantes, Nantes, France
| | - Said Moussaoui
- LS2N, CNRS UMR 6004, École centrale de Nantes, Nantes, France
| | - Jerome Idier
- LS2N, CNRS UMR 6004, École centrale de Nantes, Nantes, France
| | - Diana Mateus
- LS2N, CNRS UMR 6004, École centrale de Nantes, Nantes, France
| | - Maurizio Conti
- Physics Research Group, Siemens Medical Solution USA Inc., Knoxville, TN, USA
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6
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Wang T, Yu L, Leurgans SE, Wilson RS, Bennett DA, Boyle PA. Conditional functional clustering for longitudinal data with heterogeneous nonlinear patterns. Ann Appl Stat 2022. [DOI: 10.1214/21-aoas1542] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Tianhao Wang
- Rush Alzheimer’s Disease Center, Rush University Medical Center
| | - Lei Yu
- Rush Alzheimer’s Disease Center, Rush University Medical Center
| | - Sue E. Leurgans
- Rush Alzheimer’s Disease Center, Rush University Medical Center
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7
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Immediate solution of EM algorithm for non-blind image deconvolution. COMMUNICATIONS FOR STATISTICAL APPLICATIONS AND METHODS 2022. [DOI: 10.29220/csam.2022.29.2.277] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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8
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Ben-Bouazza FE, Bennani Y, Cabanes G, Touzani A. Unsupervised collaborative learning based on Optimal Transport theory. JOURNAL OF INTELLIGENT SYSTEMS 2021. [DOI: 10.1515/jisys-2020-0068] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Abstract
Collaborative learning has recently achieved very significant results. It still suffers, however, from several issues, including the type of information that needs to be exchanged, the criteria for stopping and how to choose the right collaborators. We aim in this paper to improve the quality of the collaboration and to resolve these issues via a novel approach inspired by Optimal Transport theory. More specifically, the objective function for the exchange of information is based on the Wasserstein distance, with a bidirectional transport of information between collaborators. This formulation allows to learns a stopping criterion and provide a criterion to choose the best collaborators. Extensive experiments are conducted on multiple data-sets to evaluate the proposed approach.
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Affiliation(s)
- Fatima-Ezzahraa Ben-Bouazza
- Université Sorbonne Paris Nord , LIPN UMR 7030 CNRS , France ; LaMSN, La Maison des Sciences Numériques, USPN , France ; Université Sidi Mohamed Ben Abdellah, LAMA , Fès , Morocco
| | - Younès Bennani
- Université Sorbonne Paris Nord , LIPN UMR 7030 CNRS , France ; LaMSN, La Maison des Sciences Numériques, USPN , France
| | - Guénaël Cabanes
- Université Sorbonne Paris Nord , LIPN UMR 7030 CNRS , France
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9
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Morvan M, Devijver E, Giacofci M, Monbet V. Prediction of the NASH through penalized mixture of logistic regression models. Ann Appl Stat 2021. [DOI: 10.1214/20-aoas1409] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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10
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Merlo L, Maruotti A, Petrella L. Two-part quantile regression models for semi-continuous longitudinal data: A finite mixture approach. STAT MODEL 2021. [DOI: 10.1177/1471082x21993603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This article develops a two-part finite mixture quantile regression model for semi-continuous longitudinal data. The proposed methodology allows heterogeneity sources that influence the model for the binary response variable to also influence the distribution of the positive outcomes. As is common in the quantile regression literature, estimation and inference on the model parameters are based on the asymmetric Laplace distribution. Maximum likelihood estimates are obtained through the EM algorithm without parametric assumptions on the random effects distribution. In addition, a penalized version of the EM algorithm is presented to tackle the problem of variable selection. The proposed statistical method is applied to the well-known RAND Health Insurance Experiment dataset which gives further insights on its empirical behaviour.
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Affiliation(s)
- Luca Merlo
- Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy
| | - Antonello Maruotti
- Department of Mathematics, University of Bergen, Bergen, Norway
- Department of Law, Economics, Political Sciences and Modern Languages, LUMSA University, Rome, Italy
| | - Lea Petrella
- MEMOTEF Department, Sapienza University of Rome, Rome, Italy
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11
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Dilernia A, Quevedo K, Camchong J, Lim K, Pan W, Zhang L. Penalized model-based clustering of fMRI data. Biostatistics 2021; 23:825-843. [PMID: 33527998 DOI: 10.1093/biostatistics/kxaa061] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2020] [Accepted: 12/21/2020] [Indexed: 11/14/2022] Open
Abstract
Functional magnetic resonance imaging (fMRI) data have become increasingly available and are useful for describing functional connectivity (FC), the relatedness of neuronal activity in regions of the brain. This FC of the brain provides insight into certain neurodegenerative diseases and psychiatric disorders, and thus is of clinical importance. To help inform physicians regarding patient diagnoses, unsupervised clustering of subjects based on FC is desired, allowing the data to inform us of groupings of patients based on shared features of connectivity. Since heterogeneity in FC is present even between patients within the same group, it is important to allow subject-level differences in connectivity, while still pooling information across patients within each group to describe group-level FC. To this end, we propose a random covariance clustering model (RCCM) to concurrently cluster subjects based on their FC networks, estimate the unique FC networks of each subject, and to infer shared network features. Although current methods exist for estimating FC or clustering subjects using fMRI data, our novel contribution is to cluster or group subjects based on similar FC of the brain while simultaneously providing group- and subject-level FC network estimates. The competitive performance of RCCM relative to other methods is demonstrated through simulations in various settings, achieving both improved clustering of subjects and estimation of FC networks. Utility of the proposed method is demonstrated with application to a resting-state fMRI data set collected on 43 healthy controls and 61 participants diagnosed with schizophrenia.
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Affiliation(s)
- Andrew Dilernia
- Division of Biostatistics, University of Minnesota, Minneapolis, MN, USA
| | - Karina Quevedo
- Department of Psychiatry, University of Minnesota, Minneapolis, MN, USA
| | - Jazmin Camchong
- Department of Psychiatry, University of Minnesota, Minneapolis, MN, USA
| | - Kelvin Lim
- Department of Psychiatry, University of Minnesota, Minneapolis, MN, USA
| | - Wei Pan
- Division of Biostatistics, University of Minnesota, Minneapolis, MN, USA
| | - Lin Zhang
- Division of Biostatistics, University of Minnesota, Minneapolis, MN, USA
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12
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Dong W, Tao S, Xu G, Chen Y. Blind Deconvolution for Poissonian Blurred Image With Total Variation and L 0-Norm Gradient Regularizations. IEEE TRANSACTIONS ON IMAGE PROCESSING : A PUBLICATION OF THE IEEE SIGNAL PROCESSING SOCIETY 2020; 30:1030-1043. [PMID: 33232236 DOI: 10.1109/tip.2020.3038518] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
This paper proposes a regularized blind deconvolution method for restoring Poissonian blurred image. The problem is formulated by utilizing the L0 -norm of image gradients and total variation (TV) to regularize the latent image and point spread function (PSF), respectively, and combining them with the negative logarithmic Poisson log-likelihood. To solve the problem, we propose an approach which combines the methods of variable splitting and Lagrange multiplier to convert the original problem into three sub-problems, and then design an alternating minimization algorithm which incorporates the estimation of PSF and latent image as well as the updation of Lagrange multiplier into account. We also design a non-blind deconvolution method based on TV regularization to further improve the quality of the restored image. Experimental results on both synthetic and real-world Poissonian blurred images show that the proposed method can achieve restored images of very high quality, which is competitive with or even better than some state of the art methods.
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13
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Gao X, Shen W, Zhang L, Hu J, Fortin NJ, Frostig RD, Ombao H. Regularized matrix data clustering and its application to image analysis. Biometrics 2020; 77:890-902. [PMID: 32799339 DOI: 10.1111/biom.13354] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2019] [Revised: 06/13/2020] [Accepted: 07/21/2020] [Indexed: 11/26/2022]
Abstract
We propose a novel regularized mixture model for clustering matrix-valued data. The proposed method assumes a separable covariance structure for each cluster and imposes a sparsity structure (eg, low rankness, spatial sparsity) for the mean signal of each cluster. We formulate the problem as a finite mixture model of matrix-normal distributions with regularization terms, and then develop an expectation maximization type of algorithm for efficient computation. In theory, we show that the proposed estimators are strongly consistent for various choices of penalty functions. Simulation and two applications on brain signal studies confirm the excellent performance of the proposed method including a better prediction accuracy than the competitors and the scientific interpretability of the solution.
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Affiliation(s)
- Xu Gao
- Department of Statistics, University of California, Irvine, California
| | - Weining Shen
- Department of Statistics, University of California, Irvine, California
| | - Liwen Zhang
- Shanghai University of Finance and Economics, Shanghai, China
| | - Jianhua Hu
- Herbert Irving Comprehensive Cancer Center, Columbia University, New York
| | - Norbert J Fortin
- Department of Neurobiology and Behavior, University of California, Irvine, California
| | - Ron D Frostig
- Department of Neurobiology and Behavior, University of California, Irvine, California.,Department of Biomedical Engineering, University of California, Irvine, California
| | - Hernando Ombao
- Statistics Program, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia
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14
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Mehranian A, Reader AJ. Model-Based Deep Learning PET Image Reconstruction Using Forward-Backward Splitting Expectation-Maximization. IEEE TRANSACTIONS ON RADIATION AND PLASMA MEDICAL SCIENCES 2020; 5:54-64. [PMID: 34056150 PMCID: PMC7610859 DOI: 10.1109/trpms.2020.3004408] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
We propose a forward-backward splitting algorithm to integrate deep learning into maximum-a-posteriori (MAP) positron emission tomography (PET) image reconstruction. The MAP reconstruction is split into regularization, expectation-maximization (EM), and a weighted fusion. For regularization, the use of either a Bowsher prior (using Markov-random fields) or a residual learning unit (using convolutional-neural networks) were considered. For the latter, our proposed forward-backward splitting EM (FBSEM), accelerated with ordered subsets (OS), was unrolled into a recurrent-neural network in which network parameters (including regularization strength) are shared across all states and learned during PET reconstruction. Our network was trained and evaluated using PET-only (FBSEM-p) and PET-MR (FBSEM-pm) datasets for low-dose simulations and short-duration in-vivo brain imaging. It was compared to OSEM, Bowsher MAPEM, and a post-reconstruction U-Net denoising trained on the same PET-only (Unet-p) or PET-MR (Unet-pm) datasets. For simulations, FBSEM-p(m) and Unet-p(m) nets achieved a comparable performance, on average, 14.4% and 13.4% normalized root-mean square error (NRMSE), respectively; and both outperformed OSEM and MAPEM methods (with 20.7% and 17.7% NRMSE, respectively). For in-vivo datasets, FBSEM-p(m), Unet-p(m), MAPEM, and OSEM methods achieved average root-sum-of-squared errors of 3.9%, 5.7%, 5.9%, and 7.8% in different brain regions, respectively. In conclusion, the studied U-Net denoising method achieved a comparable performance to a representative implementation of the FBSEM net.
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Affiliation(s)
- Abolfazl Mehranian
- School of Biomedical Engineering and Imaging Sciences, Department of Biomedical Engineering, King's College London, London SE1 7EH, U.K
| | - Andrew J Reader
- School of Biomedical Engineering and Imaging Sciences, Department of Biomedical Engineering, King's College London, London SE1 7EH, U.K
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15
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Sakai M, Parajuli RK, Kubota Y, Kubo N, Kikuchi M, Arakawa K, Nakano T. Improved iterative reconstruction method for Compton imaging using median filter. PLoS One 2020; 15:e0229366. [PMID: 32142552 PMCID: PMC7059936 DOI: 10.1371/journal.pone.0229366] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2019] [Accepted: 02/04/2020] [Indexed: 11/18/2022] Open
Abstract
A Compton camera is a device for imaging a radio-source distribution without using a mechanical collimator. Ordered-subset expectation-maximization (OS-EM) is widely used to reconstruct Compton images. However, the OS-EM algorithm tends to over-concentrate and amplify noise in the reconstructed image. It is, thus, necessary to optimize the number of iterations to develop high-quality images, but this has not yet been achieved. In this paper, we apply a median filter to an OS-EM algorithm and introduce a median root prior expectation-maximization (MRP-EM) algorithm to overcome this problem. In MRP-EM, the median filter is used to update the image in each iteration. We evaluated the quality of images reconstructed by our proposed method and compared them with those reconstructed by conventional algorithms using mathematical phantoms. The spatial resolution was estimated using the images of two point sources. Reproducibility was evaluated on an ellipsoidal phantom by calculating the residual sum of squares, zero-mean normalized cross-correlation, and mutual information. In addition, we evaluated the semi-quantitative performance and uniformity on the ellipsoidal phantom. MRP-EM reduces the generated noise and is robust with respect to the number of iterations. An evaluation of the reconstructed image quality using some statistical indices shows that our proposed method delivers better results than conventional techniques.
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Affiliation(s)
- Makoto Sakai
- Gunma University Heavy Ion Medical Center, Graduate School of Medicine, Gunma University, Showa-machi, Maebashi, Gunma, Japan
| | - Raj Kumar Parajuli
- Gunma University Heavy Ion Medical Center, Graduate School of Medicine, Gunma University, Showa-machi, Maebashi, Gunma, Japan.,Department of Molecular Imaging and Theranostics, National Institutes for Quantum and Radiological Science and Technology, Anagawa, Inage, Chiba, Japan
| | - Yoshiki Kubota
- Gunma University Heavy Ion Medical Center, Graduate School of Medicine, Gunma University, Showa-machi, Maebashi, Gunma, Japan
| | - Nobuteru Kubo
- Department of Radiation Oncology, Gunma University Graduate School of Medicine, Showa-machi, Maebashi, Gunma, Japan
| | - Mikiko Kikuchi
- Gunma University Heavy Ion Medical Center, Graduate School of Medicine, Gunma University, Showa-machi, Maebashi, Gunma, Japan
| | - Kazuo Arakawa
- Gunma University Heavy Ion Medical Center, Graduate School of Medicine, Gunma University, Showa-machi, Maebashi, Gunma, Japan
| | - Takashi Nakano
- Department of Radiation Oncology, Gunma University Graduate School of Medicine, Showa-machi, Maebashi, Gunma, Japan
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16
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Tsai YJ, Schramm G, Ahn S, Bousse A, Arridge S, Nuyts J, Hutton BF, Stearns CW, Thielemans K. Benefits of Using a Spatially-Variant Penalty Strength With Anatomical Priors in PET Reconstruction. IEEE TRANSACTIONS ON MEDICAL IMAGING 2020; 39:11-22. [PMID: 31144629 DOI: 10.1109/tmi.2019.2913889] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
In this study, we explore the use of a spatially-variant penalty strength in penalized image reconstruction using anatomical priors to reduce the dependence of lesion contrast on surrounding activity and lesion location. This work builds on a previous method to make the local perturbation response (LPR) approximately spatially invariant. While the dependence of lesion contrast on the local properties introduced by the anatomical penalty is intentional, the method aims to reduce the influence from surroundings lying along the lines of response (LORs) but not in the penalty neighborhood structure. The method is evaluated using simulated data, assuming that the anatomical information is absent or well-aligned with the corresponding activity images. Since the parallel level sets (PLS) penalty is convex and has shown promising results in the literature, it is chosen as the representative anatomical penalty and incorporated into the previously proposed preconditioned algorithm (L-BFGS-B-PC) for achieving good image quality and fast convergence rate. A 2D disc phantom with a feature at the center and a 3D XCAT thorax phantom with lesions inserted in different slices are used to study how surrounding activity and lesion location affect the visual appearance and quantitative consistency. A bias and noise analysis is also performed with the 2D disc phantom. The consistency of the algorithm convergence rate with respect to different data noise and background levels is also investigated using the XCAT phantom. Finally, an example of reconstruction for a patient dataset with inserted pseudo lesions is used as a demonstration in a clinical context. We show that applying the spatially-variant penalization with PLS can reduce the dependence of the lesion contrast on the surrounding activity and lesion location. It does not affect the bias and noise trade-off curves for matched local resolution. Moreover, when using the proposed penalization, significant improvement in algorithm convergence rate and convergence consistency is observed.
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17
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Navon A, Rosset S. Capturing between-tasks covariance and similarities using multivariate linear mixed models. Electron J Stat 2020. [DOI: 10.1214/20-ejs1764] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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18
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Zeng GL, Li Y. Extension of emission expectation maximization lookalike algorithms to Bayesian algorithms. Vis Comput Ind Biomed Art 2019; 2:14. [PMID: 32190406 PMCID: PMC7055571 DOI: 10.1186/s42492-019-0027-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2019] [Accepted: 10/11/2019] [Indexed: 11/23/2022] Open
Abstract
We recently developed a family of image reconstruction algorithms that look like the emission maximum-likelihood expectation-maximization (ML-EM) algorithm. In this study, we extend these algorithms to Bayesian algorithms. The family of emission-EM-lookalike algorithms utilizes a multiplicative update scheme. The extension of these algorithms to Bayesian algorithms is achieved by introducing a new simple factor, which contains the Bayesian information. One of the extended algorithms can be applied to emission tomography and another to transmission tomography. Computer simulations are performed and compared with the corresponding un-extended algorithms. The total-variation norm is employed as the Bayesian constraint in the computer simulations. The newly developed algorithms demonstrate a stable performance. A simple Bayesian algorithm can be derived for any noise variance function. The proposed algorithms have properties such as multiplicative updating, non-negativity, faster convergence rates for bright objects, and ease of implementation. Our algorithms are inspired by Green's one-step-late algorithm. If written in additive-update form, Green's algorithm has a step size determined by the future image value, which is an undesirable feature that our algorithms do not have.
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Affiliation(s)
- Gengsheng L. Zeng
- Department of Engineering, Utah Valley University, 800 W University Parkway, Orem, UT 84058 USA
- Department of Radiology and Imaging Sciences, University of Utah, 729 Arapeen Drive, Salt Lake City, UT 84108 USA
| | - Ya Li
- Department of Mathematics, Utah Valley University, 800 W University Parkway, Orem, UT 84058 USA
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19
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Bland J, Belzunce MA, Ellis S, McGinnity CJ, Hammers A, Reader AJ. Spatially-Compact MR-Guided Kernel EM for PET Image Reconstruction. IEEE TRANSACTIONS ON RADIATION AND PLASMA MEDICAL SCIENCES 2018; 2:470-482. [PMID: 30298139 PMCID: PMC6173308 DOI: 10.1109/trpms.2018.2844559] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
Positron emission tomography (PET) is a highly sensitive functional and molecular imaging modality which can measure picomolar concentrations of an injected radionuclide. However, the physical sensitivity of PET is limited, and reducing the injected dose leads to low count data and noisy reconstructed images. A highly effective way of reducing noise is to reparameterise the reconstruction in terms of MR-derived spatial basis functions. Spatial basis functions derived using the kernel method have demonstrated excellent noise reduction properties and maintain shared PET-MR detailed structures. However, as previously shown in the literature, the MR-guided kernel method may lead to excessive smoothing of structures that are only present in the PET data. This work makes two main contributions in order to address this problem: first, we exploit the potential of the MR-guided kernel method to form more spatially-compact basis functions which are able to preserve PET-unique structures, and secondly, we consider reconstruction at the native MR resolution. The former contribution notably improves the recovery of structures which are unique to the PET data. These adaptations of the kernel method were compared to the conventional implementation of the MR-guided kernel method and also to MLEM, in terms of ability to recover PET unique structures for both simulated and real data. The spatially-compact kernel method showed clear visual and quantitative improvements in the reconstruction of the PET unique structures, relative to the conventional kernel method for all sizes of PET unique structures investigated, whilst maintaining to a large extent the impressive noise mitigating and detail preserving properties of the conventional MR-guided kernel method. We therefore conclude that a spatially-compact parameterisation of the MR-guided kernel method, should be the preferred implementation strategy in order to obviate unnecessary losses in PET-unique details.
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Affiliation(s)
- James Bland
- King's College London, St Thomas' Hospital, London, U.K
| | | | - Sam Ellis
- King's College London, St Thomas' Hospital, London, U.K
| | - Colm J McGinnity
- King's College London & Guy's and St Thomas' PET Centre, St Thomas' Hospital, London, U.K
| | - Alexander Hammers
- King's College London & Guy's and St Thomas' PET Centre, St Thomas' Hospital, London, U.K
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Ellis S, Reader AJ. Penalized maximum likelihood simultaneous longitudinal PET image reconstruction with difference-image priors. Med Phys 2018; 45:3001-3018. [PMID: 29697144 DOI: 10.1002/mp.12937] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2017] [Revised: 02/27/2018] [Accepted: 04/12/2018] [Indexed: 11/07/2022] Open
Abstract
PURPOSE Many clinical contexts require the acquisition of multiple positron emission tomography (PET) scans of a single subject, for example, to observe and quantitate changes in functional behaviour in tumors after treatment in oncology. Typically, the datasets from each of these scans are reconstructed individually, without exploiting the similarities between them. We have recently shown that sharing information between longitudinal PET datasets by penalizing voxel-wise differences during image reconstruction can improve reconstructed images by reducing background noise and increasing the contrast-to-noise ratio of high-activity lesions. Here, we present two additional novel longitudinal difference-image priors and evaluate their performance using two-dimesional (2D) simulation studies and a three-dimensional (3D) real dataset case study. METHODS We have previously proposed a simultaneous difference-image-based penalized maximum likelihood (PML) longitudinal image reconstruction method that encourages sparse difference images (DS-PML), and in this work we propose two further novel prior terms. The priors are designed to encourage longitudinal images with corresponding differences which have (a) low entropy (DE-PML), and (b) high sparsity in their spatial gradients (DTV-PML). These two new priors and the originally proposed longitudinal prior were applied to 2D-simulated treatment response [18 F]fluorodeoxyglucose (FDG) brain tumor datasets and compared to standard maximum likelihood expectation-maximization (MLEM) reconstructions. These 2D simulation studies explored the effects of penalty strengths, tumor behaviour, and interscan coupling on reconstructed images. Finally, a real two-scan longitudinal data series acquired from a head and neck cancer patient was reconstructed with the proposed methods and the results compared to standard reconstruction methods. RESULTS Using any of the three priors with an appropriate penalty strength produced images with noise levels equivalent to those seen when using standard reconstructions with increased counts levels. In tumor regions, each method produces subtly different results in terms of preservation of tumor quantitation and reconstruction root mean-squared error (RMSE). In particular, in the two-scan simulations, the DE-PML method produced tumor means in close agreement with MLEM reconstructions, while the DTV-PML method produced the lowest errors due to noise reduction within the tumor. Across a range of tumor responses and different numbers of scans, similar results were observed, with DTV-PML producing the lowest errors of the three priors and DE-PML producing the lowest bias. Similar improvements were observed in the reconstructions of the real longitudinal datasets, although imperfect alignment of the two PET images resulted in additional changes in the difference image that affected the performance of the proposed methods. CONCLUSION Reconstruction of longitudinal datasets by penalizing difference images between pairs of scans from a data series allows for noise reduction in all reconstructed images. An appropriate choice of penalty term and penalty strength allows for this noise reduction to be achieved while maintaining reconstruction performance in regions of change, either in terms of quantitation of mean intensity via DE-PML, or in terms of tumor RMSE via DTV-PML. Overall, improving the image quality of longitudinal datasets via simultaneous reconstruction has the potential to improve upon currently used methods, allow dose reduction, or reduce scan time while maintaining image quality at current levels.
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Affiliation(s)
- Sam Ellis
- School of Biomedical Engineering and Imaging Sciences, King's College London, King's Health Partners, St Thomas' Hospital, London, SE1 7EH, UK
| | - Andrew J Reader
- School of Biomedical Engineering and Imaging Sciences, King's College London, King's Health Partners, St Thomas' Hospital, London, SE1 7EH, UK
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Bland J, Mehranian A, Belzunce MA, Ellis S, McGinnity CJ, Hammers A, Reader AJ. MR-Guided Kernel EM Reconstruction for Reduced Dose PET Imaging. IEEE TRANSACTIONS ON RADIATION AND PLASMA MEDICAL SCIENCES 2018; 2:235-243. [PMID: 29978142 PMCID: PMC6027990 DOI: 10.1109/trpms.2017.2771490] [Citation(s) in RCA: 38] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
PET image reconstruction is highly susceptible to the impact of Poisson noise, and if shorter acquisition times or reduced injected doses are used, the noisy PET data become even more limiting. The recent development of kernel expectation maximisation (KEM) is a simple way to reduce noise in PET images, and we show in this work that impressive dose reduction can be achieved when the kernel method is used with MR-derived kernels. The kernel method is shown to surpass maximum likelihood expectation maximisation (MLEM) for the reconstruction of low-count datasets (corresponding to those obtained at reduced injected doses) producing visibly clearer reconstructions for unsmoothed and smoothed images, at all count levels. The kernel EM reconstruction of 10% of the data had comparable whole brain voxel-level error measures to the MLEM reconstruction of 100% of the data (for simulated data, at 100 iterations). For regional metrics, the kernel method at reduced dose levels attained a reduced coefficient of variation and more accurate mean values compared to MLEM. However, the advances provided by the kernel method are at the expense of possible over-smoothing of features unique to the PET data. Further assessment on clinical data is required to determine the level of dose reduction that can be routinely achieved using the kernel method, whilst maintaining the diagnostic utility of the scan.
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Affiliation(s)
- James Bland
- King's College London, St Thomas' Hospital, London, U.K
| | | | | | - Sam Ellis
- King's College London, St Thomas' Hospital, London, U.K
| | - Colm J McGinnity
- King's College London & Guy's and St Thomas' PET Centre, St Thomas' Hospital, London, U.K
| | - Alexander Hammers
- King's College London & Guy's and St Thomas' PET Centre, St Thomas' Hospital, London, U.K
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Tsai YJ, Bousse A, Ehrhardt MJ, Stearns CW, Ahn S, Hutton BF, Arridge S, Thielemans K. Fast Quasi-Newton Algorithms for Penalized Reconstruction in Emission Tomography and Further Improvements via Preconditioning. IEEE TRANSACTIONS ON MEDICAL IMAGING 2018; 37:1000-1010. [PMID: 29610077 DOI: 10.1109/tmi.2017.2786865] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
This paper reports on the feasibility of using a quasi-Newton optimization algorithm, limited-memory Broyden-Fletcher-Goldfarb-Shanno with boundary constraints (L-BFGS-B), for penalized image reconstruction problems in emission tomography (ET). For further acceleration, an additional preconditioning technique based on a diagonal approximation of the Hessian was introduced. The convergence rate of L-BFGS-B and the proposed preconditioned algorithm (L-BFGS-B-PC) was evaluated with simulated data with various factors, such as the noise level, penalty type, penalty strength and background level. Data of three 18F-FDG patient acquisitions were also reconstructed. Results showed that the proposed L-BFGS-B-PC outperforms L-BFGS-B in convergence rate for all simulated conditions and the patient data. Based on these results, L-BFGS-B-PC shows promise for clinical application.
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Cal-González J, Tsoumpas C, Lassen ML, Rasul S, Koller L, Hacker M, Schäfers K, Beyer T. Impact of motion compensation and partial volume correction for 18F-NaF PET/CT imaging of coronary plaque. Phys Med Biol 2017; 63:015005. [PMID: 29240557 DOI: 10.1088/1361-6560/aa97c8] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
Recent studies have suggested that 18F-NaF-PET enables visualization and quantification of plaque micro-calcification in the coronary tree. However, PET imaging of plaque calcification in the coronary arteries is challenging because of the respiratory and cardiac motion as well as partial volume effects. The objective of this work is to implement an image reconstruction framework, which incorporates compensation for respiratory as well as cardiac motion (MoCo) and partial volume correction (PVC), for cardiac 18F-NaF PET imaging in PET/CT. We evaluated the effect of MoCo and PVC on the quantification of vulnerable plaques in the coronary arteries. Realistic simulations (Biograph TPTV, Biograph mCT) and phantom acquisitions (Biograph mCT) were used for these evaluations. Different uptake values in the calcified plaques were evaluated in the simulations, while three 'plaque-type' lesions of 36, 31 and 18 mm3 were included in the phantom experiments. After validation, the MoCo and PVC methods were applied in four pilot NaF-PET patient studies. In all cases, the MoCo-based image reconstruction was performed using the STIR software. The PVC was obtained from a local projection (LP) method, previously evaluated in preclinical and clinical PET. The results obtained show a significant increase of the measured lesion-to-background ratios (LBR) in the MoCo + PVC images. These ratios were further enhanced when using directly the tissue-activities from the LP method, making this approach more suitable for the quantitative evaluation of coronary plaques. When using the LP method on the MoCo images, LBR increased between 200% and 1119% in the simulated data, between 212% and 614% in the phantom experiments and between 46% and 373% in the plaques with positive uptake observed in the pilot patients. In conclusion, we have built and validated a STIR framework incorporating MoCo and PVC for 18F-NaF PET imaging of coronary plaques. First results indicate an improved quantification of plaque-type lesions.
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Affiliation(s)
- J Cal-González
- Center for Medical Physics and Biomedical Engineering, Medical University of Vienna, Vienna, Austria
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Abstract
Positron emission tomography (PET) is frequently used to monitor functional changes that occur over extended time scales, for example in longitudinal oncology PET protocols that include routine clinical follow-up scans to assess the efficacy of a course of treatment. In these contexts PET datasets are currently reconstructed into images using single-dataset reconstruction methods. Inspired by recently proposed joint PET-MR reconstruction methods, we propose to reconstruct longitudinal datasets simultaneously by using a joint penalty term in order to exploit the high degree of similarity between longitudinal images. We achieved this by penalising voxel-wise differences between pairs of longitudinal PET images in a one-step-late maximum a posteriori (MAP) fashion, resulting in the MAP simultaneous longitudinal reconstruction (SLR) method. The proposed method reduced reconstruction errors and visually improved images relative to standard maximum likelihood expectation-maximisation (ML-EM) in simulated 2D longitudinal brain tumour scans. In reconstructions of split real 3D data with inserted simulated tumours, noise across images reconstructed with MAP-SLR was reduced to levels equivalent to doubling the number of detected counts when using ML-EM. Furthermore, quantification of tumour activities was largely preserved over a variety of longitudinal tumour changes, including changes in size and activity, with larger changes inducing larger biases relative to standard ML-EM reconstructions. Similar improvements were observed for a range of counts levels, demonstrating the robustness of the method when used with a single penalty strength. The results suggest that longitudinal regularisation is a simple but effective method of improving reconstructed PET images without using resolution degrading priors.
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Affiliation(s)
- Sam Ellis
- Division of Imaging Sciences and Biomedical Engineering, Department of Biomedical Engineering, King's College London, St. Thomas' Hospital, London, United Kingdom
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Park C, Wang MC, Mo EB. Probabilistic penalized principal component analysis. COMMUNICATIONS FOR STATISTICAL APPLICATIONS AND METHODS 2017. [DOI: 10.5351/csam.2017.24.2.143] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Chongsun Park
- Department of Statistics, Sungkyunkwan University, Korea
| | - Morgan C. Wang
- Department of Statistics, University of Central Florida, USA
| | - Eun Bi Mo
- Department of Statistics, Sungkyunkwan University, Korea
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Tahaei MS, Reader AJ. Patch-based image reconstruction for PET using prior-image derived dictionaries. Phys Med Biol 2016; 61:6833-6855. [DOI: 10.1088/0031-9155/61/18/6833] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Polson NG, Scott JG, Willard BT. Proximal Algorithms in Statistics and Machine Learning. Stat Sci 2015. [DOI: 10.1214/15-sts530] [Citation(s) in RCA: 58] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Garg P, Chauhan A. Factors affecting the ERP implementation in Indian retail sector. BENCHMARKING-AN INTERNATIONAL JOURNAL 2015. [DOI: 10.1108/bij-11-2013-0104] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Purpose
– The purpose of this paper is to make an effort in identifying and exploring the factors which may affect the success of ERP implementation in Indian retail sector. This paper also analyses the between the factors and their impact on the successful implementation of ERP using the structured equation modeling (SEM) approach. “Organizational,” “Technological,” “People” and “Project Management” are the examined factors.
Design/methodology/approach
– A theoretical model is created that explains the factors which may affect the success of ERP implementation. Hypotheses were also developed to evaluate the interrelationship between affecting factors and success of ERP implementation. Empirical data is collected through survey questionnaire from practitioner like project sponsors, project managers, implementation consultants and team members who are involved in ERP implementation in retail sector to test the theoretical model.
Findings
– Using SEM, it is found that 62.7 percent of the variations of ERP implementation success can be explained with the help of the model suggested in the research study. The finding also confirms that there is significant positive interrelationship between “Organizational,” “Technological,” “People,” “Project Management” and success of ERP implementation in Indian retail sector.
Research limitations/implications
– The research is subject to the normal limitations of survey research. The study is using perceptual data provided by project sponsors, project managers, implementation consultants and team members who are involved in ERP implementation in retail sector, which may not provide clear measures of performance. However, this can be overcome using multiple methods to collect data in future studies.
Practical implications
– Findings from this paper can provide greater understanding in the area of ERP implementation. This study will provide valuable insights to researchers, practicing managers and those who are planning to implement ERP in retail sector.
Originality/value
– The study integrates the affecting factor with success of ERP implementation, i.e. “Organizational,” “Technological,” “People” and “Project Management” are the key drivers for the effectiveness and success of ERP implementation in Indian retail sector. Very few studies have been performed to investigate and understand this issue. Therefore, the research can make a useful contribution.
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Boonstra PS, Mukherjee B, Taylor JM. BAYESIAN SHRINKAGE METHODS FOR PARTIALLY OBSERVED DATA WITH MANY PREDICTORS. Ann Appl Stat 2013; 7:2272-2292. [PMID: 24436727 DOI: 10.1214/13-aoas668] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Abstract
Motivated by the increasing use of and rapid changes in array technologies, we consider the prediction problem of fitting a linear regression relating a continuous outcome Y to a large number of covariates X , eg measurements from current, state-of-the-art technology. For most of the samples, only the outcome Y and surrogate covariates, W , are available. These surrogates may be data from prior studies using older technologies. Owing to the dimension of the problem and the large fraction of missing information, a critical issue is appropriate shrinkage of model parameters for an optimal bias-variance tradeoff. We discuss a variety of fully Bayesian and Empirical Bayes algorithms which account for uncertainty in the missing data and adaptively shrink parameter estimates for superior prediction. These methods are evaluated via a comprehensive simulation study. In addition, we apply our methods to a lung cancer dataset, predicting survival time (Y) using qRT-PCR ( X ) and microarray ( W ) measurements.
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I. Ikediashi D, O. Ogunlana S, Udo G. Structural equation model for analysing critical risks associated with facilities management outsourcing and its impact on firm performance. JOURNAL OF FACILITIES MANAGEMENT 2013. [DOI: 10.1108/jfm-10-2012-0046] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Stsepankou D, Arns A, Ng SK, Zygmanski P, Hesser J. Evaluation of robustness of maximum likelihood cone-beam CT reconstruction with total variation regularization. Phys Med Biol 2012; 57:5955-70. [PMID: 22964760 DOI: 10.1088/0031-9155/57/19/5955] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Lauritzen S, Meinshausen N. Discussion: Latent variable graphical model selection via convex optimization. Ann Stat 2012. [DOI: 10.1214/12-aos980] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Li Y. Noise propagation for iterative penalized-likelihood image reconstruction based on Fisher information. Phys Med Biol 2011; 56:1083-103. [PMID: 21263172 DOI: 10.1088/0031-9155/56/4/013] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
Iterative reconstruction algorithms have been widely used in PET and SPECT emission tomography. Accurate modeling of photon noise propagation is crucial for quantitative tomography applications. Iteration-based noise propagation methods have been developed for only a few algorithms that have explicit multiplicative update equations. And there are discrepancies between the iteration-based methods and Fessler's fixed-point method because of improper approximations. In this paper, we present a unified theoretical prediction of noise propagation for any penalized expectation maximization (EM) algorithm where the EM approach incorporates a penalty term. The proposed method does not require an explicit update equation. The update equation is assumed to be implicitly defined by a differential equation of a surrogate function. We derive the expressions using the implicit function theorem, Taylor series and the chain rule from vector calculus. We also derive the fixed-point expressions when iterative algorithms converge and show the consistency between the proposed method and the fixed-point method. These expressions are solely defined in terms of the partial derivatives of the surrogate function and the Fisher information matrices. We also apply the theoretical noise predictions for iterative reconstruction algorithms in emission tomography. Finally, we validate the theoretical predictions for MAP-EM and OSEM algorithms using Monte Carlo simulations with Jaszczak-like and XCAT phantoms, respectively.
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Affiliation(s)
- Yusheng Li
- Department of Diagnostic Radiology, Rush University Medical Center, Chicago, IL 60612, USA.
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van Dyk DA, Meng XL. Cross-Fertilizing Strategies for Better EM Mountain Climbing and DA Field Exploration: A Graphical Guide Book. Stat Sci 2010. [DOI: 10.1214/09-sts309] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Combès B, Prima S. Setting priors and enforcing constraints on matches for nonlinear registration of meshes. MEDICAL IMAGE COMPUTING AND COMPUTER-ASSISTED INTERVENTION : MICCAI ... INTERNATIONAL CONFERENCE ON MEDICAL IMAGE COMPUTING AND COMPUTER-ASSISTED INTERVENTION 2010; 12:175-83. [PMID: 20426110 DOI: 10.1007/978-3-642-04271-3_22] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We show that a simple probabilistic modelling of the registration problem for surfaces allows to solve it by using standard clustering techniques. In this framework, point-to-point correspondences are hypothesized between the two free-form surfaces, and we show how to specify priors and to enforce global constraints on these matches with only minor changes to the optimisation algorithm. The purpose of these two modifications is to increase its capture range and to obtain more realistic geometrical transformations between the surfaces. We conclude with some validation experiments and results on synthetic and real data.
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Allen GI, Tibshirani R. TRANSPOSABLE REGULARIZED COVARIANCE MODELS WITH AN APPLICATION TO MISSING DATA IMPUTATION. Ann Appl Stat 2010; 4:764-790. [PMID: 26877823 PMCID: PMC4751046 DOI: 10.1214/09-aoas314] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
Missing data estimation is an important challenge with high-dimensional data arranged in the form of a matrix. Typically this data matrix is transposable, meaning that either the rows, columns or both can be treated as features. To model transposable data, we present a modification of the matrix-variate normal, the mean-restricted matrix-variate normal, in which the rows and columns each have a separate mean vector and covariance matrix. By placing additive penalties on the inverse covariance matrices of the rows and columns, these so called transposable regularized covariance models allow for maximum likelihood estimation of the mean and non-singular covariance matrices. Using these models, we formulate EM-type algorithms for missing data imputation in both the multivariate and transposable frameworks. We present theoretical results exploiting the structure of our transposable models that allow these models and imputation methods to be applied to high-dimensional data. Simulations and results on microarray data and the Netflix data show that these imputation techniques often outperform existing methods and offer a greater degree of flexibility.
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Affiliation(s)
- Genevera I Allen
- Department of Statistics, Stanford University, Stanford, California, 94305, USA,
| | - Robert Tibshirani
- Department of Statistics, Stanford University, Stanford, California, 94305, USA,
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Sohlberg A, Ruotsalainen U, Watabe H, Iida H, Kuikka JT. Accelerated median root prior reconstruction for pinhole single-photon emission tomography (SPET). Phys Med Biol 2003; 48:1957-69. [PMID: 12884928 DOI: 10.1088/0031-9155/48/13/308] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
Pinhole collimation can be used to improve spatial resolution in SPET. However, the resolution improvement is achieved at the cost of reduced sensitivity, which leads to projection images with poor statistics. Images reconstructed from these projections using the maximum likelihood expectation maximization (ML-EM) algorithms, which have been used to reduce the artefacts generated by the filtered backprojection (FBP) based reconstruction, suffer from noise/bias trade-off: noise contaminates the images at high iteration numbers, whereas early abortion of the algorithm produces images that are excessively smooth and biased towards the initial estimate of the algorithm. To limit the noise accumulation we propose the use of the pinhole median root prior (PH-MRP) reconstruction algorithm. MRP is a Bayesian reconstruction method that has already been used in PET imaging and shown to possess good noise reduction and edge preservation properties. In this study the PH-MRP algorithm was accelerated with the ordered subsets (OS) procedure and compared to the FBP, OS-EM and conventional Bayesian reconstruction methods in terms of noise reduction, quantitative accuracy, edge preservation and visual quality. The results showed that the accelerated PH-MRP algorithm was very robust. It provided visually pleasing images with lower noise level than the FBP or OS-EM and with smaller bias and sharper edges than the conventional Bayesian methods.
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Affiliation(s)
- Antti Sohlberg
- Department of Clinical Physiology & Nuclear Medicine, Kuopio University Hospital, PO Box 1777 FIN-70211, Kuopio, Finland.
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Abstract
The ability to theoretically model the propagation of photon noise through PET and SPECT tomographic reconstruction algorithms is crucial in evaluating the reconstructed image quality as a function of parameters of the algorithm. In a previous approach for the important case of the iterative ML-EM (maximum-likelihood-expectation-maximization) algorithm, judicious linearizations were used to model theoretically the propagation of a mean image and a covariance matrix from one iteration to the next. Our analysis extends this approach to the case of MAP (maximum a posteriori)-EM algorithms, where the EM approach incorporates prior terms. We analyse in detail two cases: a MAP-EM algorithm incorporating an independent gamma prior, and a one-step-late (OSL) version of a MAP-EM algorithm incorporating a multivariate Gaussian prior, for which familiar smoothing priors are special cases. To validate our theoretical analyses, we use a Monte Carlo methodology to compare, at each iteration, theoretical estimates of mean and covariance with sample estimates, and show that the theory works well in practical situations where the noise and bias in the reconstructed images do not assume extreme values.
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Affiliation(s)
- W Wang
- Department of Electrical Engineering, SUNY at Stony Brook 11794, USA
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