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      An L p (0 ≤  p ≤ 1)-norm regularized image reconstruction scheme for breast DOT with non-negative-constraint

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          Abstract

          Background

          In diffuse optical tomography (DOT), the image reconstruction is often an ill-posed inverse problem, which is even more severe for breast DOT since there are considerably increasing unknowns to reconstruct with regard to the achievable number of measurements. One common way to address this ill-posedness is to introduce various regularization methods. There has been extensive research regarding constructing and optimizing objective functions. However, although these algorithms dramatically improved reconstruction images, few of them have designed an essentially differentiable objective function whose full gradient is easy to obtain to accelerate the optimization process.

          Methods

          This paper introduces a new kind of non-negative prior information, designing differentiable objective functions for cases of L 1-norm, L p (0 <  p < 1)-norm and L 0-norm. Incorporating this non-negative prior information, it is easy to obtain the gradient of these differentiable objective functions, which is useful to guide the optimization process.

          Results

          Performance analyses are conducted using both numerical and phantom experiments. In terms of spatial resolution, quantitativeness, gray resolution and execution time, the proposed methods perform better than the conventional regularization methods without this non-negative prior information.

          Conclusions

          The proposed methods improves the reconstruction images using the introduced non-negative prior information. Furthermore, the non-negative constraint facilitates the gradient computation, accelerating the minimization of the objective functions.

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          Most cited references 21

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          A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems

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            An Introduction To Compressive Sampling

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              Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems

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                Author and article information

                Contributors
                wangbingyuan@tju.edu.cn
                wwbwesley@tju.edu.cn
                wangyihan@tju.edu.cn
                mawenjuan2008@163.com
                zhanglm@tju.edu.cn
                jiaoli@tju.edu.cn
                zhouzhongxing@tju.edu.cn
                huijuanzhao@tju.edu.cn
                gaofeng@tju.edu.cn
                Journal
                Biomed Eng Online
                Biomed Eng Online
                BioMedical Engineering OnLine
                BioMed Central (London )
                1475-925X
                3 March 2017
                3 March 2017
                2017
                : 16
                Affiliations
                [1 ]ISNI 0000 0004 1761 2484, GRID grid.33763.32, College of Precision Instruments and Optoelectronics Engineering, , Tianjin University, ; Tianjin, 300072 China
                [2 ]ISNI 0000 0000 9792 1228, GRID grid.265021.2, Cancer Institute and Hospital, , Tianjin Medical University, ; Tianjin, 300060 China
                [3 ]Tianjin Key Laboratory of Biomedical Detecting Techniques and Instruments, Tianjin, 300072 China
                Article
                318
                10.1186/s12938-017-0318-y
                5439119
                28253881
                © The Author(s) 2017

                Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License ( http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver ( http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

                Funding
                Funded by: FundRef http://dx.doi.org/10.13039/501100001809, National Natural Science Foundation of China;
                Award ID: 81371602
                Award Recipient :
                Funded by: the National Natural Science Foundation of China
                Award ID: 61475115
                Award ID: 61475116
                Award ID: 81671728
                Award ID: 81571723
                Award Recipient :
                Funded by: the National Natural Science Foundation of China
                Award ID: 61575140
                Award ID: 81401453
                Award Recipient :
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                © The Author(s) 2017

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