基于非负约束L1-范数正则化的乳腺扩散光学层析成像重建方法

在乳腺扩散光学层析成像中，L1-范数正则化的引入大幅改善了重建图像的质量，但目标函数的不可导性使得最优化过程异常困难。提出了一种新的基于非负约束L1-范数正则化的重建方法。非负先验信息的引入使得目标函数的一阶梯度变得简单易求，最优化过程得以简化和加速。数值模拟和仿体实验均表明，相对于传统正则化重建方法，该方法可简单、快速地获得更高质量的重建图像。

Abstract

In breast diffuse optical tomography, the introduction of the L1-norm regularization greatly improves the quality of the reconstructed image. However, the non-differentiable property of the objective function leads to exceeding difficulty in the optimization process. A new reconstruction method based on the L1-norm regularization with the non-negative restriction is proposed. To easily solve the first-order gradient of the objective function, the non-negative prior information is introduced. The optimization process is then well simplified and accelerated. Both the numerical simulations and the phantom experiments demonstrate that this new method can obtain much better results than the conventional regularization methods, and its process is more simple and faster.

参考文献

[1] Cao N, Nehorai A, Jacobs M. Image reconstruction for diffuse optical tomography using sparsity regularization and expectation-maximization algorithm[J]. Optics Express, 2007, 15(21): 13695-13708.

[2] Prakash J, Shaw C B, Manjappa R, et al. Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction[J]. IEEE Journal of Selected Topics in Quantum Electronics, 2014, 20(2): 74-82.

[3] Chen C, Tian F H, Liu H L, et al. Diffuse optical tomography enhanced by clustered sparsity for functional brain imaging[J]. IEEE Transactions on Medical Imaging, 2014, 33(12): 2323-2331.

[4] Lee O, Kim J M, Bresler Y, et al. Compressive diffuse optical tomography: noniterative exact reconstruction using joint sparsity[J]. IEEE Transactions on Medical Imaging, 2011, 30(5): 1129-1142.

[5] Okawa S, Hoshi Y, Yamada Y. Improvement of image quality of time-domain diffuse optical tomography with IP sparsity regularization[J]. Biomedical Optics Express, 2011, 2(12): 3334-3348.

[6] Guo H B, Yu J J, He X W, et al. Improved sparse reconstruction for fluorescence molecular tomography with L 1/2 regularization[J]. Biomedical Optics Express, 2015, 6(5): 1648-1664.

[7] Han D, Tian J, Zhu S, et al. A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization[J]. Optics Express, 2010, 18(8): 8630-8646.

[8] Figueiredo M A T, Nowak R D, Wright S J. Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems[J]. IEEE Journal of Selected Topics in Signal Processing, 2007, 1(4): 586-597.

[9] Beck A, Teboulle M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems[J]. SIAM Journal on Imaging Sciences, 2009, 2(1): 183-202.

[10] Nocedal J, Wright S J. Numerical optimization[M]. New York: Springer-Verlag, 1999: 474-476.

[11] Zhao L, Yang H, Cong W, et al. Lp regularization for early gate fluorescence molecular tomography[J]. Optics Letters, 2014, 39(14): 4156-4159.

[12] Chen W, Wang X, Wang B, et al. Lock-in-photon-counting-based highly-sensitive and large-dynamic imaging system for continuous-wave diffuse optical tomography[J]. Biomedical Optics Express, 2016, 7(2): 499-511.

[13] Qin D, Ma Z, Gao F, et al. Determination of optical properties in turbid medium based on time-resolved determination[C]. SPIE, 2007, 6534: 65340T.

王兵元, 陈玮婷, 马文娟, 祁瑾, 张丽敏, 赵会娟, 高峰. 基于非负约束L1-范数正则化的乳腺扩散光学层析成像重建方法[J]. 光学学报, 2016, 36(11): 1117002. Wang Bingyuan, Chen Weiting, Ma Wenjuan, Qi Jin, Zhang Limin, Zhao Huijuan, Gao Feng. Reconstruction Method of Breast Diffuse Optical Tomography Based on Non-Negative-Constraint L1-Norm Regularization[J]. Acta Optica Sinica, 2016, 36(11): 1117002.

基于非负约束L1-范数正则化的乳腺扩散光学层析成像重建方法

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