An L(p) (0 ≤ p ≤ 1)-norm regularized image reconstruction scheme for breast DOT with non-negative-constraint.
An L(p) (0 ≤ p ≤ 1)-norm regularized image reconstruction scheme for breast DOT with non-negative-constraint.
复制标题
具有非负约束的乳腺DOT Lp(0≤p≤1)≤范数正则化图像重建方案
DOI：
10.1186/s12938-017-0318-y
复制
发表时间：
2017-03-03
影响因子：
3.9
通讯作者：
Gao F
中科院分区：
文献类型：
--
作者：
Wang B;Wan W;Wang Y;Ma W;Zhang L;Li J;Zhou Z;Zhao H;Gao F
在漫射光学层析成像（DOT）中，图像重建通常是一个病态逆问题，对于乳房DOT来说，这一问题更为严重，因为在可实现的测量数量方面，需要重建的未知数大大增加。解决这种不适定性的一种常见方法是引入各种正则化方法。关于目标函数的构造和优化已经有了广泛的研究。然而，尽管这些算法极大地改善了重建图像，但它们很少设计一个本质上可微的目标函数，其全梯度易于获得，以加速优化过程。本文引入了一类新的非负先验信息，设计了l1 -范数、Lp (0 < p < 1)-范数和l0 -范数的可微目标函数。结合这种非负先验信息，可以很容易地得到这些可微目标函数的梯度，这有助于指导优化过程。通过数值实验和模拟实验进行了性能分析。在空间分辨率、定量、灰度分辨率和执行时间方面，该方法都优于不含非负先验信息的常规正则化方法。该方法利用引入的非负先验信息对重构图像进行了改进。此外，非负约束简化了梯度计算，加速了目标函数的最小化。
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. This paper introduces a new kind of non-negative prior information, designing differentiable objective functions for cases of L1-norm, Lp (0 < p < 1)-norm and L0-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. 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. 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.