Department of Physics, Indian Institute of Science, Bangalore 560012, India.
Med Phys. 2011 Jan;38(1):539-47. doi: 10.1118/1.3531572.
Fast reconstruction of interior optical parameter distribution using a new approach called Broyden-based model iterative image reconstruction (BMOBIIR) and adjoint Broyden-based MOBIIR (ABMOBIIR) of a tissue and a tissue mimicking phantom from boundary measurement data in diffuse optical tomography (DOT).
DOT is a nonlinear and ill-posed inverse problem. Newton-based MOBIIR algorithm, which is generally used, requires repeated evaluation of the Jacobian which consumes bulk of the computation time for reconstruction. In this study, we propose a Broyden approach-based accelerated scheme for Jacobian computation and it is combined with conjugate gradient scheme (CGS) for fast reconstruction. The method makes explicit use of secant and adjoint information that can be obtained from forward solution of the diffusion equation. This approach reduces the computational time many fold by approximating the system Jacobian successively through low-rank updates.
Simulation studies have been carried out with single as well as multiple inhomogeneities. Algorithms are validated using an experimental study carried out on a pork tissue with fat acting as an inhomogeneity. The results obtained through the proposed BMOBIIR and ABMOBIIR approaches are compared with those of Newton-based MOBIIR algorithm. The mean squared error and execution time are used as metrics for comparing the results of reconstruction.
We have shown through experimental and simulation studies that Broyden-based MOBIIR and adjoint Broyden-based methods are capable of reconstructing single as well as multiple inhomogeneities in tissue and a tissue-mimicking phantom. Broyden MOBIIR and adjoint Broyden MOBIIR methods are computationally simple and they result in much faster implementations because they avoid direct evaluation of Jacobian. The image reconstructions have been carried out with different initial values using Newton, Broyden, and adjoint Broyden approaches. These algorithms work well when the initial guess is close to the true solution. However, when initial guess is far away from true solution, Newton-based MOBIIR gives better reconstructed images. The proposed methods are found to be stable with noisy measurement data.
利用一种新方法——基于 Broyden 的模型迭代图像重建（BMOBIIR）和伴随 Broyden 的 MOBIIR（ABMOBIIR），从漫射光学断层扫描（DOT）的边界测量数据中重建组织和组织模拟体的内部光学参数分布。
DOT 是一个非线性和不适定的反问题。基于牛顿的 MOBIIR 算法，通常用于需要重复评估雅可比矩阵，这会消耗大量的计算时间进行重建。在这项研究中，我们提出了一种基于 Broyden 的加速方案来计算雅可比矩阵，并将其与共轭梯度法（CGS）结合用于快速重建。该方法明确利用了从扩散方程正向解中可以获得的割线和伴随信息。通过低秩更新来逐步逼近系统雅可比矩阵，这种方法将计算时间减少了很多倍。
进行了单和多个不均匀性的模拟研究。使用在含有脂肪作为不均匀性的猪肉组织上进行的实验研究验证了算法。通过提出的 BMOBIIR 和 ABMOBIIR 方法获得的结果与基于牛顿的 MOBIIR 算法的结果进行了比较。重建结果的比较使用均方误差和执行时间作为度量。
通过实验和模拟研究表明，基于 Broyden 的 MOBIIR 和伴随 Broyden 的方法能够重建组织和组织模拟体中的单和多个不均匀性。Broyden MOBIIR 和伴随 Broyden MOBIIR 方法计算简单，因为它们避免了雅可比矩阵的直接评估，所以实现速度更快。使用牛顿、Broyden 和伴随 Broyden 方法进行了不同初始值的图像重建。当初始猜测接近真实解时，这些算法效果很好。然而，当初始猜测远离真实解时，基于牛顿的 MOBIIR 给出了更好的重建图像。所提出的方法在存在噪声测量数据时是稳定的。
