Varma Hari M, Banerjee B, Roy D, Nandakumaran A K, Vasu R M
Department of Instrumentation, Indian Institute of Science, Bangalore, 560012, India.
J Opt Soc Am A Opt Image Sci Vis. 2010 Feb 1;27(2):259-67. doi: 10.1364/JOSAA.27.000259.
We propose a self-regularized pseudo-time marching scheme to solve the ill-posed, nonlinear inverse problem associated with diffuse propagation of coherent light in a tissuelike object. In particular, in the context of diffuse correlation tomography (DCT), we consider the recovery of mechanical property distributions from partial and noisy boundary measurements of light intensity autocorrelation. We prove the existence of a minimizer for the Newton algorithm after establishing the existence of weak solutions for the forward equation of light amplitude autocorrelation and its Fréchet derivative and adjoint. The asymptotic stability of the solution of the ordinary differential equation obtained through the introduction of the pseudo-time is also analyzed. We show that the asymptotic solution obtained through the pseudo-time marching converges to that optimal solution provided the Hessian of the forward equation is positive definite in the neighborhood of optimal solution. The superior noise tolerance and regularization-insensitive nature of pseudo-dynamic strategy are proved through numerical simulations in the context of both DCT and diffuse optical tomography.
我们提出一种自正则化伪时间推进方案，以解决与相干光在类组织物体中的扩散传播相关的不适定非线性逆问题。特别是，在扩散相关层析成像（DCT）的背景下，我们考虑从光强自相关的部分有噪声边界测量中恢复力学性质分布。在建立光振幅自相关的正向方程及其弗雷歇导数和伴随的弱解的存在性之后，我们证明了牛顿算法极小值的存在性。还分析了通过引入伪时间得到的常微分方程解的渐近稳定性。我们表明，只要正向方程的海森矩阵在最优解附近是正定的，通过伪时间推进得到的渐近解就会收敛到最优解。通过在DCT和扩散光学层析成像背景下的数值模拟，证明了伪动态策略具有卓越的噪声容忍度和正则化不敏感特性。
