Department of Mechanical Engineering, University of British Columbia, Vancouver, BC, Canada.
Phys Med Biol. 2012 Oct 7;57(19):5909-27. doi: 10.1088/0031-9155/57/19/5909. Epub 2012 Sep 7.
We consider the inverse problem of continuum mechanics with the tissue deformation described by a mixed displacement-pressure finite element formulation. The mixed formulation is used to model nearly incompressible materials by simultaneously solving for both elasticity and pressure distributions. To improve numerical conditioning, a common solution to this problem is to use regularization to constrain the solutions of the inverse problem. We present a sparsity regularization technique that uses the discrete cosine transform to transform the elasticity and pressure fields to a sparse domain in which a smaller number of unknowns is required to represent the original field. We evaluate the approach by solving the dynamic elastography problem for synthetic data using such a mixed finite element technique, assuming time harmonic motion, and linear, isotropic and elastic behavior for the tissue. We compare our simulation results to those obtained using the more common Tikhonov regularization. We show that the sparsity regularization is less dependent on boundary conditions, less influenced by noise, requires no parameter tuning and is computationally faster. The algorithm has been tested on magnetic resonance elastography data captured from a CIRS elastography phantom with similar results as the simulation.
我们考虑连续介质力学的反问题，其中组织变形由混合位移-压力有限元公式描述。混合公式用于通过同时求解弹性和压力分布来模拟几乎不可压缩的材料。为了改善数值条件，解决这个问题的常用方法是使用正则化来约束反问题的解。我们提出了一种稀疏正则化技术，该技术使用离散余弦变换将弹性和压力场转换为稀疏域，其中需要较少的未知数来表示原始场。我们通过使用这种混合有限元技术对合成数据求解动态弹性成像问题来评估该方法，假设组织的运动是时间谐的，线性、各向同性和弹性的。我们将我们的模拟结果与更常见的 Tikhonov 正则化的结果进行比较。我们表明，稀疏正则化对边界条件的依赖性较小，受噪声的影响较小，不需要参数调整，并且计算速度更快。该算法已经在从 CIRS 弹性体模体捕获的磁共振弹性成像数据上进行了测试，结果与模拟结果相似。
