IEEE Trans Med Imaging. 2015 Feb;34(2):357-65. doi: 10.1109/TMI.2014.2352113. Epub 2014 Sep 18.
We propose a new image recovery method to improve the resolution in microwave imaging applications. Scattered field data obtained from a simplified breast model with closely located targets is used to formulate an electromagnetic inverse scattering problem, which is then solved using the Distorted Born Iterative Method (DBIM). At each iteration of the DBIM method, an underdetermined set of linear equations is solved using our proposed sparse recovery algorithm, IMATCS. Our results demonstrate the ability of the proposed method to recover small targets in cases where traditional DBIM approaches fail. Furthermore, in order to regularize the sparse recovery algorithm, we propose a novel L(2) -based approach and prove its convergence. The simulation results indicate that the L(2)-regularized method improves the robustness of the algorithm against the ill-posed conditions of the EM inverse scattering problem. Finally, we demonstrate that the regularized IMATCS-DBIM approach leads to fast, accurate and stable reconstructions of highly dense breast compositions.
我们提出了一种新的图像恢复方法，以提高微波成像应用中的分辨率。使用简化的乳房模型中紧密相邻的目标获得的散射场数据来制定电磁逆散射问题，然后使用扭曲 Born 迭代方法 (DBIM) 来解决。在 DBIM 方法的每次迭代中，使用我们提出的稀疏恢复算法 IMATCS 来求解一个欠定的线性方程组。我们的结果表明，该方法能够在传统 DBIM 方法失败的情况下恢复小目标。此外，为了正则化稀疏恢复算法，我们提出了一种新颖的基于 L(2)的方法，并证明了其收敛性。模拟结果表明，L(2)正则化方法提高了算法对电磁逆散射问题病态条件的鲁棒性。最后，我们证明了正则化的 IMATCS-DBIM 方法可以快速、准确和稳定地重建高密度乳房成分。
