基于原始对偶内点法的EST图像重建

静电层析成像（EST）被动感应电荷的机理决定了其独立测量值数等于电极数目，远小于电容层析成像（ECT）等相对成熟的电学成像（ET）技术的测量值数，导致逆问题的欠定性更加严重。为此，对基于压缩感知理论的EST图像重建算法进行了研究。利用奇异值分解（SVD）处理灵敏度矩阵使其满足有限等距性质（RIP），采用l₁范数正则化模型和原始对偶内点法（PDIPA）实现图像重建，并在迭代过程中针对荷电磨粒稀疏分布的特点，对图像向量中非零元素个数施加约束。仿真实验表明:该算法相对于基于"Circle of Appolonius"的反投影（BP）算法和Landweber迭代算法，明显改进了成像质量，对不同位置的单个电荷可准确重建；2个电荷距离不小于1 mm时可正确分辨电荷数目与位置；对10组随机分布的3个电荷模型进行测试，荷电磨粒数目监测的准确率约为80%。 

EST image reconstruction based on primal dual interior point algorithm

The passive induction mechanism of electrostatic tomography (EST) determines that the number of independent measurements is equal to the number of electrodes, which is much less than the number of independent measurements of relatively mature electrical tomography (ET) technologies such as elelctrical capacitance tomography (ECT), resulting in a more severe underdetermined inverse problem. In order to address this problem, compressed sensing-based EST image reconstruction algorithm is studied. The sensitivity matrix is processed by singular value decomposition (SVD) to satisfy the restricted isometry property (RIP), and thereafter the l₁ norm regularization model and primal dual interior point algorithm (PDIPA) are utilized to reconstruct the image. Besides, constraint on the number of non-zero elements in the image vector is imposed in the iteration process according to the sparsity of debris distributed in oil. Simulation experiment demonstrates that compared to the "Circle of Appolonius" based back-projection (BP) algorithm and Landweber iteration algorithm, the aforementioned algorithm has obviously improved the imaging quality:accurate reconstruction can be obtained for single charge distributed at different positions; for two point charges whose distance is more than or equal to 1 mm, both the number and positions of the point charges can be correctly observed; for 10 groups of three randomly distributed point charge models, the accuracy rate of charged debris number monitoring is about 80%.