Deep learning techniques have shown significant potential in many applications through recent years. The achieved results often outperform traditional techniques. However, the quality of a neural network highly depends on the used training data. Noisy, insufficient, or biased training data leads to suboptimal results. We present a hybrid method that combines deep learning with iterated graph Laplacian and show its application in acoustic impedance inversion which is a routine procedure in seismic explorations. A neural network is used to obtain a first approximation of the underlying acoustic impedance and construct a graph Laplacian matrix from this approximation. Afterwards, we use a Tikhonov-like variational method to solve the impedance inversion problem where the regularizer is based on the constructed graph Laplacian. The obtained solution can be shown to be more accurate and stable with respect to noise than the initial guess obtained by the neural network. This process can be iterated several times, each time constructing a new graph Laplacian matrix from the most recent reconstruction. The method converges after only a few iterations returning a much more accurate reconstruction. We demonstrate the potential of our method on two different datasets and under various levels of noise. We use two different neural networks that have been introduced in previous works. The experiments show that our approach improves the reconstruction quality in the presence of noise.

翻译：深度学习技术近年来在众多应用中展现出显著潜力，所取得的成果往往优于传统方法。然而，神经网络的质量高度依赖于所使用的训练数据。包含噪声、数据不足或存在偏差的训练数据会导致次优结果。我们提出了一种将深度学习与迭代图拉普拉斯相结合的混合方法，并将其应用于声阻抗反演——地震勘探中的常规流程。首先利用神经网络获得地下声阻抗的初始逼近，并基于该逼近构建图拉普拉斯矩阵；随后采用基于Tikhonov正则化的变分方法求解阻抗反演问题，其中正则化项以所构建的图拉普拉斯矩阵为基础。结果显示，相比于神经网络给出的初始估计值，该求解过程对噪声具有更高的精度和稳定性。上述过程可多次迭代，每次迭代均基于最新重建结果构建新的图拉普拉斯矩阵。该方法仅需数次迭代即可收敛，并返回显著更精确的重建结果。我们在两个不同数据集及多种噪声水平下验证了该方法的潜力，并采用了两类前期研究中提出的神经网络。实验表明，我们的方法在存在噪声的情况下能有效提升重建质量。