Full-waveform inversion (FWI) is an efficient technique for capturing the subsurface physical features by iteratively minimizing the misfit between simulated and observed seismograms. As such a problem is ill-posed, a significant ingredient for a satisfactory solution is to incorporate desirable priors. Most traditional regularized FWI approaches suffer from the non-adaptiveness and sensitivity of regularizers. Deep learning-assisted inversion methods can use pre-trained priors or parametric network priors as regularizers. We develop a novel FWI method based on a physics-constrained iterative algorithm with a learned regularization (FWIPLR). The introduced framework easily enables high-quality inversion by integrating two complementary terms: the physical constraints of the imaging system characterized by its forward model and a priori knowledge of the expected results characterized by a deep convolutional neural network (CNN) based regularizer. In particular, the advanced CNN denoiser, which corresponds to an implicit regularization term, is firstly trained with large-scale natural images and then fine-tuned with small-scale geological images. Such a transfer learning strategy seems appealing as it makes FWIPLR more generic to distinct geological models. To stabilize the optimization, we employ the spectral normalization instead of batch normalization to impose Lipschitz constraint on the networks. We validate the method effectiveness on Marmousi, Overthrust, and 2004 BP models. The comparable results illustrate the ability of FWIPLR for producing high-resolution subsurface structures compared with total variation regularized FWI, conventional denoiser and other CNN denoiser regularized FWI, in particular, when the initial model is inaccurate, data lose low-frequency information or model contains high-contrast media.

Full-waveform inversion (FWI) is a powerful technique for building high-quality subsurface geological structures. It is known to suffer from local minima problems when a good starting model is lost. To obtain a desirable solution, regularization constraints are needed to impose suitable priors, in particular for salt models. Recent studies have allowed cooperating the denoising operator as a specific prior with optimization algorithms to effectively solve various image reconstruction tasks. Inspired by the promising performance of regularization by denoising (RED), we propose a flexible unsupervised learning FWI framework, in which the regularizer is an extensive variant of RED powered by learned gradient for addressing salt models’ inversion. To further mitigate local minima issues, the Wasserstein distance induced by the optimal transport (OT) theory with a new preprocessing transformation is applied as a measure in data domain. Integrating the physical constraints featured by the wave equation and the model priors featured by the deep convolutional neural network (CNN), our method is able to produce measurement consistent and high-resolution results. We experimentally compare the proposed method with the traditional total variation regularized FWI and RED regularized FWI on the well-known geological models. The numerical results demonstrate the effectiveness of our method for handling the inversion task of high-contrast media in the presence of a free-surface case. Moreover, our framework is adaptive to restrict the solutions by leveraging the regularizer with learned gradient, whose training does not need any geological images, thus paving the way to develop FWI algorithms with state-of-the-art deep learning (DL) techniques in interdisciplinary research.

Random noise attenuation is an important step in seismic data processing. Unfortunately, most conventional denoising methods heavily rely on specific prior knowledge and fine-tuning of the parameters. Therefore, they often fail to suppress random noise. Recent works based on supervised learning techniques for seismic noise suppression show outstanding performance. However, this paradigm needs large-scale labeled training datasets that are not available for seismic field data. Inspired by the self-supervised learning, we propose a promising unsupervised learning scheme that aims at suppressing the random noise with only a noisy shot gather. The method is based on a specific$\mathcal {J}$-invariant function and an assumption that the noise is statistical independent while the useful signal exhibits some correlation. To further improve the denoising quality, we integrate the transfer learning strategy. We experimentally demonstrate that the proposed framework faithfully recovers the denoised data on both prestack and poststack synthetic and field data although the pretrained network is trained with the prestack synthetic dataset. The preliminary comparisons with traditional and learning-based approaches indicate the effectiveness and robustness as well.

Quantitative phase imaging (QPI) is an emerging label-free technique that produces images containing morphological and dynamical information without contrast agents. Unfortunately, the phase is wrapped in most imaging system. Phase unwrapping is the computational process that recovers a more informative image. It is particularly challenging with thick and complex samples such as organoids. Recent works that rely on supervised training show that deep learning is a powerful method to unwrap the phase; however, supervised approaches require large and representative datasets which are difficult to obtain for complex biological samples. Inspired by the concept of deep image priors, we propose a deep-learning-based method that does not need any training set. Our framework relies on an untrained convolutional neural network to accurately unwrap the phase while ensuring the consistency of the measurements. We experimentally demonstrate that the proposed method faithfully recovers the phase of complex samples on both real and simulated data. Our work paves the way to reliable phase imaging of thick and complex samples with QPI.