Hongsun Fu

As a non-invasive imaging modality, Electrical Impedance Tomography (EIT) derives its value from the ability to estimate internal conductivity distributions based on measurements taken at the boundary. A central challenge in EIT image reconstruction stems from its ill-posed nature, necessitating the application of regularization. Conventionally, the selection of regularization parameters involves manual and often tedious tuning, a step that critically determines the fidelity of the reconstructed images. This paper introduces a novel, fully automated approach for regularization parameter estimation based on maximum marginal likelihood estimation, enabling unsupervised parameter determination directly from observational data without manual intervention or ground truth references. Our method establishes a statistically principled framework that optimally balances data fidelity and prior constraints, yielding high-quality reconstructed images with clear boundaries and minimal artifacts. Extensive numerical experiments across diverse two and three dimensional EIT scenarios demonstrate the method's robustness, adaptability, and superior performance compared to conventional approaches. The proposed technique not only eliminates the subjectivity inherent in manual parameter selection but also provides a rigorous probabilistic foundation for EIT reconstruction, offering a significant advancement in the field of medical and industrial imaging.

Finding a way to effectively suppress random noise in seismic images has great significance. Deep learning techniques have shown great potential in seismic image denoising. Attention has gradually become the most important mechanism in the deep learning field, which can be applied to address many different problems across various domains. We propose an encoder–decoder architecture that uses a channel‐attention mechanism to suppress random noise in seismic data. Our autoencoder structure consists of three parts: an encoder module, a decoder module, and an attention skip connection module, which is a type of unsupervised deep learning model that uses the patching technique. Both encoder and decoder modules use fully connected layers, which allow for comprehensive information integration and feature extraction. The mechanisms of attention are composed of two parts. One is the encoder part. The input is initially entered into one fully connected layer, batch normalization, and nonlinearity in the form of Mish. Then, the output is subjected to a dual‐branch attention block for further extracting deep features. Another part is the skip connection. A channel attention mechanism is introduced to achieve effective information fusion through the connection of the encoder and decoder modules. Comprehensive experiments show that the proposed network significantly outperforms the best‐performing baseline method, improving the signal‐to‐noise ratio by 1.34 dB on three‐dimensional synthetic data, as well as performing well in other synthetic and real seismic denoising tasks based on both quantitative and qualitative evaluations.

Full waveform inversion (FWI) is a powerful technique for reconstructing subsurface physical parameters. However, conventional FWI often suffers from cycle-skipping and local-minimum issues. With the rapid development of deep learning, data-driven methods have attracted increasing attention in FWI, where the inversion problem is reformulated as an end-to-end reconstruction task and neural networks are employed to directly estimate velocity models from seismic data. Most existing approaches rely on convolutional neural networks (CNNs) to extract local features from input data. However, compared with natural images, seismic data exhibit strong long-range dependencies that CNNs struggle to model effectively, since information associated with a single reflection interface is spatially distributed across the seismic data. Although CNNs perform well in computer vision, their local feature extraction mechanism limits reconstruction performance in FWI. To address this issue, we have proposed a novel FWI method based on the vision transformer (ViT). Unlike CNN-based approaches, the proposed method leverages the self-attention mechanism to model long-range dependencies in the input data. By stacking multiple transformer blocks, global physical information in seismic data is effectively encoded into the inversion process, resulting in improved reconstruction performance. Numerical results demonstrated that the proposed method outperforms CNN-based approaches in terms of reconstruction accuracy.

Effective denoising of seismic data is a critical step in the exploration workflows. The dictionary learning (DL) method has attracted great attention because the learned dictionary can provide an adaptive sparse representation for an unprocessed signal. Nevertheless, the dictionary learned from the noisy signal contains atoms representing both seismic signals and noise. This issue can be subsequently resolved through low-rank extraction. To overcome this, we propose a novel denoising strategy that synergistically combines DL with an adaptive rank-reduction method. Our approach has two major steps. Specifically, unlike traditional K-singular value decomposition (K-SVD) method, we employ an efficient Top bottom Two-dimensional Subspace Partition (TTSP) algorithm to obtain the sparse representation of seismic data, which combines a clustering method and the best rank-1 approximation of the mean (center) matrix. Then, we introduce the localized optimal damped rank-reduction method with adaptively selected ranks (LODRRA), which adopts an adaptive ranks selection strategy based on the energy intensity of singular values and singular-values distribution of the Hankel matrix in high frequency. The dictionary, learned directly from the data, enhances the robustness to noise of the LODRRA. Moreover, LODRRA effectively suppresses the noise components within the learned dictionary. Experiments on synthetic and field data reveal that our DL-LODRRA combination outperforms methods that solely employ a learned dictionary and rank reduction.

Adaptive optics (AO)-corrected retina flood illumination imaging technology is widely used for investigating both structural and functional aspects of the retina. Given the inherent low-contrast nature of original retinal images, it is necessary to perform image restoration. Total variation (TV) regularization is an efficient regularization technique for AO retinal image restoration. However, a main shortcoming of TV regularization is its potential to experience the staircase effects, particularly in smooth regions of the image. To overcome the drawback, a new image restoration model is proposed for AO retinal images. This model utilizes the overlapping group sparse total variation (OGSTV) as a regularization term. Due to the structural characteristics of AO retinal images, only partial information regarding the PSF is known. Consequently, we have to solve a more complicated myopic deconvolution problem. To address this computational challenge, we propose an ADMM-MM-LAP method to solve the proposed model. First, we apply the alternating direction method of multiplier (ADMM) as the outer-layer optimization method. Then, appropriate algorithms are employed to solve the ADMM subproblems based on their inherent structures. Specifically, the majorization–minimization (MM) method is applied to handle the asymmetry OGSTV regularization component, while a modified version of the linearize and project (LAP) method is adopted to address the tightly coupled subproblem. Theoretically, we establish the complexity analysis of the proposed method. Numerical results demonstrate that the proposed model outperforms the existing state-of-the-art TV model across several metrics.

In this work, we investigate a stochastic gradient descent (SGD) method for solving inverse problems that can be written as systems of linear or nonlinear ill-posed equations in Banach spaces. The method uses only a randomly selected equation at each iteration and employs the convex function as the penalty term, and thus it is scalable to the problem size and has the ability to detect special features of solutions such as nonnegativity and piecewise constancy. To suppress the oscillation in iterates and reduce the semi-convergence of such methods, by incorporating the spirit of discrepancy principle, an adaptive strategy for choosing the step size is suggested. Under certain conditions, we establish the regularization results of the method under an a priori stopping rule. Further, we study an a posteriori stopping rule for SGD-θ method and show the finite iterations termination property. Several numerical simulations on computed tomography and schlieren imaging are provided to demonstrate the effectiveness of the method.

In this work, we investigate a stochastic gradient descent method for solving inverse problems that can be written as systems of linear or nonlinear ill-posed equations in Banach spaces. The method uses only a randomly selected equation at each iteration and employs the convex function as the penalty term, and thus it is scalable to the problem size and has the ability to detect special features of solutions such as nonnegativity and piecewise constancy. To suppress the oscillation in iterates and reduce the semi-convergence of such methods, by incorporating the spirit of discrepancy principle, an adaptive strategy for choosing the step size is suggested. Under certain conditions, we establish the regularization results of the method under an {\it a priori} stopping rule. Several numerical simulations on computed tomography and schlieren imaging are provided to demonstrate the effectiveness of the method. Finally, we study an {\it a posteriori} stopping rule for SGD-$θ$ method and show the finite iterations termination property.

Nonlinear inverse problems arise in various fields ranging from scientific computation to engineering technology. Inverse problems are intrinsically ill-posed, and effective regularization techniques are necessary. The core of a suitable regularization method is to introduce the prior information of the model via an explicit or implicit regularization function. Plug-and-play regularization is a flexible framework that integrates the most effective denoising priors into an iterative algorithm, and it has recently shown great potential in the solution of linear ill-posed problems. Unlike traditional regularization methods, plug-and-play regularization does not require an explicit regularization function to represent the prior information of the model. In this work, by using total variation, block-matching and three-dimensional filtering, and fast and flexible denoising convolutional neural network denoisers, we propose a novel iterative regularization algorithm based on the alternating direction method of multipliers method. The combination of total variation and block-matching three-dimensional filtering regularizers can take advantage of the sparsity and nonlocal similarity in the solution of inverse problems. When combined with traditional and novel regularizers, deep neural networks have been shown to be an effective regularization approach, which can achieve state-of-the-art performance. Finally, we apply the proposed algorithm to the full waveform inversion problem to show the effectiveness of our method. Numerical results demonstrate that the proposed algorithm outperforms existing inversion methods in terms of quantitative measures and visual perceptual quality.