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Non-invasive surface wave methods have become a popular alternative to traditional invasive forms of site-characterization for inferring a site's subsurface shear wave velocity (Vs) structure. The advantage of surface wave methods over…
Deep learning is an increasingly popular approach for inverting surface wave dispersion curves to obtain Vs profiles. However, its generalizability is constrained by the depth and velocity scales of training data. We propose a unified deep…
Frequency-domain electromagnetic instruments allow the collection of data in different configurations, that is, varying the intercoil spacing, the frequency, and the height above the ground. Their handy size makes these tools very practical…
Traveltime tomography is a very effective tool to reconstruct acoustic, seismic or electromagnetic wave speed distribution. To infer the velocity image of the medium from the measurements of first arrivals is a typical example of ill-posed…
The importance of regularization has been well established in image reconstruction -- which is the computational inversion of imaging forward model -- with applications including deconvolution for microscopy, tomographic reconstruction,…
Regularization is a central tool for addressing ill-posedness in inverse problems and statistical estimation, with the choice of a suitable penalty often determining the reliability and interpretability of downstream solutions. While recent…
The inversion of surface wave dispersion curves poses significant challenges due to the non-uniqueness, nonlinear, & ill-posed nature of the problem. Local search methods get trapped in suboptimal minima, whereas global search methods are…
We present a method for supervised learning of sparsity-promoting regularizers for image denoising. Sparsity-promoting regularization is a key ingredient in solving modern image reconstruction problems; however, the operators underlying…
The removal of multiplicative Gamma noise is a critical research area in the application of synthetic aperture radar (SAR) imaging, where neural networks serve as a potent tool. However, real-world data often diverges from theoretical…
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…
We present a method for supervised learning of sparsity-promoting regularizers for denoising signals and images. Sparsity-promoting regularization is a key ingredient in solving modern signal reconstruction problems; however, the operators…
In many imaging applications where segmented features (e.g. blood vessels) are further used for other numerical simulations (e.g. finite element analysis), the obtained surfaces do not have fine resolutions suitable for the task. Increasing…
This paper introduces a novel approach to robust surface reconstruction from photometric stereo normal vector maps that is particularly well-suited for reconstructing surfaces from noisy gradients. Specifically, we propose an adaptive…
Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…
During the inversion of discrete linear systems noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during…
Variational regularization is a classical technique to solve statistical inference tasks and inverse problems, with modern data-driven approaches parameterizing regularizers via deep neural networks showcasing impressive empirical…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
Generative (diffusion) priors demonstrate remarkable performance in addressing inverse problems in imaging. Yet, for scientific and medical imaging, it is crucial that reconstruction techniques remain stable and reliable under imperfect…
It's well-known that inverse problems are ill-posed and to solve them meaningfully one has to employ regularization methods. Traditionally, popular regularization methods have been the penalized Variational approaches. In recent years, the…
How to extract more and useful information for single image super resolution is an imperative and difficult problem. Learning-based method is a representative method for such task. However, the results are not so stable as there may exist…