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Pre-trained vision foundation models (VFMs) provide strong semantic representations, yet their patch-level features are inherently coarse, limiting their effectiveness on tasks requiring fine-grained localization, dense prediction, and…
The well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial domain. The fast procedure for this generalization is referred to as nonequispaced fast Fourier transform (NFFT). Various…
We consider an $\ell_1$-regularized inverse problem where both the forward and regularization operators have a Kronecker product structure. By leveraging this structure, a joint decomposition can be obtained using generalized singular value…
Machine Learning (ML) methods and tools have gained great success in many data, signal, image and video processing tasks, such as classification, clustering, object detection, semantic segmentation, language processing, Human-Machine…
Our world is full of physics-driven data where effective mappings between data manifolds are desired. There is an increasing demand for understanding combined model-based and data-driven methods. We propose a nonlinear, learned singular…
Building on the well-known total-variation (TV), this paper develops a general regularization technique based on nonlinear isotropic diffusion (NID) for inverse problems with piecewise smooth solutions. The novelty of our approach is to be…
Total variation (TV) is a powerful regularization method that has been widely applied in different imaging applications, but is difficult to apply to diffuse optical tomography (DOT) image reconstruction (inverse problem) due to complex and…
A supervised learning approach is proposed for regularization of large inverse problems where the main operator is built from noisy data. This is germane to superresolution imaging via the sampling indicators of the inverse scattering…
In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the…
Full Waveform Inversion (FWI) is a powerful wave-based imaging technique, but its inherent ill-posedness and non-convexity lead to local minima and poor convergence. Regularization methods stabilize FWI by incorporating prior information…
Inverse problems are inherently ill-posed, suffering from non-uniqueness and instability. Classical regularization methods provide mathematically well-founded solutions, ensuring stability and convergence, but often at the cost of reduced…
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…
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…
Decomposing discrete signals such as images into components is vital in many applications, and this paper propose a framework to produce filtering banks to accomplish this task. The framework is an equation set which is ill-posed, and thus…
We consider the variational reconstruction framework for inverse problems and propose to learn a data-adaptive input-convex neural network (ICNN) as the regularization functional. The ICNN-based convex regularizer is trained adversarially…
We consider a filter stabilization technique with a deconvolution-based indicator function for the simulation of advection dominated advection-diffusion-reaction (ADR) problems with under-refined meshes. The proposed technique has been…
Wavefront-free behavior and the resulting quantification difficulties are intrinsic limitations of vibrothermography due to the diffusive nature of thermal fields. This work proposes a generalized virtual wave reconstruction framework to…
In this work, we introduce a function space setting for a wide class of structural/weighted total variation (TV) regularization methods motivated by their applications in inverse problems. In particular, we consider a regularizer that is…
In this work we deal with parametric inverse problems, which consist in recovering a finite number of parameters describing the structure of an unknown object, from indirect measurements. State-of-the-art methods for approximating a…
We shall investigate randomized algorithms for solving large-scale linear inverse problems with general regularizations. We first present some techniques to transform inverse problems of general form into the ones of standard form, then…