A neural network learns a convex regularizer for better image reconstruction.
problem Improving image reconstruction in inverse problems.
method Adversarial training of a data-adaptive ICNN as a convex regularizer.
result The convex regularizer leads to better convergence and error reduction in image reconstruction.
The aim of this paper is to show how the homotopy type of compact metric spaces can be reconstructed by the inverse limit of an inverse sequence of finite approximations of the corresponding space. This recovering allows us to define inverse persistence as a new kind of persistence process.
Bayesian framework learns prior from data to quantify uncertainty in MRI reconstruction.
problem Quantifying uncertainty in deep learning solutions for inverse problems.
method Adopting denoising score matching to learn prior from data, using it in an annealed Hamiltonian Monte-Carlo scheme.
result The approach yields high-quality reconstructions and assesses uncertainty on specific features.
Finite approximations help reconstruct countable metric and ultrametric spaces.
problem Reconstructing countable metric and ultrametric spaces.
method Topological reconstruction using inverse limits of finite T0 spaces. result Countable metric and ultrametric spaces can be reconstructed as finite approximations.
Survey on inverse exponential Radon transform methods.
problem Analytical methods for inverse exponential Radon transform.
method Derivation of classical inversion formula, finite Hilbert transform, exact reconstruction from partial measurements, diverging-beam data.
result Exact reconstruction from 180 degree data using finite Hilbert transform.
Geometric framework for inverse problems using foliations and dual connections.
problem Reconstruction problems in inverse problems.
method Vaisman foliations and Atiyah--Molino sequences to induce transverse foliations and dual connections.
result Unique, path-independent reconstruction with vanishing torsion and curvature duality.
Paper improves deep learning models for cardiac potential reconstruction.
problem Improving generalization of sequence models for cardiac potential reconstruction.
method Constrained stochasticity and global aggregation of temporal information in latent space.
result Improved generalization of inverse reconstruction networks.
New method uses generative models to improve phase retrieval stability.
problem Improving stability of solutions in phase retrieval problems.
method Unified reconstruction approach using generative models to mitigate overfitting.
result Mitigates overfitting to generative model for varying noise levels.
Currents in higher dimensions can be reconstructed from projections.
problem Reconstructing currents from their projections in higher dimensions.
method Inversion formula for the exterior k-plane transform. result Currents in Rn can be reconstructed from their projections onto Rk. Improves deep network generalization for image sequence reconstruction.
problem Improving generalization of deep networks for inverse image reconstruction.
method Proposes a network optimized by a variational approximation of the information bottleneck principle with stochastic latent space.
result Demonstrates improved generalization ability of inverse reconstruction networks through stochasticity and information bottleneck.
This paper explores deep learning for improving X-ray CT image reconstruction from undersampled data.
problem Improving image reconstruction from undersampled X-ray CT data.
method Analysis of classical and deep learning methods for solving inverse problems.
result Deep learning methods show promise in improving image quality from undersampled data.
This work uses GANs to improve CT image reconstruction from limited angles.
problem Under-determined linear inverse problem in limited angle CT reconstruction.
method Robust GAN prior for image manifold projection.
result Significant improvement in reconstruction quality.
Proposes a constant memory iterative inverse model using invertible networks.
problem Memory limitations in iterative learning approaches for inverse problems.
method Invertible networks to avoid storing intermediate activations, constant memory model.
result Trains 400-layer models on 3D MRI volumes, achieving state-of-the-art image reconstruction.
Convolutional neural network improves MRE image reconstruction.
problem Reconstructing MRE images from displacement data is computationally intensive and costly.
method Proposes a CNN architecture to directly map MRE displacement data into elastograms, introducing a secondary loss for training.
result CNN-generated images compare favorably with nonlinear inversion methods.
This work analyzes the generalization properties of learned reconstruction methods for inverse problems.
problem Understanding the reliability and stability of learned reconstruction methods for inverse problems.
method Develops a general framework to interpret learned reconstruction methods in statistical learning context and performs their sample error analysis.
result Estimates the dependence of learned operators on training data, providing insights into their generalization properties.
Sparse elasticity reconstruction from local displacements reduces error.
problem Reconstructing elasticity from limited data.
method Sparse elasticity reconstruction theory, local clustering, alternating optimization.
result Higher spatial resolution elasticity distribution estimation.
Bayesian approach improves rain field reconstruction using CMLs and DMs.
problem Challenges in accurately reconstructing ground-level rainfall from CML path-integrated measurements.
method Bayesian inverse problem with Diffusion Models as priors.
result Improved performance in rainfall estimation compared to existing methods.
Regularizes 3D inverse scattering with tangent-point energy for better solutions.
problem Ill-conditioned inverse obstacle scattering problems in 3D.
method Tikhonov regularization using tangent-point energy to penalize surface roughness and ensure well-posedness.
result Regularized solutions converge to true solution as noise level decreases.
A new method for accurately reconstructing signals without knowing the kernel or signal regularity.
problem Recovering signals from noisy measurements without prior knowledge of the convolution kernel or signal regularity.
method Parametrizing the convolution kernel and prior length-scales, jointly estimated in the inversion procedure.
result Accurate reconstructions of signals with varying regularity and unknown kernel size.
A new method learns high-frequency components for better image reconstruction.
problem Efficiently reconstructing feature details in under-sampled imaging.
method Proposes HF-DAEP, a denoising autoencoder using multi-profile high-frequency components.
result Demonstrates improved reconstruction of feature details in MRI and CT.
Reconstructing Finsler manifolds from sphere data.
problem Recovering a Finsler manifold from sphere data.
method Solving the geometrical inverse problem locally along geodesics.
result Local reconstruction of Finsler manifolds.
Faster reconstruction of compressed signals using conditional GAN and NPGD.
problem Recovering compressed signals from measurements.
method Network-based projected gradient descent (NPGD) combined with measurement-conditional generative adversarial networks (GANs/BEGANs).
result Significant speed-up in reconstruction (up to 140-175 times faster).
Proposes a new method for efficient model reconstruction with uncertain parameters.
problem Reconstructing models with latent variables or parameters of unknown distribution.
method Local squared Wasserstein-2 (W_2) method.
result Efficiently reconstructs output distributions from observation data.
New framework assesses AI hallucinations in inverse problems.
problem Artificial intelligence can produce incorrect details in imaging problems.
method Theoretical framework and algorithms to estimate and assess hallucinations.
result Developed necessary and sufficient conditions for hallucinations and computable bounds.
The inverse Ising problem seeks to reconstruct the parameters of an Ising Hamiltonian on the basis of spin configurations sampled from the Boltzmann measure. Over the last decade, many applications of the inverse Ising problem have arisen, driven by the advent of large-scale data across different scientific disciplines…
This paper learns variational models and solvers for inverse problems from incomplete data.
problem Solving inverse problems with partially observed data.
method Joint learning of variational cost and gradient-based solver as neural networks.
result Joint learning leads to improved reconstruction performance.
Neural Optimal Design of Experiments improves inverse problem solving efficiency.
problem Optimal experimental design in inverse problems.
method Jointly trains a reconstruction model and design variables in a single loop.
result Significantly reduces computational complexity and improves reconstruction accuracy.
New attack recovers user-level information from large batch images.
problem Recovering private information from user-level gradients in distributed learning.
method Proposes a gradient inversion attack using a denoising diffusion model as a prior.
result Demonstrates recovery of realistic facial images and private attributes.
Study shows stability of travel time data reconstruction from closed subsets.
problem Reconstruction of length spaces from travel time data on a closed subset.
method Lipschitz stability proof for certain types of length spaces.
result Reconstruction of length spaces is Lipschitz stable from travel time data on a closed subset.
Inverse Problems in medical imaging and computer vision are traditionally solved using purely model-based methods. Among those variational regularization models are one of the most popular approaches. We propose a new framework for applying data-driven approaches to inverse problems, using a neural network as a regular…
Deep learning solves imaging inverse problems without ground truth.
problem Solving imaging problems without perfect data.
method Taxonomy of deep learning approaches for imaging inverse problems.
result Trade-offs and failure modes identified for different methods.
New spatiotemporal Besov process improves CT image reconstruction and other inverse problems.
problem Handling abrupt changes and sharp contrasts in spatiotemporal data.
method Generalized Besov process (STBP) with Q-exponential process for temporal correlation.
result STBP outperforms traditional methods in dynamic reconstruction and inverse problems.
New method reconstructs hidden structures from noisy data.
problem Resurrecting hidden structures from incomplete or distorted data.
method Integrates Atiyah--Molino framework and Hantjies tensor.
result Exceptional robustness in noisy conditions with error-bounded reconstructions.
A fast method approximates likelihood scores for noisy linear inverse problems.
problem Solving noisy linear inverse problems efficiently.
method Proposes a simple closed-form approximation to the likelihood score for diffusion and flow-based models.
result Significantly faster than baseline methods while maintaining competitive or better reconstruction performances.
Unified geometric approach to image reconstruction from incomplete data.
problem Reconstruction of hidden structures from incomplete data.
method Geometric decomposition of configuration spaces into invariant foliations and moment maps, combining Vaisman and Neifeld's insights.
result Noise-resistant framework for robust computational reconstruction in imaging and structural analysis.
Deep learning methods improve Bayesian inversion for efficient 3D imaging.
problem Efficiently solving large-scale inverse problems in medical imaging.
method Two novel deep learning approaches: WGAN with mini-discriminator and neural network loss function.
result Both methods compute posterior mean and standard deviation efficiently, demonstrating promising performance in 3D imaging.
This work tackles uncertainty quantification in tomography reconstruction.
problem Ill-posed nature of tomographic reconstruction leading to no unique solution.
method Gaussian process modeling to incorporate prior knowledge and experimental noises.
result Efficient uncertainty quantification in tomographic reconstruction.
A new method uses DMs as priors for imaging problems, offering more accurate reconstructions.
problem Accurate probabilistic imaging for complex inverse problems.
method Markov chain Monte Carlo algorithm using DMs as plug-and-play priors for solving Bayesian inverse problems.
result Offers more accurate reconstructions and posterior estimation compared to existing methods.
Exact inversion of deep ReLU models is possible for single layers and with high probability for deep models.
problem Inverting deep generative models with ReLU activations.
method Theoretical analysis and algorithms for exact inversion of single and multiple layers of deep generative models.
result Exact recovery of latent codes is possible for single layers and with high probability for deep models, under certain conditions.
Study tackles inverse problems on low-dimensional manifolds, proving stability and proposing a reconstruction algorithm.
problem Inverse problems in infinite-dimensional spaces with nonlinear and ill-posed nature.
method Assumption of low-dimensional manifold, proving stability, proposing Landweber-type algorithm.
result Global convergence of the proposed algorithm, Lipschitz stability for specific inverse problems.
A general method for analytic inversion in integral geometry is proposed. All classical and some new reconstruction formulas of Radon-John type are obtained by this method. No harmonic analysis and PDE is used.
Shape manifold and elastic energy regularization help reconstruct complex obstacles from scattering data.
problem Reconstructing non-star-shaped obstacles from scattered waves.
method Shape manifold, Tikhonov regularization, Möbius energy penalization.
result The approach yields stable and accurate reconstructions of complex obstacles.
New method improves DMs for solving inverse problems by maximizing conditional mutual information.
problem Efficiently solving noisy linear inverse problems without additional task-specific training.
method Maximizing conditional mutual information between reconstructed signal and measurement.
result Significantly improves the quality of generated images in inverse problems.
Improved computed tomography reconstruction with deep learning and deep image prior.
problem Low data efficiency in computed tomography reconstruction.
method Combining learned primal-dual methods with deep image prior for improved quality and generalization.
result Proposed methods outperform state-of-the-art in low data regime.
Under a convexity assumption on the boundary we solve a local inverse problem, namely we show that the geodesic X-ray transform can be inverted locally in a stable manner; one even has a reconstruction formula. We also show that under an assumption on the existence of a global foliation by strictly convex hypersurfaces…
A new algorithm speeds up EEG source localization using ℓ1 regularization.
problem Challenging inverse problem in mapping EEG readings to brain activity.
method Formulated as a graphical generalized elastic net inverse problem, solved with a variable projected algorithm (VPAL).
result VPAL provides faster and more accurate EEG source localization compared to existing methods.
Paper shows stability of metric reconstruction for orbifolds from spectral data.
problem Determining the metric structure of collapsing orbifolds from spectral data.
method Improved quantitative unique continuation for wave operator on Riemannian manifolds.
result Quantitative stability of inverse problem for Riemannian orbifolds.
CNNs reconstruct medium properties from wave probing responses.
problem Determining medium properties from wave responses.
method Deep convolutional neural networks (CNNs) for nonlinear wave equations.
result Quantitative dependence of network depth and units on medium complexity.