This work connects LLE, factor analysis, and probabilistic PCA through a stochastic perspective.
problem Exploring the theoretical connection between LLE, factor analysis, and probabilistic PCA.
method Solving the stochastic linear reconstruction of LLE using expectation maximization.
result LLE, factor analysis, and probabilistic PCA are shown to be connected through a stochastic perspective.
Generative LLE modifies LLE to generate stochastic embeddings.
problem Nonlinear dimensionality reduction and manifold learning.
method Generative LLE modifies LLE by using stochastic linear reconstruction.
result Generative LLE can generate various LLE embeddings stochastically.
Linear reconstruction works for MRI compression without prior signal knowledge.
problem Compressive MRI reconstruction without signal structure knowledge.
method Learn sub-sampling pattern from training data, use linear reconstruction.
result Theoretical and experimental validation of linear reconstruction effectiveness.
A faster X-ray CT image reconstruction method using relaxed linearized algorithms.
problem Reduced X-ray dose while maintaining image quality in CT scans.
method Relaxed linearized augmented Lagrangian (AL) method with over-relaxation.
result The proposed method is about twice as fast as existing unrelaxed fast algorithms.
New method improves network reconstruction accuracy and speed.
problem Inefficient lasso for weighted networks in noisy data.
method Variational Bayesian weighted linear regression.
result New method outperforms lasso in accuracy and speed.
New method solves large-scale linear programming problems for sparse signal reconstruction.
problem Efficiently solving large-scale linear programming problems for sparse signal reconstruction.
method Combining constraint and column generation techniques with simplex method initialization.
result Highly efficient solutions for many settings.
This work interprets SFA through variational inference, relaxing linearity constraints.
problem Recover non-linear SFA from variational inference.
method Probabilistic interpretation of SFA through variational inference, relaxing linearity constraints.
result Reinterprets SFA as a variational framework, allowing slowness as a regularizer to reconstruction loss.
This paper is concerned with the question of reconstructing a vector in a finite-dimensional real Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We analyze various Lipschitz bounds of the nonlinear analysis map and we establish theoretical performance bo…
Single linear solve combines surface reconstruction and uncertainty quantification.
problem Reconstructing surfaces from partial point clouds with uncertainty.
method Geometric Gaussian processes for stochastic surface reconstruction.
result Single linear solve for surface reconstruction with probabilistic capabilities.
Reconstructing signature features from randomized vector fields in differential equations.
problem Reconstructing signature features from controlled differential equations with random vector fields.
method Using controlled ordinary differential equations driven by continuous bounded variation curves, the study explores the extent to which signature features can be reconstructed from the non-linear flow of these equations.
result The number of signature features that can be reconstructed from the non-linear flow of controlled ordinary differential equations with random vector fields is exponential in the hidden dimension, under certain conditions.
Noiseless linear estimation results are found to be universal across various structured matrices.
problem Reconstructing a vector from linear projections with noiseless data.
method Development of message passing methods to analyze the l1 transition and optimal Bayesian reconstruction.
result The l1 transition and optimal Bayesian reconstruction are universal across various structured matrices.
New algorithm for signal reconstruction from multi-layered measurements.
problem Reconstructing signals from multi-layered non-linear measurements.
method Multi-Layer Approximate Message Passing (ML-AMP) algorithm and state evolution equations.
result Asymptotic free energy and minimal achievable error derived.
Algorithm reconstructs interaction topology in linear dynamical systems.
problem Learning influence pathways in dynamically related processes.
method Physics-informed multivariate Wiener filtering.
result Topology of interactions can be exactly recovered for certain classes.
New study analyzes security of neural network data reconstruction attacks.
problem Data reconstruction attacks pose a threat to private training data.
method Analyzes security boundary of data reconstruction attacks via neuron exclusivity state.
result Characterizes insecure/secure boundary of data reconstruction attacks.
Proves formula for reconstruction performance in generalized linear models.
problem Analyzing reconstruction performance in generalized linear models with arbitrary bounded spectrum.
method Message passing algorithms and dynamical system stability analysis.
result Analytical formula confirms replica method conjecture for convex models.
New algorithm learns stable LDSs with lower error and better control performance.
problem Learning stable LDSs from data with minimal reconstruction error and stability constraints.
method Proposes an optimization method using a recent characterization of stable matrices, iteratively improving reconstruction error and ensuring stability.
result Achieves orders-of-magnitude improvement in reconstruction error compared to existing methods.
The augmented Lagrangian (AL) method that solves convex optimization problems with linear constraints has drawn more attention recently in imaging applications due to its decomposable structure for composite cost functions and empirical fast convergence rate under weak conditions. However, for problems such as X-ray co…
A new BO method tackles high-dimensional optimization without reconstruction.
problem Optimizing high-dimensional black-box functions is challenging, especially when low-dimensional structures are assumed.
method Tackles the problem in the original high-dimensional space using learned low-dimensional structure.
result Our method explores the high-dimensional space more effectively than existing approaches.
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.
Study the tradeoff between signal distortion and human perception over finite channels.
problem Characterize the distortion-perception tradeoff for finite channels with arbitrary metrics.
method Solve linear programming problems to compute the distortion-perception function and optimal reconstructions.
result DP function is piecewise linear in the perception index.
Study examines stability of image-reconstruction algorithms using variational regularization.
problem Stability and robustness of image-reconstruction algorithms in medical imaging.
method Review and novel stability results for ℓp-regularized linear inverse problems, focusing on p∈(1,∞). result Guarantees Lipschitz continuity for small p and Hölder continuity for larger p in Lp(Ω) function spaces. Convolutional neural networks make astronomical image reconstruction faster and more efficient.
problem Efficiently reconstructing astronomical images from noisy or incomplete data.
method Use of convolutional neural networks for image reconstruction.
result Neural networks enable a linear complexity prediction step, making reconstruction computationally efficient.
New neural networks flatten and reconstruct manifolds from samples.
problem Learning from high-dimensional data embedded in submanifolds.
method Flattening Networks (FlatNet) that linearize and reconstruct embedded submanifolds.
result FlatNet achieves balance of interpretability, feasibility, and generalization.
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.
Improved neural network reconstruction from sparse measurements with theoretical guarantees.
problem Improving neural network performance in sparse signal reconstruction from few measurements.
method Combining iterative reconstruction algorithms with neural networks, analyzing generalization properties, and deriving a generalization bound.
result Theoretical guarantees for neural network reconstruction from compressive linear measurements, with generalization error scaling logarithmically in the number of layers and linearly in the number of measurements.
Bayesian optimization speeds up parameter reconstruction in optical nano-metrology.
problem Efficiently reconstructing parameters from time-consuming measurements in optical nano-metrology.
method Combines Bayesian optimization and curve fitting for faster, more efficient model fitting.
result The presented Bayesian Target Vector Optimization scheme achieves similar reconstruction performance with fewer model function calls.
New deep learning model for image reconstruction using Fourier space relations.
problem Image reconstruction efficiency and complexity reduction.
method Model-based off-the-grid algorithm with deep learned non-linear annihilation relations.
result Significant reduction in computational complexity compared to structured low-rank methods.
The paper analyzes privacy leakage in federated learning using linear algebra and optimization theory.
problem Privacy leakage in federated learning despite its promise for data privacy.
method Theoretical analysis from linear algebra and optimization theory perspectives.
result Derives sufficient conditions to prevent data reconstruction attacks and establishes an upper bound on privacy leakage.
Learning codes for non-linear computations improves resilience in machine learning.
problem Resilience of machine learning models in the face of unavailability.
method Learning neural network architectures to design codes for non-linear computations.
result Learned codes can reconstruct up to 98% of unavailable predictions from neural networks.
Framework for confidence estimation in deep CT reconstructions.
problem Uncertainty in deep learning-based CT reconstructions.
method Sequential likelihood mixing framework with log-linear forward model.
result Deep models yield tighter confidence regions than classical methods.
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.
OnAIR reconstructs dynamic images from sparse measurements online.
problem Reconstructing dynamic images from limited or corrupted measurements.
method Online adaptive reconstruction using sparsity and low-rank models with dictionary learning.
result Memory-efficient online algorithms for sequential estimation of dictionary and images.
New CT image reconstruction method reduces X-ray dose while improving image quality.
problem Reducing X-ray dose in CT while maintaining image quality.
method Combines PWLS with learned sparsifying transform using alternating optimization and relaxed OS-LALM.
result Proposed method improves image quality for low dose levels compared to existing methods.
Paper develops a novel kernel-based method for MRI data recovery.
problem Reconstructing dynamic MRI data on manifolds.
method Kernel bi-linear modeling in reproducing kernel Hilbert spaces.
result Validated on synthetic dMRI data, the method outperforms state-of-the-art approaches.
Enhances deep neural networks for MRI reconstruction by increasing expressivity.
problem Balancing network complexity and performance in deep learning MRI reconstruction.
method Geometric approach using bootstrapping and subnetwork aggregation with attention module.
result Significant improvement in MRI reconstruction performance with minimal complexity increase.
A method extracts binary features directly from CS measurements for compressive image classification.
problem Efficiently classify images using compressive sensing without reconstruction.
method DCT-based approach for binary feature extraction from CS measurements, feature fusion with CNN features.
result Fused features outperform state-of-the-art methods in image classification.
Deep Ptych uses generative models to reconstruct images with fewer samples.
problem Highly ill-posed and non-linear Fourier ptychography problem.
method Proposes a novel framework using generative models to regularize the Fourier ptychography problem.
result Deep Ptych outperforms existing techniques in image reconstruction quality and robustness.
Study Tikhonov regularization for non-linear inverse problems to improve image reconstruction accuracy.
problem Reconstructing quantities from noisy, non-linearly transformed observations.
method Tikhonov regularization using reproducing kernel Hilbert spaces.
result Developed optimal convergence rates for the estimator.
Proposes a Monte-Carlo method for sparse signal reconstruction.
problem Reconstructing sparse signals in high-dimensional settings.
method Greedy Monte-Carlo (GMC) search algorithm.
result GMC can achieve perfect reconstruction in undersampling situations.
Deep learning improves image reconstruction, but scaling up training sets doesn't significantly boost performance.
problem Understanding the impact of training set size on deep learning image reconstruction.
method Empirical study and analytical characterization of performance scaling laws.
result Scaling up training set size does not significantly improve reconstruction quality for deep learning.
New method uses VAEs for blind channel equalization and decoding.
problem Blind channel equalization and decoding without pilot symbols.
method Variational autoencoders (VAEs) for blind channel equalization and decoding.
result Significant improvement in error rate compared to existing methods.
Paper evaluates and mitigates privacy risks in deep learning models.
problem Quantifying and defending against privacy attacks in deep learning.
method Quantitative evaluation of trade-offs, reformulating attacks, and proposing a novel SPN.
result Model accuracy improved by 5-20% while maintaining data privacy.
New method reconstructs strain and lattice spacing from neutron data.
problem Jointly reconstructing strain and lattice spacing from neutron data.
method Solves non-linear problem ensuring strain field equilibrium with knowledge of boundary conditions.
result Demonstrates ability to jointly reconstruct strain and lattice spacing from simulated data.
New approach improves deep learning robustness in medical imaging.
problem Deep learning models are vulnerable to adversarial examples in medical imaging.
method Propose a min-max learning scheme to generate adversarial examples and filter them out.
result Proposed method significantly improves robustness of deep learning models in medical imaging.
Paper tackles outlier detection in signals modeled by generative models with theoretical guarantees.
problem Recovering signals from linear measurements with sparse outliers.
method Proposes an iterative ADMM algorithm and gradient descent algorithm for outlier detection using ℓ1 and squared ℓ1 norm minimization. result Establishes theoretical recovery guarantees for signal reconstruction under sparse outliers.
We develop latent variable models for Bayesian learning based low-rank matrix completion and reconstruction from linear measurements. For under-determined systems, the developed methods are shown to reconstruct low-rank matrices when neither the rank nor the noise power is known a-priori. We derive relations between th…
A central problem in neuroscience is reconstructing neuronal circuits on the synapse level. Due to a wide range of scales in brain architecture such reconstruction requires imaging that is both high-resolution and high-throughput. Existing electron microscopy (EM) techniques possess required resolution in the lateral p…
A fast deep learning method for parallel MRI without calibration.
problem Calibration issues in parallel MRI reconstruction.
method Model-based deep learning, self-learning non-linear annihilation filters, Fourier domain pre-learning.
result Significantly faster than SLR methods (3 orders of magnitude), improved performance with spatial domain prior.