We consider the problem of reconstructing signals and images from periodic nonlinearities. For such problems, we design a measurement scheme that supports efficient reconstruction; moreover, our method can be adapted to extend to compressive sensing-based signal and image acquisition systems. Our techniques can be pote…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,051 papers · 148 categories
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48 results for “nonlinear reconstruction”
The paper extends lossy coding to nonlinear latent representations.
problem Learning finite-dimensional coding schemes with nonlinear reconstruction maps.
method Generalizes Maurer--Pontil framework to nonlinear maps, connects to generative modeling, and provides generalization bounds.
result Established a connection to approximate generative modeling and presented generalization bounds.
Framework for reconstructing nonlinear systems from multi-modal time series data.
problem Reconstructing nonlinear dynamical systems from multi-modal time series data.
method Dynamic interpretable recurrent neural networks coupled with generalized linear models for multi-modal data integration.
result Framework efficiently compensates for noisy or missing information in one data channel using other channels.
Dual Objective Approach Using A Convolutional Neural Network for Magnetic Resonance Elastographyphysics.med-ph
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 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…
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.
Unsupervised Linear and Nonlinear Channel Equalization and Decoding using Variational Autoencoderscs.LG
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.
NKI integrates obfuscated datasets using nonlinear kernels for improved data collaboration.
problem Privacy-preserving data collaboration with reduced reconstruction risk.
method Formulates linear kernel integration, kernelizes it, and introduces graph regularization and centering constraints.
result NKI improves classification accuracy over existing linear integration methods under nonlinear dimensionality reduction.
This work uses diffusion models for accurate signal recovery from semi-parametric models.
problem Recovering signals from semi-parametric single index models with discontinuous link functions.
method Proposes an efficient reconstruction method using diffusion models that requires one round of sampling and inversion.
result Demonstrates more accurate reconstructions with fewer evaluations compared to competing methods.
Theoretical Connection between Locally Linear Embedding, Factor Analysis, and Probabilistic PCAstat.ML
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.
Deep network improves electrical tomography across multiple frequencies.
problem Nonlinear multi-frequency electrical impedance tomography (mfEIT) for tissue conductivity estimation.
method Integrates graph neural networks (GNNs) into the iterative Proximal Regularized Gauss Newton (PRGN) framework to reconstruct tissue concentrations accurately.
result Accurate reconstruction of overlapping tissue fraction concentrations across multiple frequencies.
Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstructioneess.IV
Develops a robust method for image reconstruction from limited data.
problem Inference of unknown images from few measurements, often ill-posed.
method Introduces DPnP, a diffusion plug-and-play method combining likelihood and score-based samplers.
result Establishes performance guarantees for DPnP, demonstrating robustness and efficiency.
Sparse Shape Reconstructionmath.FA
This paper introduces a new shape-based image reconstruction technique applicable to a large class of imaging problems formulated in a variational sense. Given a collection of shape priors (a shape dictionary), we define our problem as choosing the right elements and geometrically composing them through basic set opera…
New model reconstructs flow from sparse data with uncertainty quantification.
problem Reconstructing nonlinear flow from limited observations.
method Semi-Conditional Variational Autoencoder (SCVAE) for probabilistic flow reconstruction.
result SCVAE improves reconstruction accuracy compared to Gappy Proper Orthogonal Decomposition (GPOD).
Proposes FunNoL for better curve classification and reconstruction in multivariate functional data.
problem Linear methods fail to capture nonlinear structures in multivariate functional data.
method Functional nonlinear learning (FunNoL) method using nonlinear mapping.
result FunNoL outperforms FPCA in curve classification and reconstruction, especially in multivariate settings.
New variational model preserves image contrasts and features using Weingarten map minimization.
problem Image reconstruction with preservation of contrasts and features.
method Variational model with norm of Weingarten map, ADMM algorithm, gradient descent.
result The proposed models preserve image contrasts and features efficiently.
FsNet selects features for high-dimensional biological data efficiently.
problem Efficient feature selection for high-dimensional biological data.
method FsNet combines selection and reconstruction layers with tiny networks for weight prediction.
result FsNet outperforms standard DNNs on high-dimensional biological datasets.
Equation discovery method reconstructs model structure and parameters from data.
problem Nonlinear system identification challenges.
method Two interlaced parts: model structure identification and parameter estimation.
result Equation discovery method successfully reconstructs model structure and parameters from data.
New approach uses secants to improve sensor placement and feature selection for nonlinear systems.
problem Inadequacy of linear methods for minimal sensor placement and feature selection in nonlinear systems.
method Data-driven approach using secant vectors to develop greedy algorithms for robust, near-minimal reconstruction guarantees.
result Demonstrated on two problems where linear techniques fail, secant-based approach provides robust solutions.
A method for learning complex functions from data with reduced memory usage.
problem Learning highly nonlinear, multivariate functions from examples.
method Transforming function learning into tensor reconstruction, incrementally building tensors from rank-one terms.
result Efficient gradient-based algorithm with linear time complexity in sample size and tensor dimensions.
NDI enables high-quality QSM without parameter tuning.
problem Quantitative Susceptibility Mapping (QSM) with regularization tuning issues.
method Nonlinear Dipole Inversion (NDI) using a physics-based forward model and a Variational Network (VN).
result NDI achieves high-quality QSM from as few as 2-direction data.
Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learningstat.ML
This paper introduces a new nonlinear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim is to reconstruct histograms using so-called displacement interpolations (a.k.a. Wasserstein barycenters) between dictionary atoms; such at…
Deep adversarial neural decodingq-bio.NC
Here, we present a novel approach to solve the problem of reconstructing perceived stimuli from brain responses by combining probabilistic inference with deep learning. Our approach first inverts the linear transformation from latent features to brain responses with maximum a posteriori estimation and then inverts the …
BO optimized for high dimensions using feature space learning.
problem Scalability of BO to high-dimensional problems.
method Joint learning of low-dimensional feature space and reconstruction mapping.
result Optimization in lower-dimensional subspace simplifies BO problem.
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.
Probabilistic Autoencoder learns latent space weights' distribution.
problem Nonlinear model reconstruction error and sample quality.
method Normalizing flow for latent space weights' probability distribution.
result PAE achieves small reconstruction errors, high sample quality, and good performance.
Two strategies for embedding new data points from proximity data are explored.
problem Embedding new data points using proximity data.
method Two competing strategies: projection and restricted reconstruction.
result Projection and restricted reconstruction can be derived from kernel methods.
Signature tensors uniquely identify ODE solutions.
problem Identifying ODE solutions from signature tensors.
method Geometric theory of nonlinear systems of ODEs.
result Necessary and sufficient algebraic conditions for signature tensors to represent ODE solutions.
Normalizing flows improve ptychography reconstruction quality and uncertainty quantification.
problem Challenges in ptychography due to large-scale nonlinear and non-convex inverse problems and photon statistics.
method Use of normalizing flows to model the posterior distribution and quantify reconstruction uncertainty.
result Normalizing flows enable better characterization and uncertainty quantification in ptychography reconstructions.
Nonlinear Evolution via Spatially-Dependent Linear Dynamics for Electrophysiology and Calcium Datastat.ML
VIND infers smooth nonlinear dynamics from electrophysiology data.
problem Analyzing smooth, nonlinear time series data from neuroscience experiments.
method Variational Inference for Nonlinear Dynamics (VIND) with structured approximate posterior and fixed-point iteration.
result VIND reconstructs 5D latent space variables similar to Hodgkin-Huxley models, and excels in predicting future neural activity.
Study recasts learning non-linear functions from noisy data as robust regression, proving reconstruction guarantees.
problem Learning non-linear functions from corrupted and dependent data.
method Sparse robust linear regression with -optimization, incorporating unknown coefficients and corruptions.
result Reconstruction guarantees for -optimization problem with dependent data, proving null and stable null space properties.
Study reconstructs causal graph from latent variables using mixture oracles.
problem Reconstructing causal graphical model from data with latent variables.
method Reduction to mixture oracle to identify latent representations and causal structure.
result Conditions for identifying latent representations and causal model.
This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a useful data-driven approximation of the Koopman operator for analyzing dynamical syst…
New method reconstructs missing variables in time series using autoencoders and automatic differentiation.
problem Reconstruct missing variables in time series with flexible input and output combinations.
method Train an autoencoder with all features, optimize missing variables as inputs, and use automatic differentiation.
result Flexible input and output combinations can be achieved without retraining the autoencoder.
Adaptive-Rate Sparse Signal Reconstruction With Application in Compressive Background Subtractionmath.OC
We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear dynamical model. Our algorithm, based on recent theoretical results for -$…
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.
We present a new method for nonlinear prediction of discrete random sequences under minimal structural assumptions. We give a mathematical construction for optimal predictors of such processes, in the form of hidden Markov models. We then describe an algorithm, CSSR (Causal-State Splitting Reconstruction), which approx…
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 and squared norm minimization.
result Establishes theoretical recovery guarantees for signal reconstruction under sparse outliers.
An efficient method to construct Hamiltonian structures for nonlinear evolution equations is described. It is based on the notions of variational Schouten bracket and l*-covering. The latter serves the role of the cotangent bundle in the category of nonlinear evolution PDEs. We first consider two illustrative examples …
Unified framework for inference in complex nonlinear processes.
problem Challenges in inferring nonlinear continuous stochastic processes with sparse observations and complex topologies.
method Neural Backward Filtering Forward Guiding (NBFFG) framework that constructs a variational posterior using a proxy linear-Gaussian process.
result Empirical results show NBFFG outperforms baselines on synthetic benchmarks and high-dimensional phylogenetic analysis tasks.
In this paper we propose a new identification scheme for Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be described as a linear combination of basis functions. We reconstruct the …
We solve a high-dimensional model where nonlinear autoencoders detect hidden structure missed by PCA.
problem Hidden structure in high-dimensional data not detected by PCA.
method Tractable spiked model with two latent factors, one visible and one uncorrelated.
result Nonlinear autoencoders can extract hidden structure missed by PCA, even if reconstruction loss is higher.
ISB learns nonlinear diffusion processes between images.
problem Image restoration tasks, especially with limited structural information.
method Conditional diffusion models, Schrödinger bridge approach.
result ISB outperforms standard models in various image restoration tasks.
New algorithm discovers causal relationships from observational data efficiently.
problem Inferring direct causal parents from a large set of variables.
method Orthogonal structure search approach, scaling to large graphs, guarantees for nonlinear relationships.
result Significant improvements over existing methods in causal discovery from observational data.
We test whether the futures prices of some commodity and energy markets are determined by stochastic rules or exhibit nonlinear deterministic endogenous fluctuations. As for the methodologies, we use the maximal Lyapunov exponents (MLE) and a determinism test, both based on the reconstruction of the phase space. In par…
Parameter Estimation with Dense and Convolutional Neural Networks Applied to the FitzHugh-Nagumo ODEstat.ML
Deep neural networks solve parameter estimation for FitzHugh-Nagumo ODEs.
problem Estimating parameters of a nonlinear dynamical system from noisy time series data.
method Dense and convolutional neural networks for inverse problem solving.
result Deep neural networks accurately estimate FitzHugh-Nagumo model parameters from noisy data.
A new probabilistic model for PET image reconstruction.
problem Conventional PET image reconstruction ignores uncertainty in TACs.
method Probabilistic Graphical Modeling (PGM) with gradient-based iterative algorithm.
result Incorporates uncertainty in TACs, improving image reconstruction.
Novel method learns time series dynamics without reconstruction.
problem Learning nonlinear stochastic dynamics from video data.
method Recognition-parametrized Gaussian state space model (RP-GSSM) using maximum likelihood.
result Outperforms alternatives on nonlinear stochastic dynamics learning.