New method simplifies tomographic reconstruction using RKHS.
problem Tomographic reconstruction challenges.
method RKHS framework for X-ray transform.
result Sharp stability results without Fourier transform.
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48 results for “Filtered Back-Projection”
We study the weighted light ray transform of integrating functions on a Lorentzian manifold over lightlike geodesics. We analyze as a Fourier Integral Operator and show that if there are no conjugate points, one can recover the spacelike singularities of a function from its the weighted light ray transform …
The paper explores properties of the Radon transform in relation to neural networks and ridges.
problem Understanding the Radon transform and its application to neural networks and ridges.
method Investigates properties of the Radon transform, introduces new subspaces, and characterizes ridges for any distributional profile.
result Clarifies and simplifies results on the optimality of ReLU networks using the Radon transform.
X-ray computed tomography (CT) using sparse projection views is a recent approach to reduce the radiation dose. However, due to the insufficient projection views, an analytic reconstruction approach using the filtered back projection (FBP) produces severe streaking artifacts. Recently, deep learning approaches using la…
Paper examines convergence rate of PGD for BP objective in inverse problems.
problem Optimizing ill-posed linear inverse problems using BP vs LS.
method Analysis of PGD convergence rate for BP objective, comparison with proximal gradient method.
result PGD converges faster for BP objective due to inherent properties.
The field of medical image reconstruction has seen roughly four types of methods. The first type tended to be analytical methods, such as filtered back-projection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform for magnetic resonance imaging (MRI), based on simple mathematical models for the …
Deep Neural Mapscs.LG
We introduce a new unsupervised representation learning and visualization using deep convolutional networks and self organizing maps called Deep Neural Maps (DNM). DNM jointly learns an embedding of the input data and a mapping from the embedding space to a two-dimensional lattice. We compare visualizations of DNM with…
In transmission X-ray microscopy (TXM) systems, the rotation of a scanned sample might be restricted to a limited angular range to avoid collision to other system parts or high attenuation at certain tilting angles. Image reconstruction from such limited angle data suffers from artifacts due to missing data. In this wo…
Deep Kernelized Autoencodersstat.ML
In this paper we introduce the deep kernelized autoencoder, a neural network model that allows an explicit approximation of (i) the mapping from an input space to an arbitrary, user-specified kernel space and (ii) the back-projection from such a kernel space to input space. The proposed method is based on traditional a…
Generative Adversarial networks (GANs) have obtained remarkable success in many unsupervised learning tasks and unarguably, clustering is an important unsupervised learning problem. While one can potentially exploit the latent-space back-projection in GANs to cluster, we demonstrate that the cluster structure is not re…
The article studies mapping properties of Radon transform and backprojection on a unit ball.
problem Polyhomogeneous mapping properties of Radon transform and backprojection operator on the unit ball.
method Constructs a double b-fibration to desingularize the point-hyperplane relation, provides formulas and sharper estimates.
result Sharper estimates on polyhomogeneous mapping properties of Radon transform and backprojection compared to classic estimates.
This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A distribution-free analysis shows that by observing just a single linear measure…
This paper focuses on spectral filters on graphs, namely filters defined as elementwise multiplication in the frequency domain of a graph. In many graph signal processing settings, it is important to transfer a filter from one graph to another. One example is in graph convolutional neural networks (ConvNets), where the…
A new SOHP filter improves trend estimation in economic time series.
problem Improving trend estimation in nonlinear economic time series.
method Recursive application of one-sided HP filter on updated cyclical components, combined with an incremental HP filtering algorithm.
result Better performance of SOHP filter compared to other HP-type filters on real economic data.
Deep density methods improve filtering in high-dimensional systems.
problem Nonlinear filtering in high-dimensional systems.
method Two deep density methods based on Feynman-Kac formulas and neural networks.
result Logarithmic deep backward stochastic differential equation filter outperforms classical methods in high dimensions.
The sophisticated structure of Convolutional Neural Network (CNN) allows for outstanding performance, but at the cost of intensive computation. As significant redundancies inevitably present in such a structure, many works have been proposed to prune the convolutional filters for computation cost reduction. Although ex…
Gradient filters track moving parameters under noisy data and misspecification.
problem Tracking multidimensional time-varying parameters under noisy observations and model misspecification.
method Gradient-based filters update parameters using the gradient of a postulated objective function, evaluated at either the predicted or updated parameters.
result Novel sufficient conditions for exponential stability of the filtered parameter path, and finite-sample and asymptotic mean squared error bounds.
We simplify Bayesian filtering by framing it as optimization, making it practical for high-dimensional systems.
problem Bayesian filtering struggles in high-dimensional state spaces like neural networks.
method We frame Bayesian filtering as optimization, using gradient descent for nonlinear cases.
result Our method results in effective, robust, and scalable filters for high-dimensional systems.
Inverse Particle Filtermath.OC
Develops an inverse particle filter for cognitive systems.
problem Tracking cognitive adversaries in counter-adversarial applications.
method Global filtering approach using Monte Carlo methods and differentiable I-PF.
result Demonstrates convergence to optimal inverse filter and improved estimation performance.
Convolutional neural networks (CNNs) achieve state-of-the-art performance in a wide variety of tasks in computer vision. However, interpreting CNNs still remains a challenge. This is mainly due to the large number of parameters in these networks. Here, we investigate the role of compression and particularly pruning fil…
A novel method reduces dimensionality for filtering SRNs with observed variables.
problem Challenges in estimating hidden state variables in SRNs with limited observations.
method Filtered Markovian Projection (Filtered MP) for dimensionality reduction in filtering.
result Filtered MP guarantees consistency and superior computational efficiency in high dimensions.
Kernel learning FBSDE filter improves nonlinear filtering efficiency.
problem Nonlinear filtering problem in high-dimensional systems.
method Iterative and adaptive meshfree approach using forward backward SDE and KDE.
result Rigorous convergence analysis provided, supporting empirical results.
New method filters large networks from financial data to reveal key subnetworks.
problem Filtering large dimensional networks to isolate key constituents.
method Exploits spectral properties of high-dimensional data networks, tuning for sparsity and consistency.
result Shows method can interpolate between zero and maximal filtering, preserving spectral properties.
Many nonlinear extensions of the Kalman filter, e.g., the extended and the unscented Kalman filter, reduce the state densities to Gaussian densities. This approximation gives sufficient results in many cases. However, this filters only estimate states that are correlated with the observation. Therefore, sequential esti…
Paper proves convergence of Kalman filter on Stiefel manifolds with measurement errors.
problem Filtering constant particle with measurement errors on Stiefel manifolds.
method Extended Kalman filter applied to Stiefel manifold-valued observations.
result Convergence of the extended Kalman filter proved for constant system process.
Improved Kalman filter for non-linear, non-Gaussian data.
problem Estimating hidden variables with non-linear, non-Gaussian observations.
method Reproduces and extends Burkhart et al.'s discriminative Kalman filter.
result Enhanced filter performance for complex observation models.
This work analyzes the stability of graph filters under large perturbations.
problem Stability of graph filters under large edge rewires.
method Proves a bound on stability using frequency response and community structure.
result Graph filter stability depends on perturbation to community structure.
Advances deep network embedding through multi-filtering GCN.
problem Existing attribute embedding methods fail to capture different aspects of node features.
method Multi-filtering Graph Convolution Neural Network (GCN) framework.
result Significant improvement in link prediction and node classification tasks with limited training data.
This work preserves linear invariants in ensemble filters for non-Gaussian data assimilation.
problem Maintaining critical invariants like mass, stoichiometric balance, and charge in non-Gaussian data assimilation.
method Introducing a novel class of nonlinear ensemble filters using measure transport theory.
result Recovery of a constrained Kalman filter for Gaussian settings and combination with regularization techniques.
Convolutional Bayesian filtering generalizes state estimation by incorporating inequality conditions.
problem Standard Bayesian filtering assumes exact conditional probabilities, limiting its applicability.
method Introducing inequality conditions transforms conditional probabilities into convolutional forms, expanding the filtering framework.
result Convolutional Bayesian filtering encompasses standard Bayesian filtering and allows for more nuanced model consideration.
EnSF improves accuracy in tracking high-dimensional nonlinear systems.
problem Low accuracy in high-dimensional, nonlinear filtering problems.
method Score-based diffusion model, mini-batch Monte Carlo estimator.
result EnSF outperforms state-of-the-art methods in tracking high-dimensional systems.
Improved Kalman filter for Stiefel manifold measurements.
problem Improving accuracy in measurements on Stiefel manifolds.
method Generalization of extended Kalman filter for Stiefel manifold-valued measurements.
result Significant improvement over raw measurements.
Latent FxLMS accelerates ANC by adapting along low-dimensional filter weights.
problem Improving active noise control with neural adaptive filters.
method Training an auto-encoder on filter coefficients, constraining weights to latent variables, and updating in latent space.
result Latent FxLMS converges in fewer steps with comparable error to standard FxLMS.
In this paper we introduce a projection method for the space of probability distributions based on the differential geometric approach to statistics. This method is based on a direct L2 metric as opposed to the usual Hellinger distance and the related Fisher Information metric. We explain how this apparatus can be used…
Robust Kalman filtering method for outlier detection.
problem Outliers and misspecified measurement models in state-space models.
method Combines generalised Bayesian inference with Kalman filters for robustness and efficiency.
result Matches or outperforms other robust filtering methods at lower computational cost.
Recent work has suggested enhancing Bloom filters by using a pre-filter, based on applying machine learning to determine a function that models the data set the Bloom filter is meant to represent. Here we model such learned Bloom filters,, with the following outcomes: (1) we clarify what guarantees can and cannot be as…
This paper presents the construction of a particle filter, which incorporates elements inspired by genetic algorithms, in order to achieve accelerated adaptation of the estimated posterior distribution to changes in model parameters. Specifically, the filter is designed for the situation where the subsequent data in on…
Develops inverse unscented Kalman filter for non-linear systems.
problem Estimating defender's state in adversarial settings.
method Formulated inverse unscented Kalman filter (I-UKF) and reproducing kernel Hilbert space-based UKF (RKHS-UKF).
result Proposed filters are conservative estimators with upper-bounded error covariance.
Filtering data with a pre-trained model improves multimodal contrastive learning performance.
problem Improving the quality of internet-scale multimodal datasets.
method Characterized the performance of filtered contrastive learning under a bimodal data generation model.
result Data filtering using a pre-trained model reduces contrastive learning error by a factor of in the large regime.
The Score Kalman Filtereess.SY
A new filter reduces density fitting to a linear solve, improving performance on nonlinear systems.
problem Nonlinear Bayesian filtering challenges in representing belief distributions.
method Combines score matching with Stein's identity to avoid partition function evaluation.
result The Score Kalman Filter (SKF) outperforms existing methods on nonlinear systems.
Net2Vec: Quantifying and Explaining how Concepts are Encoded by Filters in Deep Neural Networkscs.CV
In an effort to understand the meaning of the intermediate representations captured by deep networks, recent papers have tried to associate specific semantic concepts to individual neural network filter responses, where interesting correlations are often found, largely by focusing on extremal filter responses. In this …
HKF uses neural networks to adapt Kalman filters for dynamic channel tracking.
problem Tracking channels with varying dynamics and Doppler values.
method Combines Kalman filters with hypernetworks for dynamic adaptation.
result HKF achieves up to 2dB gain over Kalman filters at high Doppler values.
Triangular, overlapping Mel-scaled filters ("f-banks") are the current standard input for acoustic models that exploit their input's time-frequency geometry, because they provide a psycho-acoustically motivated time-frequency geometry for a speech signal. F-bank coefficients are provably robust to small deformations in…
A new ML-based filter improves data assimilation for nonlinear systems.
problem Improving data assimilation for nonlinear systems using ensemble methods.
method Developed a machine learning-based conditional mean filter (ML-EnCMF) integrating ANN and linear functions.
result ML-EnCMF outperforms EnKF and likelihood-based EnCMF in nonlinear systems.
Adaptive Heston model calibration using PCRLB and switching filters.
problem Estimating volatility in stochastic volatility models like Heston.
method Bayesian filtering (EKF, UKF, PF) with PCRLB for parameter estimation.
result Adaptive estimation of Heston model parameters improves volatility estimation.
NBF combines deep learning with classical filtering for better belief tracking.
problem Maintaining distributions over hidden states in partially observable systems.
method Trains neural networks to map beliefs to fixed-length vectors, updating them with incoming observations and dynamics.
result NBF efficiently tracks shifting, multimodal beliefs without particle impoverishment.
Filtered conformal ellipsoids for graph-native time series
problem Joint prediction sets for multivariate time series
method Filtered conformal ellipsoids
result Sharper at-target ellipsoids than static-covariance and non-filter baselines
The paper develops a computational method for efficient online filtering of diffusion processes.
problem Online filtering of discretely observed nonlinear diffusion processes.
method The approach involves Doob's -transforms approximated by solving backward Kolmogorov equations using nonlinear Feynman-Kac formulas and neural networks.
result The proposed method can be orders of magnitude more efficient than state-of-the-art particle filters.