In this paper we consider the geodesic X-ray transform with attenuation coefficient as a combination of smooth complex function and 1-form. We show that attenuated X-ray transform applied to the pair of tensors is injective modulo the natural obstruction.
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.
169,291 papers · 148 categories
Trend · papers per month
48 results for “attenuated transform”
We show that the attenuated geodesic ray transform on two dimensional simple surfaces is injective. Moreover we give a stability estimate and develop a reconstruction procedure.
For a compact Riemannian surface with boundary we study attenuated geodesic transform of functions and differential forms. We generalize several known results on uniqueness and stability of this transform dropping condition of absence of conjugate points.
Study characterizes geodesic ray transform on surfaces, isolating and separating sub-ranges.
problem Characterizing the range of the attenuated geodesic ray transform on surfaces.
method Isolating and separating sub-ranges of sums of functions and one-forms, deriving new inversion formulas.
result Range characterizations and new inversion formulas for geodesic ray transform.
For a two-dimensional simple magnetic system, we study the attenuated magnetic ray transform , with attenuation given by a unitary connection and a skew-Hermitian Higgs field . We give a description for the range of acting on -valued tensor fields.
We describe the range of the attenuated ray transform of a unitary connection on a simple surface acting on functions and 1-forms. We use this to determine the range of the ray transform acting on symmetric tensor fields.
It has been shown in [Pa1] that on a simple, compact Riemannian 2-manifold the attenuated geodesic ray transform, with attenuation given by a connection and Higgs field, is injective on functions and 1-forms modulo the natural obstruction. Furthermore, the scattering relation determines the connection and Higgs field m…
We show that for a simple surface with boundary the attenuated ray transform in the presence of a unitary connection and a skew-Hermitian Higgs field is injective modulo the natural obstruction for functions and vector fields. We also show that the connection and the Higgs field are uniquely determined by the scatterin…
We study the problem of recovery both the attenuation and the source in the attenuated X-ray transform in the plane. We study the linearization as well. It turns out that there are natural Hamiltonian flow that determines which singularities we can recover. If the perturbations , are supported in a com…
Article examines stability of geodesic X-ray transforms and artifacts.
problem Stability of geodesic X-ray transforms and artifacts.
method Analyzes the impact of weight and geometry on stability, and examines artifacts in unstable cases.
result Landweber algorithm cannot provide accurate reconstruction in unstable cases.
We study the geodesic X-ray transform on compact Riemannian surfaces with conjugate points. Regardless of the type of the conjugate points, we show that we cannot recover the singularities and therefore, this transform is always unstable (ill-posed). We describe the microlocal kernel of and relate it to the con…
Solves open problem on simple surfaces with novel twistor correspondence.
problem Existence of nontrivial holomorphic vector bundles on simple surfaces.
method Novel twistor correspondence, Nash-Moser inverse function theorem, and microlocal analysis.
result Simple surface twistor space supports no nontrivial holomorphic vector bundles.
We derive explicit reconstruction formulas for the attenuated geodesic X-ray transform over functions and, in the case of non-vanishing attenuation, vector fields, on a class of simple Riemannian surfaces with boundary. These formulas partly rely on new explicit approaches to construct continuous right-inverses for bac…
The paper studies ray transforms on surfaces with negative curvature, proving injectivity and determining connections and Higgs fields.
problem Injectivity of ray transforms on surfaces with negative curvature and determination of connections and Higgs fields.
method Analysis of Gaussian thermostats on compact Riemannian surfaces with negative curvature, proving injectivity and determining connections and Higgs fields.
result Injectivity of the thermostat ray transform and determination of connections and Higgs fields.
Causal forests underestimate treatment effect heterogeneity, a correction is proposed.
problem Causal forests underestimate treatment effect heterogeneity in fixed-effects panel settings.
method Cross-fitted correction to estimate and restore the spread of conditional average treatment effects.
result The correction reduces mean-squared error by 25-42% in simulations and restores heterogeneity in a real-world panel study.
We reduce boundary determination of an unknown function and its normal derivatives from the (possibly weighted and attenuated) broken ray data to the injectivity of certain geodesic ray transforms on the boundary. For determination of the values of the function itself we obtain the usual geodesic ray transform, but for…
We consider the tomography problem of recovering a covector field on a simple Riemannian manifold based on its weighted Doppler transformation over a family of curves . This is a generalization of the attenuated Doppler transform. Uniqueness is proven for a generic set of weights and families of curves under a condi…
Two new methods for injective ray transforms of tensor fields on surfaces are introduced.
problem Injective ray transforms for tensor fields on surfaces.
method Two approaches: weights varying along geodesic flow and transverse ray transforms.
result Constructive solutions for tensor tomography on simple surfaces.
Attenuation correction for brain PET imaging using deep neural network based on dixon and ZTE MR imagesphysics.med-ph
Deep neural networks improve PET attenuation correction from MR images.
problem Challenges in PET attenuation correction from MR images in PET/MR hybrid systems.
method Deep neural networks, specifically U-net and GroupU-net structures, to derive continuous attenuation coefficients.
result Proposed neural network methods outperform standard methods in PET quantification accuracy.
Researchers study injectivity of magnetic and thermostatic nonabelian ray transforms on compact surfaces.
problem Injectivity of magnetic and thermostatic nonabelian ray transforms on compact surfaces.
method Loop group factorization method for nontrapping -geodesic flows and the general linear group of invertible complex matrices.
result General injectivity question of the nonabelian ray transform for simple magnetic flows is settled.
Study geodesic X-ray transforms on curved manifolds using Carleman estimates.
problem Invertibility of geodesic X-ray transforms on curved manifolds.
method Using Carleman estimates to show invertibility of geodesic vector field.
result Geodesic X-ray transform is invertible on negatively curved simple manifolds.
In this article we consider the anisotropic Calderon problem and related inverse problems. The approach is based on limiting Carleman weights, introduced in Kenig-Sjoestrand-Uhlmann (Ann. of Math. 2007) in the Euclidean case. We characterize those Riemannian manifolds which admit limiting Carleman weights, and give a c…
Deep Boosted Regression for MR to CT Synthesisphysics.med-ph
Deep neural network improves CT synthesis from MRI.
problem Generating accurate CT images from MRI for PET reconstruction.
method Deep fully convolutional neural network that recursively reduces residuals.
result Decreased PET reconstruction error from 14.3% to 7.2%.
LatentNN corrects neural network attenuation bias in astronomical data.
problem Neural networks underestimate extreme values due to measurement errors.
method Jointly optimizes network parameters and latent input values.
result LatentNN reduces attenuation bias across various signal-to-noise ratios.
Framework predicts and prepares for rain-induced microwave link attenuation.
problem Severe signal attenuation due to weather conditions degrades network performance.
method Predictive Network Reconfiguration (PNR) framework using LSTM for attenuation prediction and MSNR for dynamic routing.
result Framework improves network utilization by more than 200% compared to reactive algorithms.
This paper addresses anisotropy in Transformer models, providing geometric insights and empirical support.
problem Anisotropy phenomenon in Transformer models, challenging their geometric interpretation.
method Derive geometric arguments and use concept-based mechanistic interpretability during training.
result Activation-derived directions capture large gradient energy and a larger share of gradient anisotropy than normal controls.
Consider a compact Riemannian manifold of dimension with strictly convex boundary, such that the manifold admits a strictly convex function. We show that the attenuated ray transform in the presence of an arbitrary connection and Higgs field is injective modulo the natural obstruction for functions and one-for…
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.
New methods reduce bias in machine learning predictions for causal inference without extra data.
problem Machine learning predictions from satellite data shrink toward the mean, leading to biased causal estimates.
method Two post-hoc correction methods: Linear Calibration Correction (LCC) and Tweedie's approach, reduce shrinkage-induced bias.
result Tweedie's method yields nearly unbiased treatment-effect estimates, enabling multiple trials with a single map.
We consider the anisotropic Calderon problem of recovering a conductivity matrix or a Riemannian metric from electrical boundary measurements in three and higher dimensions. In the earlier work \cite{DKSaU}, it was shown that a metric in a fixed conformal class is uniquely determined by boundary measurements under two …
We consider integral geometry inverse problems for unitary connections and skew-Hermitian Higgs fields on manifolds with negative sectional curvature. The results apply to manifolds in any dimension, with or without boundary, and also in the presence of trapped geodesics. In the boundary case, we show injectivity of th…
The paper reviews machine learning methods in PET imaging.
problem Improving accuracy in PET attenuation correction and reconstruction.
method Summarizes recent machine learning-based studies in PET imaging.
result Discusses the performance and challenges of current methods.
In this paper, a geometric function is introduced to reflect the attenuation speed of impact of one firm's default to its partner. If two firms are competitions (copartners), the default intensity of one firm will decrease (increase) abruptly when the other firm defaults. As time goes on, the impact will decrease gradu…
We consider the problem of developing a method to reconstruct a potential from the partial data Dirichlet-to-Neumann map for the Schrödinger equation on a fixed admissible manifold . If the part of the boundary that is inaccessible for measurements satisfies a flatness condition in one directio…
L2F learns to forget, improving few-shot learning performance.
problem Few-shot learning challenges in adapting to unseen tasks.
method Task-and-layer-wise attenuation on compromised initialization to reduce prior knowledge influence.
result Faster adaptation and improved performance demonstrated experimentally.
Inverts operator on hyperbolic surfaces, constructing invariant distributions.
problem Constructing explicit inversion formula for X-ray normal operator.
method First, inversion formula for attenuated normal operator on Poincaré disk and closed hyperbolic surfaces. Then, explicit construction of invariant distributions.
result Explicit construction of invariant distributions with prescribed pushforward.
LAWN normalizes logits to improve deep network adaptability and generalization.
problem Large logits and weights lead to overfitting in deep networks.
method Logit Attenuating Weight Normalization (LAWN) constrains weight norms in the final sub-network.
result LAWN improves generalization and adaptability of deep networks.
A deep learning model improves seismic noise reduction.
problem Seismic noise attenuation in pre-stack data processing.
method N2N-Seismic model based on residual neural networks.
result The model significantly outperforms conventional approaches in noise reduction metrics.
New method prevents gradient attenuation in Lipschitz constrained convolutional networks.
problem Gradient norm attenuation in Lipschitz constrained convolutional networks.
method Block Convolution Orthogonal Parameterization (BCOP) to train scalable, expressive, provably Lipschitz convolutional networks.
result Empirically, BCOP parameterization is competitive with existing approaches to provable adversarial robustness and Wasserstein distance estimation.
Researchers solve inverse problems for connections and Higgs fields on Riemannian manifolds.
problem Determining connections and Higgs fields from parallel transport data.
method Pseudolinearization argument and attenuated geodesic ray transform.
result Injectivity and stability estimates for generic simple metrics and connections.
New solar tracking system uses computer vision and low-cost hardware.
problem Current solar tracking systems are expensive and have operational issues.
method Low-cost hardware, computer vision, and deep learning.
result The new system shows great potential and can improve solar tracking performance.
Proposes a method to improve classification robustness against label noise.
problem Improving classification robustness against label noise.
method Extends a simple regression approach to classification, modeling labels as samples from a logistic-normal distribution.
result The method improves robustness against label noise in classification.
A new recurrent unit alleviates vanishing gradients for long-term dependencies.
problem Vanishing gradients in recurrent neural networks make long-term dependencies hard to model.
method Proposes a new NRU architecture that avoids saturating activation functions and gates.
result Demonstrates superior performance across various tasks with and without long-term dependencies.
In this paper, we reveal the attenuation mechanism of anchor of the commodity money from the perspective of logistics warehousing costs, and propose a novel Decayed Commodity Money (DCM) for the store of value across time and space. Considering the logistics cost of commodity warehousing by the third financial institut…
Study shows feedback effect between capital flows volatility and financial stability in DRC.
problem Volatility of capital flows can undermine financial stability in DRC.
method Dynamic regression model and vector autoregressive (VAR) model to analyze feedback effects and policy impacts.
result Feedback effect between capital flows volatility and financial stability exists in DRC, but policies do not effectively mitigate volatility.
The Critical Horizon: Inspection Design Principles for Multi-Stage Operations and Deep Reasoningstat.ML
New insights into how to inspect and learn from multi-stage processes and AI reasoning.
problem Understanding how to attribute outcomes to early stages in multi-stage operations and AI reasoning.
method Information-theoretic analysis and mathematical proofs of four key results.
result Uniform checkpoint spacing is minimax-optimal for inspection design under homogeneous signal attenuation.
Complex-valued neural networks improve seismic data analysis by preserving phase information.
problem Low-frequency aliasing in seismic data due to discarded phase information.
method Developed complex-valued deep convolutional networks to leverage phase information in deterministic physical data.
result Complex-valued networks outperform real-valued networks in training and inference from deterministic physical data.
This study quantifies uncertainty in comparing treatments using RCTs with before-and-after measures.
problem Uncertainty in comparing treatments using RCTs with before-and-after measures.
method New statistical modeling principle called ETZ enables counterfactual uncertainty quantification (CUQ) in RCTs with Before-and-After Repeated Measures.
result CUQ typically has lower variability than factual uncertainty quantification and can be achieved in RCTs.