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Accelerating magnetic resonance image (MRI) reconstruction process is a challenging ill-posed inverse problem due to the excessive under-sampling operation in k-space. In this paper, we propose a recurrent transformer model, namely…

Image and Video Processing · Electrical Eng. & Systems 2022-01-31 Pengfei Guo , Yiqun Mei , Jinyuan Zhou , Shanshan Jiang , Vishal M. Patel

Reconstructing noise-driven nonlinear networks from time series of output variables is a challenging problem, which turns to be very difficult when nonlinearity of dynamics, strong noise impacts and low measurement frequencies jointly…

Statistical Mechanics · Physics 2017-10-20 Rundong Shi , Gang Hu , Shihong Wang

Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also…

Machine Learning · Computer Science 2026-05-04 Saeed Mohseni-Sehdeh , Walid Saad , Kei Sakaguchi , Tao Yu

We consider the problem of recovering material parameters in a transversely isotropic medium from the qP and qSV waves' travel times, given the axis of isotropy and the material parameters associated to the qSH wave speed. The operators…

Analysis of PDEs · Mathematics 2022-07-28 Yuzhou Zou

We improve a phase retrieval approach that uses correlation-based measurements with compactly supported measurement masks [27]. The improved algorithm admits deterministic measurement constructions together with a robust, fast recovery…

Numerical Analysis · Mathematics 2016-12-07 Mark A. Iwen , Brian Preskitt , Rayan Saab , Aditya Viswanathan

In this paper we develop a time reversal method for the radiative transport equation to solve two problems: an inverse problem for the recovery of an initial condition from boundary measurements, and the exact boundary controllability of…

Analysis of PDEs · Mathematics 2013-08-06 Sebastian Acosta

A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…

Other Computer Science · Computer Science 2015-05-28 Nelly Pustelnik , Jean-Christophe Pesquet , Caroline Chaux

We analyze the time reversal of waves in a turbulent medium using the parabolic Markovian model. We prove that the time reversal resolution can be a nonlinear function of the wavelength and independent of the aperture. We establish a…

Optics · Physics 2009-11-11 Albert Fannjiang , Knut Solna

This paper presents an innovative approach to computational acoustic imaging of biperiodic surfaces, exploiting the capabilities of an acoustic superlens to overcome the diffraction limit. We address the challenge of imaging physical…

Analysis of PDEs · Mathematics 2026-01-05 Yuliang Wang

Precession electron diffraction has in the past few decades become a powerful technique for structure solving, strain analysis, and orientation mapping, to name a few. One of the benefits of precessing the electron beam, is increased…

Instrumentation and Detectors · Physics 2025-12-12 Gregory Nordahl , Lewys Jones , Emil Frang Christiansen , Kasper Aas Hunnestad , Magnus Nord

Computational time reversal imaging can be used to locate the position of multiple scatterers in a known background medium. Here, we discuss a sparse approximation method for computational time-reversal imaging. The method is formulated…

Other Quantitative Biology · Quantitative Biology 2009-04-23 M. Andrecut

Time-resolved illumination provides rich spatio-temporal information for applications such as accurate depth sensing or hidden geometry reconstruction, becoming a useful asset for prototyping and as input for data-driven approaches.…

Signal Processing · Electrical Eng. & Systems 2023-08-31 Diego Royo , Zesheng Huang , Yun Liang , Boyan Song , Adolfo Muñoz , Diego Gutierrez , Julio Marco

This paper investigates the inverse random source problem for elastic waves in three dimensions, where the source is assumed to be driven by an additive white noise. A novel computational method is proposed for reconstructing the variance…

Numerical Analysis · Mathematics 2025-11-04 Hao Gu , Tianjiao Wang , Xiang Xu , Yue Zhao

We develop a linearized boundary control method for the inverse boundary value problem of determining the damping coefficient in the damped wave equation. The objective is to reconstruct an unknown perturbation in a known background damping…

Analysis of PDEs · Mathematics 2026-03-11 Tianyu Yang , Yang Yang

The paper surveys recent progress in establishing uniqueness and developing inversion formulas and algorithms for the thermoacoustic tomography. In mathematical terms, one deals with a rather special inverse problem for the wave equation.…

Analysis of PDEs · Mathematics 2009-02-02 M. Agranovsky , P. Kuchment , L. Kunyansky

We explore a planar GaAs/AlAs photonic microcavity using pump-probe spectroscopy. Free carriers are excited in the GaAs with short pump pulses. The time-resolved reflectivity is spectrally resolved short probe pulses. We show experimentally…

Algorithmic recourse provides actionable recommendations to alter unfavorable predictions of machine learning models, enhancing transparency through counterfactual explanations. While significant progress has been made in algorithmic…

Machine Learning · Computer Science 2025-08-05 Xiao Han , Lu Zhang , Yongkai Wu , Shuhan Yuan

Accelerating the data acquisition of dynamic magnetic resonance imaging (MRI) leads to a challenging ill-posed inverse problem, which has received great interest from both the signal processing and machine learning community over the last…

Computer Vision and Pattern Recognition · Computer Science 2018-10-16 Chen Qin , Jo Schlemper , Jose Caballero , Anthony Price , Joseph V. Hajnal , Daniel Rueckert

Man-made environments typically comprise planar structures that exhibit numerous geometric relationships, such as parallelism, coplanarity, and orthogonality. Making full use of these relationships can considerably improve the robustness of…

Computer Vision and Pattern Recognition · Computer Science 2019-05-21 Yangbin Lin , Jialian Li , Cheng Wang , Zhonggui Chen , Zongyue Wang , Jonathan Li

Inverse obstacle scattering is the recovery of an obstacle boundary from the scattering data produced by incident waves. This shape recovery can be done by iteratively solving a PDE-constrained optimization problem for the obstacle…

Numerical Analysis · Mathematics 2023-08-02 Travis Askham , Carlos Borges , Jeremy Hoskins , Manas Rachh