相关论文: A Novel Interpretation of the Radon Transform's Ra…
Poisson distributed measurements in inverse problems often stem from Poisson point processes that are observed through discretized or finite-resolution detectors, one of the most prominent examples being positron emission tomography (PET).…
The advent of advanced crystallographic techniques has shifted structural biology from static, single-conformer models toward probing protein dynamics. Extracting cooperative motions from temporally and spatially averaged electron density…
The circular Radon transform integrates a function over the set of all spheres with a given set of centers. The problem of injectivity of this transform (as well as inversion formulas, range descriptions, etc.) arises in many fields from…
Estimating camera poses is a fundamental task for 3D reconstruction and remains challenging given sparsely sampled views (<10). In contrast to existing approaches that pursue top-down prediction of global parametrizations of camera…
Superresolution theory and techniques seek to recover signals from samples in the presence of blur and noise. Discrete image registration can be an approach to fuse information from different sets of samples of the same signal. Quantization…
We consider the inverse problem of the broken ray transform (sometimes also referred to as the V-line transform). Explicit image reconstruction formulas are derived and tested numerically. The obtained formulas are generalizations of the…
We consider an inverse problem arising in thermo-/photo- acoustic tomography that amounts to reconstructing a function $f$ from its circular or spherical means with the centers lying on a given measurement surface. (Equivalently, these…
Clinical diagnosis is a highly specialized discipline requiring both domain expertise and strict adherence to rigorous guidelines. While current AI-driven medical research predominantly focuses on knowledge graphs or natural text…
Exploring motion information is important for the motion deblurring task. Recent the window-based transformer approaches have achieved decent performance in image deblurring. Note that the motion causing blurry results is usually composed…
Numerous regularization methods for deformable image registration aim at enforcing smooth transformations, but are difficult to tune-in a priori and lack a clear physical basis. Physically inspired strategies have emerged, offering a sound…
This paper develops projection pursuit for discrete data using the discrete Radon transform. Discrete projection pursuit is presented as an exploratory method for finding informative low dimensional views of data such as binary vectors,…
We study inversion of the spherical Radon transform with centers on a sphere (the data acquisition set). Such inversions are essential in various image reconstruction problems arising in medical, radar and sonar imaging. In the case of…
We study numerical methods of tomography in domains with a reflecting obstacle. It will be shown that tomography with sets containing both broken rays, i.e. rays reflecting at the obstacle, as well as unbroken rays, has a smaller error…
The MARS scanner is designed for the x-ray spectroscopic study of samples with the aid of computer tomography methods. Computer tomography allows the reconstruction of slices of an investigated sample using a set of shadow projections…
Photon counting detection is a promising approach toward effectively reducing the radiation dose in x-ray computed tomography (CT). Full CT reconstruction from a fraction of the detected photons required by scintillation-based detectors has…
Extracting approximate eigenpairs from a prescribed subspace is of fundamental importance in eigenvalue computation. While projecting the target eigenvector onto the subspace yields satisfactory accuracy, extracting an approximate eigenpair…
This work develops new numerical methods for the solution of the tomography problem in domains with reflecting obstacles. We compare the solution's performance for Lambertian reflection, for classical tomography with unbroken rays and for…
We want to approximate general multivariate probability density functions by deterministic sample sets. For optimal sampling, the closeness to the given continuous density has to be assessed. This is a difficult challenge in multivariate…
An explicit series solution is proposed for the inversion of the spherical mean Radon transform. Such an inversion is required in problems of thermo- and photo- acoustic tomography. Closed-form inversion formulae are currently known only…
We introduce a novel, computationally inexpensive approach for imaging with an active array of sensors, which probe an unknown medium with a pulse and measure the resulting waves. The imaging function uses a data driven estimate of the…