Related papers: Irregular sampling and the Radon transform
Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…
English: This paper concerns the image reconstruction from a few projections in Computed Tomography (CT). The main objective of this paper is to show that the problem is so ill posed that no classical method, such as analytical methods…
Common ISAR radar images and signals can be reconstructed from much fewer samples than the sampling theorem requires since they are usually sparse. Unavailable randomly positioned samples can result from heavily corrupted parts of the…
The problem of image reconstruction in thermoacoustic tomography requires inversion of a generalized Radon transform, which integrates the unknown function over circles in 2D or spheres in 3D. The paper investigates implementation of the…
In most work to date, graph signal sampling and reconstruction algorithms are intrinsically tied to graph properties, assuming bandlimitedness and optimal sampling set choices. However, practical scenarios often defy these assumptions,…
Integral field spectroscopy can map astronomical objects spatially and spectroscopically. Due to instrumental and atmospheric effects, it is common for integral field instruments to yield a sampling of the sky image that is both irregular…
Multi-modality (or multi-channel) imaging is becoming increasingly important and more widely available, e.g. hyperspectral imaging in remote sensing, spectral CT in material sciences as well as multi-contrast MRI and PET-MR in medicine.…
Modulo sampling is a promising technology to preserve amplitude information that exceeds the observable range of analog-to-digital converters during the digitization of analog signals. Since conventional methods typically reconstruct the…
We address the problem of image reconstruction from incomplete measurements, encompassing both upsampling and inpainting, within a learning-based framework. Conventional supervised approaches require fully sampled ground truth data, while…
The Lorentz Integral Transform approach allows microscopic calculations of electromagnetic reaction cross sections without explicit knowledge of final state wave functions. The necessary inversion of the transform has to be treated with…
Conventional sampling and interpolation commonly rely on discrete measurements. In this paper, we develop a theoretical framework for extrapolation of signals in higher dimensions from knowledge of the continuous waveform on bounded…
With the rapid growth of data, how to extract effective information from data is one of the most fundamental problems. In this paper, based on Tikhonov regularization, we propose an effective method for reconstructing the function and its…
In material testing applications, Computed Tomography is a well established imaging technique that allows the recovery of the attenuation map of an object. Conventional modalities exploit only primary radiation and although in the energy…
Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is…
When approximating a function that depends on a parameter, one encounters many practical examples where linear interpolation or linear approximation with respect to the parameters prove ineffective. This is particularly true for responses…
Limited angular resolution is one of the main obstacles for practical applications of light fields. Although numerous approaches have been proposed to enhance angular resolution, view selection strategies have not been well explored in this…
The iterative refinement method (IRM) has been very successfully applied in many different fields for examples the modern quantum chemical calculation and CT image reconstruction. It is proved that the refinement method can create an exact…
Let $\mR$ be the restriction of the spherical Radon transform to the set of spheres centered on a hypersurface $\mS$. We study the inversion of $\mR$ by a closed-form formula. We approach the problem by studying an oscillatory integral,…
Even though image signals are typically defined on a regular two-dimensional grid, there also exist many scenarios where this is not the case and the amplitude of the image signal only is available for a non-regular subset of pixel…
A modular method was suggested before to recover a band limited signal from the sample and hold and linearly interpolated (or, in general, an nth-order-hold) version of the regular samples. In this paper a novel approach for compensating…