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We present a new computed tomography (CT) method for inverting the Radon transform in 2D. The idea relies on the geometry of the flat torus, hence we call the new method Torus CT. We prove new inversion formulas for integrable functions,…
X-ray computed tomography (CT) reconstructs cross-sectional images from projection data. However, ionizing X-ray radiation associated with CT scanning might induce cancer and genetic damage. Therefore, the reduction of radiation dose has…
This work is concerned with applying iterative image reconstruction, based on constrained total-variation minimization, to low-intensity X-ray CT systems that have a high sampling rate. Such systems pose a challenge for iterative image…
Computed Tomography (CT) imaging is one of the most influential diagnostic methods. In clinical reconstruction, an effective energy is used instead of total X-ray spectrum. This approximation causes an accuracy decline. To increase the…
In this work, we investigate the application of deep learning methods for computed tomography in the context of having a low-data regime. As motivation, we review some of the existing approaches and obtain quantitative results after…
Tomographic investigations are a central tool in medical applications, allowing doctors to image the interior of patients. The corresponding measurement process is commonly modeled by the Radon transform. In practice, the solution of the…
In this paper, we propose a sinogram inpainting network (SIN) to solve limited-angle CT reconstruction problem, which is a very challenging ill-posed issue and of great interest for several clinical applications. A common approach to the…
This revisit gives a survey on the analytical methods for the inverse exponential Radon transform which has been investigated in the past three decades from both mathematical interests and medical applications such as nuclear medicine…
We present a deep learning-based computational algorithm for inversion of circular Radon transforms in the partial radial setup, arising in photoacoustic tomography. We first demonstrate that the truncated singular value decomposition-based…
X-ray Computed Tomography (CT) is an important tool in medical imaging to obtain a direct visualization of patient anatomy. However, the x-ray radiation exposure leads to the concern of lifetime cancer risk. Low-dose CT scan can reduce the…
The inversion of linear systems is a fundamental step in many inverse problems. Computational challenges exist when trying to invert large linear systems, where limited computing resources mean that only part of the system can be kept in…
The traditional approaches to computerized tomography (CT) depend on the samples of Radon transform at multiple angles. In optics, the real time imaging requires the reconstruction of an object by the samples of Radon transform at a single…
Computed Tomography (CT) is an essential non-destructive three dimensional imaging modality used in medicine, security screening, and inspection of manufactured components. Typical CT data acquisition entails the collection of a thousand or…
The image reconstruction problem consists in finding an approximation of a function f starting from its Radon transform Rf. This problem arises in the ambit of medical imaging when one tries to reconstruct the internal structure of the…
Defective and inconsistent responses in CT detectors can cause ring and streak artifacts in the reconstructed images, making them unusable for clinical purposes. In recent years, several ring artifact reduction solutions have been proposed…
Limited-angle computed tomography (CT) image reconstruction is a challenging reconstruction problem in the fields of CT. With the development of deep learning, the generative adversarial network (GAN) perform well in image restoration by…
The Radon transform is a linear integral transform that mimics the data formation process in medical imaging modalities like X-ray Computerized Tomography and Positron Emission Tomography. The Hough transform is a pattern recognition…
We introduce a new CT image reconstruction algorithm that is less affected by various artifacts. The new reconstruction algorithm is a method of minimizing the difference between synchrotron X-ray tomography data and sinograms generated…
Reconstruction of few-view x-ray Computed Tomography (CT) data is a highly ill-posed problem. It is often used in applications that require low radiation dose in clinical CT, rapid industrial scanning, or fixed-gantry CT. Existing analytic…
We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…