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Very long baseline interferometry (VLBI) makes it possible to recover images of astronomical sources with extremely high angular resolution. Most recently, the Event Horizon Telescope (EHT) has extended VLBI to short millimeter wavelengths…
We propose a novel discrete concept for the total generalized variation (TGV), which has originally been derived to reduce the staircasing effect in classical total variation (TV) regularization, in image denoising problems. We describe…
Next-generation radio interferometers, such as the Square Kilometre Array (SKA), will revolutionise our understanding of the universe through their unprecedented sensitivity and resolution. However, to realise these goals significant…
In inverse problems, prior information and a priori-based regularization techniques play important roles. In this paper, we focus on image restoration problems, especially on restoring images whose texture mainly follow one direction. In…
In this paper we demonstrate that the framework of nonlinear spectral decompositions based on total variation (TV) regularization is very well suited for image fusion as well as more general image manipulation tasks. The well-localized and…
The Event Horizon Telescope (EHT) has produced images of the plasma flow around the supermassive black holes in Sgr A* and M87* with a resolution comparable to the projected size of their event horizons. Observations with the…
The problem of image blurring is one of the most studied topics in the field of image processing. Image blurring is caused by various factors such as hand or camera shake. To restore the blurred image, it is necessary to know information…
Spatial Heterodyne Spectroscopy (SHS) is a relatively novel interferometric technique similar to the Fourier transform spectroscopy with heritage from the Michelson Interferometer. An imaging detector is used at the output of a SHS to…
Super-resolution (SR) is a technique that allows increasing the resolution of a given image. Having applications in many areas, from medical imaging to consumer electronics, several SR methods have been proposed. Currently, the best…
Neural Radiance Field (NeRF) technology has made significant strides in creating novel viewpoints. However, its effectiveness is hampered when working with sparsely available views, often leading to performance dips due to overfitting.…
In this paper, we consider the efficient numerical minimization of Tikhonov functionals resulting from total-variation (TV) regularization of linear inverse problems. Since the TV penalty is non-smooth, this is typically done either via…
While diffusion models have achieved state-of-the-art performance in Image Super-Resolution (SR), their prohibitive computational and memory demands restrict their training and inference to fixed-size inputs. The standard workaround to…
The Event Horizon Telescope (EHT) is a project to assemble a Very Long Baseline Interferometry (VLBI) network of mm wavelength dishes that can resolve strong field General Relativistic signatures near a supermassive black hole. As planned,…
Owing to its significant success, the prior imposed on gradient maps has consistently been a subject of great interest in the field of image processing. Total variation (TV), one of the most representative regularizers, is known for its…
In large-scale spatial surveys, such as the forthcoming ESA Euclid mission, images may be undersampled due to the optical sensors sizes. Therefore, one may consider using a super-resolution (SR) method to recover aliased frequencies, prior…
Total least squares (TLS) is an effective method for solving linear equations with the situations, when noise is not just in observation matrices but also in mapping matrices. Moreover, the Tikhonov regularization is widely used in plenty…
There are a large number of methods for solving under-determined linear inverse problem. Many of them have very high time complexity for large datasets. We propose a new method called Two-Stage Sparse Representation (TSSR) to tackle this…
The 3-D total variation (3DTV) is a powerful regularization term, which encodes the local smoothness prior structure underlying a hyper-spectral image (HSI), for general HSI processing tasks. This term is calculated by assuming identical…
A computational method is introduced for choosing the regularization parameter for total variation (TV) regularization. The approach is based on computing reconstructions at a few different resolutions and various values of regularization…
Strong gravitational lensing offers a wealth of astrophysical information on the background source it affects, provided the lensed source can be reconstructed as if it was seen in the absence of lensing. In the present work, we illustrate…