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We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularisation, exploiting sparsity in both axisymmetric and directional scale-discretised wavelet space. Denoising, inpainting, and deconvolution problems,…
Wave equation techniques have been an integral part of geophysical imaging workflows to investigate the Earth's subsurface. Least-squares reverse time migration (LSRTM) is a linearized inversion problem that iteratively minimizes a misfit…
The CLEAN algorithm, widely used in radio interferometry for the deconvolution of radio images, performs well only if the raw radio image (dirty image) is, to good approximation, a simple convolution between the instrumental point-spread…
Modern radio telescopes will daily generate data sets on the scale of exabytes for systems like the Square Kilometre Array (SKA). Massive data sets are a source of unknown and rare astrophysical phenomena that lead to discoveries.…
Subspace learning is an important problem, which has many applications in image and video processing. It can be used to find a low-dimensional representation of signals and images. But in many applications, the desired signal is heavily…
We present a new method designed for optimal subtraction of two images with different seeing. Using image subtraction appears to be essential for the full analysis of the microlensing survey images, however a perfect subtraction of two…
Astronomy at or below the 'survey threshold' has expanded significantly since the publication of the original 'Science with the Square Kilometer Array' in 1999 and its update in 2004. The techniques in this regime may be broadly (but far…
The solution of sequences of shifted linear systems is a classic problem in numerical linear algebra, and a variety of efficient methods have been proposed over the years. Nevertheless, there still exist challenging scenarios witnessing a…
This paper presents a formulation of Snapshot Positioning as a mixed-integer least-squares problem. In snapshot positioning one estimates a position from code-phase and possibly Doppler observations of a Global Navigation Satellite Systems…
Digital co-addition of astronomical images is a common technique for increasing signal-to-noise and image depth. A modification of this simple technique has been applied to the detection of minor bodies in the Solar System: first stationary…
Astronomical images are of crucial importance for astronomers since they contain a lot of information about celestial bodies that can not be directly accessible. Most of the information available for the analysis of these objects starts…
We propose a new technique to obtain super-resolution images with radio interferometer using sparse modeling. In standard radio interferometry, sampling of ($u$, $v$) is quite often incomplete and thus obtaining an image from observed…
This paper presents two new augmented flexible (AF)-Krylov subspace methods, AF-GMRES and AF-LSQR, to compute solutions of large-scale linear discrete ill-posed problems that can be modeled as the sum of two independent random variables,…
In radio astronomy, the science output of a telescope is often limited by computational resources. This is especially true for transient and technosignature surveys that need to search high-resolution data across a large parameter space.…
We present a new method for the analysis of images, a fundamental task in observational astronomy. It is based on the linear decomposition of each object in the image into a series of localised basis functions of different shapes, which we…
Optical interferometers provide multiple wavelength measurements. In order to fully exploit the spectral and spatial resolution of these instruments, new algorithms for image reconstruction have to be developed. Early attempts to deal with…
Simply by rearranging the regions of an image, we can create a new image of any subject matter. The definition of regions is user definable, ranging from regularly and irregularly-shaped blocks, concentric rings, or even individual pixels.…
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…
The image deblurring problem consists of reconstructing images from blur and noise contaminated available data. In this AMS Notices article, we provide an overview of some well known numerical linear algebra techniques that are use for…
We have developed a novel method for co-adding multiple under-sampled images that combines the iteratively reweighted least squares and divide-and-conquer algorithms. Our approach not only allows for the anti-aliasing of the images but also…