Related papers: Modal decomposition of astronomical images with ap…
Astronomical source deblending is the process of separating the contribution of individual stars or galaxies (sources) to an image comprised of multiple, possibly overlapping sources. Astronomical sources display a wide range of sizes and…
Images from adaptive optics systems are generally affected by significant distortions of the point spread function (PSF) across the field of view, depending on the position of natural and artificial guide stars. Image reduction techniques…
Application of deconvolution algorithms to astronomical images is often limited by variations in PSF structure over the domain of the images. One major difficulty is that Fourier methods can no longer be used for fast convolutions over the…
Photographers routinely compose multiple manipulated photos of the same scene (layers) into a single image, which is better than any individual photo could be alone. Similarly, 3D artists set up rendering systems to produce layered images…
Image decomposition is a crucial subject in the field of image processing. It can extract salient features from the source image. We propose a new image decomposition method based on convolutional neural network. This method can be applied…
Recovering high-fidelity images of the night sky from blurred observations is a fundamental problem in astronomy, where traditional methods typically fall short. In ground-based astronomy, combining multiple exposures to enhance…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
As a common image editing operation, image composition (object insertion) aims to combine the foreground from one image and another background image, to produce a composite image. However, there are many issues that could make the composite…
Intrinsic decomposition is a fundamental mid-level vision problem that plays a crucial role in various inverse rendering and computational photography pipelines. Generating highly accurate intrinsic decompositions is an inherently…
We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…
Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. The reassembly problem requires understanding the attributes…
Dynamic mode decomposition (DMD) has recently become a popular tool for the non-intrusive analysis of dynamical systems. Exploiting Proper Orthogonal Decomposition (POD) as a dimensionality reduction technique, DMD is able to approximate a…
Compositing is one of the most common operations in photo editing. To generate realistic composites, the appearances of foreground and background need to be adjusted to make them compatible. Previous approaches to harmonize composites have…
We present a two-dimensional (2-D) fitting algorithm (GALFIT, Version 3) with new capabilities to study the structural components of galaxies and other astronomical objects in digital images. Our technique improves on previous 2-D fitting…
The advancement of imaging devices and countless images generated everyday pose an increasingly high demand on image denoising, which still remains a challenging task in terms of both effectiveness and efficiency. To improve denoising…
The study of astronomical phenomena through ground-based observations is always challenged by the distorting effects of Earth's atmosphere. Traditional methods of post-facto image correction, essential for correcting these distortions,…
We consider the problem of atmospheric tomography, as it appears for example in adaptive optics systems for extremely large telescopes. We derive a frame decomposition, i.e., a decomposition in terms of a frame, of the underlying…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
Most raw data download from satellites are useless, resulting in transmission waste, one solution is to process data directly on satellites, then only transmit the processed results to the ground. Image processing is the main data…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…