Related papers: Some convolution inversion questions
Image deblurring is an ill-posed problem with multiple plausible solutions for a given input image. However, most existing methods produce a deterministic estimate of the clean image and are trained to minimize pixel-level distortion. These…
The bending of lightrays by the gravitational field of a ``lens'' that is moving relative to the observer is calculated within the approximation of weak fields, small angles and thin lenses. Up to first order in $v/c$ -- and assuming the…
We show that symmetrically padded convolution can be analytically inverted via DFT. We comprehensively analyze several different symmetric and anti-symmetric padding modes and show that multiple cases exist where the inversion can be…
A slab of negatively refracting material, thickness d, can focus an image at a distance 2d from the object. The negative slab cancels an equal thickness of positive space. This result is a special case of a much wider class of focussing:…
We show that the errors due to atmospheric refraction are present in the magnitudes determined with the Difference Images Analysis method. In case of single, unblended stars the size of the effect agrees with the theoretical prediction. But…
Blended light is an important source of degeneracy in the characterization of microlensing events, particularly in binary-lens and high magnification events. We show how the techniques of image subtraction can be applied to form an image of…
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…
This paper presents a blind detection and compensation technique for camera lens geometric distortions. The lens distortion introduces higher-order correlations in the frequency domain and in turn it can be detected using higher-order…
This paper reviews recent results on hybrid inverse problems, which are also called coupled-physics inverse problems of multi-wave inverse problems. Inverse problems tend to be most useful in, e.g., medical and geophysical imaging, when…
It is known that a relative translational motion between the deflector and the observer affects gravitational lensing. In this paper, a lens equation is obtained to describe such effects on actual lensing observables. Results can be easily…
Several recent works have empirically observed that Convolutional Neural Nets (CNNs) are (approximately) invertible. To understand this approximate invertibility phenomenon and how to leverage it more effectively, we focus on a theoretical…
Inversion of function sinc(x) is studied. New series and integral representations of branches of inverse function are obtained using Fourier analysis.
The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…
Capturing photographs with wrong exposures remains a major source of errors in camera-based imaging. Exposure problems are categorized as either: (i) overexposed, where the camera exposure was too long, resulting in bright and washed-out…
With the inexorable digitalisation of the modern world, every subset in the field of technology goes through major advancements constantly. One such subset is digital images which are ever so popular. Images can not always be as visually…
We present a rigorous mathematical solution to photometric redshift estimation and the more general inversion problem. The challenge we address is to meaningfully constrain unknown properties of astronomical sources based on given…
We propose an experiment using a conventional optical telescope to determine whether aberration of starlight results from special relativistic effects external to a measurement sensor or from optical effects within a sensor. The proposed…
The large variety of Fourier transforms in geometric algebras inspired the straight forward definition of ``A General Geometric Fourier Transform`` in Bujack et al., Proc. of ICCA9, covering most versions in the literature. We showed which…
Convolutional neural networks (CNNs) have demonstrated remarkable success in vision-related tasks. However, their susceptibility to failing when inputs deviate from the training distribution is well-documented. Recent studies suggest that…
A new model-based image adjustment for the enhancement of multi-resolution image fusion or pansharpening is proposed. Such image adjustment is needed for most pansharpening methods using panchromatic band and/or intensity image (calculated…