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This paper is devoted to the construction of order reduced method of fourth order problems. A framework is presented such that a problem on a high-regularity space can be deduced in a constructive way to an equivalent problem on three…
While Fourier ptychography (FP) offers super-resolution for macroscopic imaging, its real-world application is severely hampered by atmospheric turbulence, a challenge largely unaddressed in existing macroscopic FP research operating under…
Atom interferometers are sensitive to a wide range of forces by encoding their signals in interference patterns of matter waves. To estimate the magnitude of these forces, the underlying phase shifts they imprint on the atoms must be…
We review work on `decomposition,' a property of two-dimensional theories with 1-form symmetries and, more generally, d-dimensional theories with (d-1)-form symmetries. Decomposition is the observation that such quantum field theories are…
Phase unwrapping is a key problem in many coherent imaging systems, such as synthetic aperture radar (SAR) interferometry. A general formulation for redundant integration of finite differences for phase unwrapping (Costantini et al., 2010)…
We present a learning-based approach for removing unwanted obstructions, such as window reflections, fence occlusions, or adherent raindrops, from a short sequence of images captured by a moving camera. Our method leverages motion…
It is proposed a few-atom Doppler-sensitive absorption spectroscopy scheme resolving the long-standing dilemma regarding the nature of an atomic quantum translational motion (superpositional or non-superpositional) and its measurement…
In this paper, we present methods for image compression on the basis of eigenvalue decomposition of normal matrices. The proposed methods are convenient and self-explanatory, requiring fewer and easier computations as compared to some…
We propose a novel Auto-Regressive (AR) image generation approach that models images as hierarchical compositions of interpretable visual layers. While AR models have achieved transformative success in language modeling, replicating this…
We generalize the definition of convolution of vectors and tensors on the 2-sphere, and prove that it commutes with differential operators. Moreover, vectors and tensors that are normal/tangent to the spherical surface remain so after the…
We characterize when a coherent state or continuous frame for a Hilbert space may be sampled to obtain a frame, which solves the discretization problem for continuous frames. In particular, we prove that every bounded continuous frame for a…
In this work, we study the perception problem for sampled surfaces (possibly with boundary) using tools from computational topology, specifically, how to identify their underlying topology starting from point-cloud samples in space, such as…
Aero-optical beam control relies on the development of low-latency forecasting techniques to quickly predict wavefronts aberrated by the Turbulent Boundary Layer (TBL) around an airborne optical system, and its study applies to a…
Although many long-range imaging systems are designed to support extended vision applications, a natural obstacle to their operation is degradation due to atmospheric turbulence. Atmospheric turbulence causes significant degradation to…
Inverse medium problems involve the reconstruction of a spatially varying unknown medium from available observations by exploring a restricted search space of possible solutions. Standard grid-based representations are very general but all…
Decomposing discrete signals such as images into components is vital in many applications, and this paper propose a framework to produce filtering banks to accomplish this task. The framework is an equation set which is ill-posed, and thus…
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…
All-sky observations of the Milky Way show both Galactic and non-Galactic diffuse emission, for example from interstellar matter or the cosmic microwave background (CMB). The different emitters are partly superimposed in the measurements,…
Object detectors achieve strong performance under nominal imaging conditions but can fail silently when exposed to blur, noise, compression, adverse weather, or resolution changes. In safety-critical settings, it is therefore insufficient…
Tensors naturally model many real world processes which generate multi-aspect data. Such processes appear in many different research disciplines, e.g, chemometrics, computer vision, psychometrics and neuroimaging analysis. Tensor…