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Phase retrieval is the nonlinear inverse problem of recovering a true signal from its Fourier magnitude measurements. It arises in many applications such as astronomical imaging, X-Ray crystallography, microscopy, and more. The problem is…
The problem of automated separation of stars and galaxies on photographic plates is revisited with two goals in mind : First, to separate galaxies from everything else (as opposed to most previous work, in which galaxies were lumped…
The detection limit of astronomical imaging observations is limited by several noise sources. Some of that noise is correlated between neighbouring image pixels and exposures, so in principle could be learned and corrected. We present an…
The work identifies the first lattice decoding solution that achieves, in the general outage-limited MIMO setting and in the high-rate and high-SNR limit, both a vanishing gap to the error-performance of the (DMT optimal) exact solution of…
In a previous paper {GN2} an effective solution of the lattice point counting problem in general domains in semisimple S-algebraic groups and affine symmetric varieties was established. The method relies on the mean ergodic theorem for the…
In this work, we consider a class of differentiable criteria for sparse image computing problems, where a nonconvex regularization is applied to an arbitrary linear transform of the target image. As special cases, it includes…
We aim to improve the Inverted Neural Radiance Fields (iNeRF) algorithm which defines the image pose estimation problem as a NeRF based iterative linear optimization. NeRFs are novel neural space representation models that can synthesize…
Sentences containing multiple semantic operators with overlapping scope often create ambiguities in interpretation, known as scope ambiguities. These ambiguities offer rich insights into the interaction between semantic structure and world…
Mixed-integer nonlinear programs (MINLPs) arise in domains such as energy systems, process engineering, and transportation, and are notoriously difficult to solve at scale due to the interplay of discrete decisions and nonlinear…
Many problems in nonlinear analysis and optimization, among them variational inequalities and minimization of convex functions, can be reduced to finding zeros (namely, roots) of set-valued operators. Hence numerous algorithms have been…
Deep learning has been widely used for solving image reconstruction tasks but its deployability has been held back due to the shortage of high-quality training data. Unsupervised learning methods, such as the deep image prior (DIP),…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
In the past years modern mathematical methods for image analysis have led to a revolution in many fields, from computer vision to scientific imaging. However, some recently developed image processing techniques successfully exploited by…
Recently, deep learning-based facial landmark detection has achieved significant improvement. However, the semantic ambiguity problem degrades detection performance. Specifically, the semantic ambiguity causes inconsistent annotation and…
In the fast developing countries it is hard to trace new buildings construction or old structures destruction and, as a result, to keep the up-to-date cadastre maps. Moreover, due to the complexity of urban regions or inconsistency of data…
We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in…
Primal-dual interior-point methods solve constrained convex optimization problems to tight tolerances with speed and robustness. Their solutions are also efficiently differentiable with respect to the problem data through the implicit…
Generative AI systems have revolutionized human interaction by enabling natural language-based coding and problem solving. However, the inherent ambiguity of natural language often leads to imprecise instructions, forcing users to…
Resolving ambiguities through interaction is a hallmark of natural language, and modeling this behavior is a core challenge in crafting AI assistants. In this work, we study such behavior in LMs by proposing a task-agnostic framework for…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…