Related papers: The Computational Complexity of Orientation Search…
In this work we consider the problem of recovering $n$ discrete random variables $x_i\in \{0,\ldots,k-1\}, 1 \leq i \leq n$ (where $k$ is constant) with the smallest possible number of queries to a noisy oracle that returns for a given…
Pose estimation is a general problem in computer vision with wide applications. The relative orientation of a 3D reference object can be determined from a 3D rotated version of that object, or from a projection of the rotated object to a 2D…
Orientation mapping is a widely used technique for revealing the microstructure of a polycrystalline sample. The crystalline orientation at each point in the sample is determined by analysis of the diffraction pattern, a process known as…
Cryogenic electron microscopy (Cryo-EM) has become an essential tool for capturing high-resolution biological structures. Despite its advantage in visualizations, the large storage size of Cryo-EM data file poses significant challenges for…
Cryogenic electron microscopy is widely used in structural biology, but its resolution is often limited by the dynamics of the macromolecule. Here, we developed a refinement protocol based on Gaussian mixture models that integrates particle…
We present a thorough study of the complexity of optical localized modes in two-dimensional disordered photonic crystals. Direct experimental measurements of complexity were made using an interferometric setup that allowed for extraction of…
Achieving quantum-limited motional control of optically trapped particles beyond the sub-micrometer scale is an outstanding problem in levitated optomechanics. A key obstacle is solving the light scattering problem and identifying particle…
The basic tool for solving problems in metric geometry and isotonic regression is the metric projection onto closed convex cones. Isotonicity of these projections with respect to a given order relation can facilitate finding the solutions…
Cryo-electron microscopy (cryo-EM) has become a tool of fundamental importance in structural biology, helping us understand the basic building blocks of life. The algorithmic challenge of cryo-EM is to jointly estimate the unknown 3D poses…
Super-resolution localization microscopy is based on determining the positions of individual fluorescent markers in a sample. The major challenge in reaching an ever higher localization precision lies in the limited number of collected…
A practical method utilising three-dimensional image pattern matching is proposed which, in principle, is capable of unambiguous determination of the types and positions of atoms in small molecules from defocus series collected at only a…
Motivated by applications in single-cell biology and metagenomics, we investigate the problem of matrix reordering based on a noisy disordered monotone Toeplitz matrix model. We establish the fundamental statistical limit for this problem…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
The reduced cost and computational and calibration requirements of monocular cameras make them ideal positioning sensors for mobile robots, albeit at the expense of any meaningful depth measurement. Solutions proposed by some scholars to…
Strong localization of light in three-dimensional disordered dielectric systems remains challenging to establish because it requires extremely strong recurrent scattering, while the long-lived localized contribution can be weak and masked…
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by Poisson noise. A proper data fidelity term (log-likelihood) is introduced to reflect the Poisson statistics of the noise. On…
We study the problem of localizing multiple sources of forced oscillations (FOs) and estimating their characteristics, such as frequency, phase, and amplitude, using noisy PMU measurements. For each source location, we model the input…
Single Particle Imaging techniques at X-ray lasers have made significant strides, yet the challenge of determining the orientation of freely rotating molecules during delivery remains. In this study, we propose a novel method to partially…
The Optimal Morse Matching (OMM) problem asks for a discrete gradient vector field on a simplicial complex that minimizes the number of critical simplices. It is NP-hard and has been studied extensively in heuristic, approximation, and…
In this paper, we study nonconvex constrained optimization problems with both equality and inequality constraints, covering deterministic and stochastic settings. We propose a novel first-order algorithm framework that employs a…