Related papers: Manifold Optimization for High Accuracy Spatial Lo…
Radio maps provide radio frequency metrics, such as the received signal strength, at every location of a geographic area. These maps, which are estimated using a set of measurements collected at multiple positions, find a wide range of…
A new algorithm for 3D localization in multiplatform radar networks, comprising one transmitter and multiple receivers, is proposed. To take advantage of the monostatic sensor radiation pattern features, ad-hoc constraints are imposed in…
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…
There has been an emerging trend in non-Euclidean statistical analysis of aiming to recover a low dimensional structure, namely a manifold, underlying the high dimensional data. Recovering the manifold requires the noise to be of certain…
We introduce a new approach to the anisotropic Calder\'on problem, based on a map called Poisson embedding that identifies the points of a Riemannian manifold with distributions on its boundary. We give a new uniqueness result for a large…
Orthogonality constrained optimization is widely used in applications from science and engineering. Due to the nonconvex orthogonality constraints, many numerical algorithms often can hardly achieve the global optimality. We aim at…
Driven by technological breakthroughs, indoor tracking and localization have gained importance in various applications including the Internet of Things (IoT), robotics, and unmanned aerial vehicles (UAVs). To tackle some of the challenges…
In this paper, we attempt to study the conditioning of the Spherical Harmonic Matrix (SHM), which is widely used in the discrete, limited order orthogonal representation of sound fields. SHM's has been widely used in the audio applications…
We propose super-resolution MIMO channel estimators for millimeter-wave (mmWave) systems that employ hybrid analog and digital beamforming and generalized spatial modulation, respectively. Exploiting the inherent sparsity of mmWave…
Reliable positioning services are extremely important for users and devices in mountainous environments as it enables a variety of location-based applications. However, in such environments, the service reliability of conventional wireless…
In machine learning, data is usually represented in a (flat) Euclidean space where distances between points are along straight lines. Researchers have recently considered more exotic (non-Euclidean) Riemannian manifolds such as hyperbolic…
We introduce a new paradigm, $\textit{measure synchronization}$, for synchronizing graphs with measure-valued edges. We formulate this problem as maximization of the cycle-consistency in the space of probability measures over relative…
In Ultrasound Localization Microscopy (ULM), achieving high-resolution images relies on the precise localization of contrast agent particles across a series of beamformed frames. However, our study uncovers an enormous potential: The…
Many machine learning applications are naturally formulated as optimization problems on Riemannian manifolds. The main idea behind Riemannian optimization is to maintain the feasibility of the variables while moving along a descent…
Gradient descent methods are fundamental first-order optimization algorithms in both Euclidean spaces and Riemannian manifolds. However, the exact gradient is not readily available in many scenarios. This paper proposes a novel inexact…
Riemannian structures on infinite-dimensional manifolds arise naturally in shape analysis and shape optimization. These applications lead to optimization problems on manifolds which are not modeled on Banach spaces. The present article…
Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging. This is because of the…
Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…
In the machine learning field, dimensionality reduction is an important task. It mitigates the undesired properties of high-dimensional spaces to facilitate classification, compression, and visualization of high-dimensional data. During the…
The ability of robots to estimate their location is crucial for a wide variety of autonomous operations. In settings where GPS is unavailable, measurements of transmissions from fixed beacons provide an effective means of estimating a…