Related papers: Grassmannian Fusion Frames
Multilayer (or deep) networks are powerful probabilistic models based on multiple stages of a linear transform followed by a non-linear (possibly random) function. In general, the linear transforms are defined by matrices and the non-linear…
The integration of semantic information in a map allows robots to understand better their environment and make high-level decisions. In the last few years, neural networks have shown enormous progress in their perception capabilities.…
We present a signal representation framework called the sparse manifold transform that combines key ideas from sparse coding, manifold learning, and slow feature analysis. It turns non-linear transformations in the primary sensory signal…
While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However,…
A fundamental problem in robotic perception is matching identical objects or data, with applications such as loop closure detection, place recognition, object tracking, and map fusion. While the problem becomes considerably more challenging…
Generative diffusion processes are an emerging and effective tool for image and speech generation. In the existing methods, the underline noise distribution of the diffusion process is Gaussian noise. However, fitting distributions with…
In this paper, we consider optimal linear sensor fusion for obtaining a remote state estimate of a linear process based on the sensor data transmitted over lossy channels. There is no local observability guarantee for any of the sensors. It…
A randomized subspace action algorithm is investigated for fusion frame signal recovery problems. It is noted that Kaczmarz bounds provide upper bounds on the algorithm's error moments. The main question of which probability distributions…
The composite fermion formalism elegantly describes some of the most fascinating behaviours of interacting two-dimensional carriers at low temperatures and in strong perpendicular magnetic fields. In this framework, carriers minimize their…
Collections of time- and frequency-shifts of suitably chosen generators (Alltop or random vectors) proved successful for many applications in sparse recovery and related fields. It was shown in \cite{xia2005achieving} that taking a…
This paper introduces {\em fusion subspace clustering}, a novel method to learn low-dimensional structures that approximate large scale yet highly incomplete data. The main idea is to assign each datum to a subspace of its own, and minimize…
This paper introduces an online approach for identifying time-varying subspaces defined by linear dynamical systems. The approach of representing linear systems by non-parametric subspace models has received significant interest in the…
Seismic imaging from sparsely acquired data faces challenges such as low image quality, discontinuities, and migration swing artifacts. Existing convolutional neural network (CNN)-based methods struggle with complex feature distributions…
Multimodality and multichannel monitoring have become increasingly popular and accessible in engineering, Internet of Things, wearable devices, and biomedical applications. In these contexts, given the diverse and complex nature of data…
A new Riemannian geometry for the Compound Gaussian distribution is proposed. In particular, the Fisher information metric is obtained, along with corresponding geodesics and distance function. This new geometry is applied on a change…
Disturbance noises are always bounded in a practical system, while fusion estimation is to best utilize multiple sensor data containing noises for the purpose of estimating a quantity--a parameter or process. However, few results are…
Graph matching is an important and persistent problem in computer vision and pattern recognition for finding node-to-node correspondence between graph-structured data. However, as widely used, graph matching that incorporates pairwise…
Airfoil shape design is a classical problem in engineering and manufacturing. Our motivation is to combine principled physics-based considerations for the shape design problem with modern computational techniques informed by a data-driven…
In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected…
Graph neural networks (GNNs) have received tremendous attention due to their power in learning effective representations for graphs. Most GNNs follow a message-passing scheme where the node representations are updated by aggregating and…