Related papers: Autonomous Gaussian Decomposition
The Hermite-Gaussian (HG) modes make up a complete and orthonormal basis, which have been extensively used to describe optical fields. Here, we demonstrate, for the first time to our knowledge, deep learning-based modal decomposition (MD)…
Automatic differentiation (AD) is an ensemble of techniques that allow to evaluate accurate numerical derivatives of a mathematical function expressed in a computer programming language. In this paper we use AD for stating and solving solid…
Active Appearance Models (AAMs) are one of the most popular and well-established techniques for modeling deformable objects in computer vision. In this paper, we study the problem of fitting AAMs using Compositional Gradient Descent (CGD)…
Large scale datasets created from crowdsourced labels or openly available data have become crucial to provide training data for large scale learning algorithms. While these datasets are easier to acquire, the data are frequently noisy and…
The volume of image repositories continues to grow. Despite the availability of content-based addressing, we still lack a lightweight tool that allows us to discover images of distinct characteristics from a large collection. In this paper,…
We propose a Standing Wave Decomposition (SWD) approximation to Gaussian Process regression (GP). GP involves a costly matrix inversion operation, which limits applicability to large data analysis. For an input space that can be…
We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike…
The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…
Surgical reconstruction of dynamic tissues from endoscopic videos is a crucial technology in robot-assisted surgery. The development of Neural Radiance Fields (NeRFs) has greatly advanced deformable tissue reconstruction, achieving…
Reconstructing and segmenting scenes from unconstrained photo collections obtained from the Internet is a novel but challenging task. Unconstrained photo collections are easier to get than well-captured photo collections. These…
Dynamic Mode Decomposition (DMD) is a data based modeling tool that identifies a matrix to map a quantity at some time instant to the same quantity in future. We design a new version which we call Adaptive Dynamic Mode Decomposition (ADMD)…
Recently, 3D Gaussian Splatting (3D-GS) has prevailed in novel view synthesis, achieving high fidelity and efficiency. However, it often struggles to capture rich details and complete geometry. Our analysis reveals that the 3D-GS…
Anomaly detection with multivariate Gaussian distribution, which we refer to as Gassian anomaly detection (GAD), is a prominent task in data mining and machine learning. The core task of GAD is to obtain the mean value vector and the…
Experimental spatio-temporal flow data often contain gaps or other types of undesired artifacts. To reconstruct flow data in the compromised or missing regions, a data completion method based on spectral proper orthogonal decomposition…
A new method is proposed to get image features' geometric information. Using Gaussian as an input signal, a theoretical optimal solution to calculate feature's affine shape is proposed. Based on analytic result of a feature model, the…
Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown parameter from independent samples of data by iteratively…
In this paper, we introduce a new, fast data assimilation algorithm for a 2D linear advection equation with divergence-free coefficients. We first apply the nodal discontinuous Galerkin (DG) method to discretize the advection equation, and…
Directed acyclic graphs (DAGs) are used for modeling causal relationships, dependencies, and flows in various systems. However, spectral analysis becomes impractical in this setting because the eigendecomposition of the adjacency matrix…
We present a new iterative deblending method to separate the host galaxy (HG) and their Active Galactic Nuclei (AGN) emission with the use of Integral Field spectroscopic (IFS) data. The method decomposes the resolved HG emission from the…
This paper investigates the recovery of a spectrally sparse signal from its partially revealed noisy entries within the framework of spectral compressive sensing. Nonconvex optimization approaches have recently been proposed based on…