Related papers: Probabilistic Recovery of Multiple Subspaces in Po…
The Johnson-Lindenstrauss (JL) Lemma introduced the concept of dimension reduction via a random linear map, which has become a fundamental technique in many computational settings. For a set of $n$ points in $\mathbb{R}^d$ and any fixed…
Poisson Surface Reconstruction is a widely-used algorithm for reconstructing a surface from an oriented point cloud. To facilitate applications where only partial surface information is available, or scanning is performed sequentially, a…
We here study whether training biases can make hidden neurons specialize in minimal one-hidden-layer MLPs, and whether such specialization improves prototype-based reconstruction of the training dataset from the learned weights. We consider…
We introduce a continuous global optimization method to the field of surface reconstruction from discrete noisy cloud of points with weak information on orientation. The proposed method uses an energy functional combining flux-based…
In this work, we propose an algorithm for solving exact sparse linear regression problems over a network in a distributed manner. Particularly, we consider the problem where data is stored among different computers or agents that seek to…
3D Point clouds (PCs) are commonly used to represent 3D scenes. They can have millions of points, making subsequent downstream tasks such as compression and streaming computationally expensive. PC sampling (selecting a subset of points) can…
Given a set of points \F in a high dimensional space, the problem of finding a union of subspaces \cup_i V_i\subset \R^N that best explains the data \F increases dramatically with the dimension of \R^N. In this article, we study a class of…
In this paper we consider a new problem of minimizing an M-convex function under L1-distance constraint (MML1); the constraint is given by an upper bound for L1-distance between a feasible solution and a given "center." This is motivated by…
We study the recovery of functions in various norms, including $L_p$ with $1\le p\le\infty$, based on function evaluations. We obtain worst case error bounds for general classes of functions in terms of the best $L_2$-approximation from a…
This paper studies the problem of approximating a function $f$ in a Banach space $X$ from measurements $l_j(f)$, $j=1,\dots,m$, where the $l_j$ are linear functionals from $X^*$. Most results study this problem for classical Banach spaces…
Point cloud compression plays a crucial role in reducing the huge cost of data storage and transmission. However, distortions can be introduced into the decompressed point clouds due to quantization. In this paper, we propose a novel…
In this paper, we propose a deep hierarchical attention context model for lossless attribute compression of point clouds, leveraging a multi-resolution spatial structure and residual learning. A simple and effective Level of Detail (LoD)…
Due to the diverse sparsity, high dimensionality, and large temporal variation of dynamic point clouds, it remains a challenge to design an efficient point cloud compression method. We propose to code the geometry of a given point cloud by…
We study the cluster recovery problem in the semi-supervised active clustering framework. Given a finite set of input points, and an oracle revealing whether any two points lie in the same cluster, our goal is to recover all clusters…
Designing computational experiments involving $\ell_1$ minimization with linear constraints in a finite-dimensional, real-valued space for receiving a sparse solution with a precise number $k$ of nonzero entries is, in general, difficult.…
We address the following generalization $P$ of the Lowner-John ellipsoid problem. Given a (non necessarily convex) compact set $K\subset R^n$ and an even integer $d$, find an homogeneous polynomial $g$ of degree $d$ such that $K\subset…
The typical approach for recovery of spatially correlated signals is regularized least squares with a coupled regularization term. In the Bayesian framework, this algorithm is seen as a maximum-a-posterior estimator whose postulated prior…
The low-degree polynomial framework has been highly successful in predicting computational versus statistical gaps for high-dimensional problems in average-case analysis and machine learning. This success has led to the low-degree…
We study the problem of exact support recovery based on noisy observations and present Refined Least Squares (RLS). Given a set of noisy measurement $$ \myvec{y} = \myvec{X}\myvec{\theta}^* + \myvec{\omega},$$ and $\myvec{X} \in…
In this paper we theoretically study exact recovery of sparse vectors from compressed measurements by minimizing a general nonconvex function that can be decomposed into the sum of single variable functions belonging to a class of smooth…