Related papers: Robust Dimension Reduction, Fusion Frames, and Gra…

Detecting or classifying already known sparse signals contaminated by Gaussian noise from compressive measurements is different from reconstructing sparse signals, as its objective is to minimize the error probability which describes…

Minimum mean square error (MMSE) estimation of block sparse signals from noisy linear measurements is considered. Unlike in the standard compressive sensing setup where the non-zero entries of the signal are independently and uniformly…

This paper investigates theoretical properties of subsampling and hashing as tools for approximate Euclidean norm-preserving embeddings for vectors with (unknown) additive Gaussian noises. Such embeddings are sometimes called…

We proposed a new criterion \textit{noise-stability}, which revised the classical rigidity theory, for evaluation of MDS algorithms which can truthfully represent the fidelity of global structure reconstruction; then we proved the…

We introduce a new technique for reducing the dimension of the ambient space of low-degree polynomials in the Gaussian space while preserving their relative correlation structure, analogous to the Johnson-Lindenstrauss lemma. As…

Real-time density estimation is ubiquitous in many applications, including computer vision and signal processing. Kernel density estimation is arguably one of the most commonly used density estimation techniques, and the use of "sliding…

This paper presents and analyses a new family of linear subdivision schemes to refine noisy data given on triangular meshes. The subdivision rules consist of locally fitting and evaluating a weighted least squares approximating first-degree…

Support vector machines (SVMs) are powerful supervised learning tools developed to solve classification problems. However, SVMs are likely to perform poorly in the classification of imbalanced data. The rough set theory presents a…

The minimum error entropy (MEE) criterion has been verified as a powerful approach for non-Gaussian signal processing and robust machine learning. However, the implementation of MEE on robust classification is rather a vacancy in the…

Consider the minimum mean-square error (MMSE) of estimating an arbitrary random variable from its observation contaminated by Gaussian noise. The MMSE can be regarded as a function of the signal-to-noise ratio (SNR) as well as a functional…

We investigate a Gaussian mixture model (GMM) with component means constrained in a pre-selected subspace. Applications to classification and clustering are explored. An EM-type estimation algorithm is derived. We prove that the subspace…

This paper investigates the minimum mean square error (MMSE) estimation of x, given the observation y = Hx+n, when x and n are independent and Gaussian Mixture (GM) distributed. The introduction of GM distributions, represents a…

Stochastic Neighbor Embedding (SNE) algorithms like UMAP and tSNE often produce visualizations that do not preserve the geometry of noisy and high dimensional data. In particular, they can spuriously separate connected components of the…

We study the problem of scheduling sensors in a resource-constrained linear dynamical system, where the objective is to select a small subset of sensors from a large network to perform the state estimation task. We formulate this problem as…

This paper extends the concepts of Minimal Redundancy Condition (MRC) and robustness of erasures for infinite frames in Hilbert spaces. We begin by establishing a comprehensive framework for the MRC, emphasizing its importance in ensuring…

The goal of compressed sensing is to estimate a high dimensional vector from an underdetermined system of noisy linear equations. In analogy to classical compressed sensing, here we assume a generative model as a prior, that is, we assume…

Robust parameter estimation is a crucial task in several 3D computer vision pipelines such as Structure from Motion (SfM). State-of-the-art algorithms for robust estimation, however, still suffer from difficulties in converging to…

Compressed sensing (CS) demonstrates that sparse signals can be estimated from under-determined linear systems. Distributed CS (DCS) further reduces the number of measurements by considering joint sparsity within signal ensembles. DCS with…

We study the fundamental problem of learning the parameters of a high-dimensional Gaussian in the presence of noise -- where an $\varepsilon$-fraction of our samples were chosen by an adversary. We give robust estimators that achieve…

Optimization of sensor selection has been studied to monitor complex and large-scale systems with data-driven linear reduced-order modeling. An algorithm for greedy sensor selection is presented under the assumption of correlated noise in…