相关论文: Permutation recovery of spikes in noisy high-dimen…
In this paper, we find a sample complexity bound for learning a simplex from noisy samples. Assume a dataset of size $n$ is given which includes i.i.d. samples drawn from a uniform distribution over an unknown simplex in $\mathbb{R}^K$,…
We consider the problem of signal recovery on graphs as graphs model data with complex structure as signals on a graph. Graph signal recovery implies recovery of one or multiple smooth graph signals from noisy, corrupted, or incomplete…
Replica exchange stochastic gradient Langevin dynamics (reSGLD) has shown promise in accelerating the convergence in non-convex learning; however, an excessively large correction for avoiding biases from noisy energy estimators has limited…
We study symmetric spiked matrix models with respect to a general class of noise distributions. Given a rank-1 deformation of a random noise matrix, whose entries are independently distributed with zero mean and unit variance, the goal is…
This article discusses a generalization of the 1-dimensional multi-reference alignment problem. The goal is to recover a hidden signal from many noisy observations, where each noisy observation includes a random translation and random…
Recent progress in robust statistical learning has mainly tackled convex problems, like mean estimation or linear regression, with non-convex challenges receiving less attention. Phase retrieval exemplifies such a non-convex problem,…
In this paper, we study the estimation of a rank-one spiked tensor in the presence of heavy tailed noise. Our results highlight some of the fundamental similarities and differences in the tradeoff between statistical and computational…
A variational approach to reconstruction of phase and amplitude of a complex-valued object from Poissonian intensity observations is developed. The observation model corresponds to the typical optical setups with a phase modulation of…
In this paper we consider the problem of sparse signal recovery in Multiple Measurement Vectors (MMVs) case. Recently, ample researches have been conducted to solve this problem and diverse methods are proposed, one of which is deep neural…
In diverse microscopy modalities, sensors measure only real-valued intensities. Additionally, the sensor readouts are affected by Poissonian-distributed photon noise. Traditional restoration algorithms typically aim to minimize the mean…
The sequential analysis of the problem of joint signal detection and signal-to-noise ratio (SNR) estimation for a linear Gaussian observation model is considered. The problem is posed as an optimization setup where the goal is to minimize…
Much of studies on neural computation are based on network models of static neurons that produce analog output, despite the fact that information processing in the brain is predominantly carried out by dynamic neurons that produce discrete…
With the rapid development of diffusion models and flow-based generative models, there has been a surge of interests in solving noisy linear inverse problems, e.g., super-resolution, deblurring, denoising, colorization, etc, with generative…
Inverse rendering aims to recover scene geometry, material properties, and lighting from multi-view images. Given the complexity of light-surface interactions, importance sampling is essential for the evaluation of the rendering equation,…
In many applications, flow measurements are usually sparse and possibly noisy. The reconstruction of a high-resolution flow field from limited and imperfect flow information is significant yet challenging. In this work, we propose an…
Fabrication process variations can significantly influence the performance and yield of nano-scale electronic and photonic circuits. Stochastic spectral methods have achieved great success in quantifying the impact of process variations,…
A host of problems involve the recovery of structured signals from a dimensionality reduced representation such as a random projection; examples include sparse signals (compressive sensing) and low-rank matrices (matrix completion). Given…
Fluid flows are omnipresent in nature and engineering disciplines. The reliable computation of fluids has been a long-lasting challenge due to nonlinear interactions over multiple spatio-temporal scales. The compressible Navier-Stokes…
Hyperspectral images (HSIs) are often corrupted by a mixture of several types of noise during the acquisition process, e.g., Gaussian noise, impulse noise, dead lines, stripes, and many others. Such complex noise could degrade the quality…
We consider the \textit{phase retrieval} problem of recovering a sparse signal $\mathbf{x}$ in $\mathbb{R}^d$ from intensity-only measurements in dimension $d \geq 2$. Phase retrieval can be equivalently formulated as the problem of…