Related papers: Deconvolution with unknown noise distribution is p…
This paper focuses on solving a challenging problem of blind deconvolution demixing involving modulated inputs. Specifically, multiple input signals $s_n(t)$, each bandlimited to $B$ Hz, are modulated with known random sequences $r_n(t)$…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…
Non-stationary blind super-resolution is an extension of the traditional super-resolution problem, which deals with the problem of recovering fine details from coarse measurements. The non-stationary blind super-resolution problem appears…
This article describes a fast iterative algorithm for image denoising and deconvolution with signal-dependent observation noise. We use an optimization strategy based on variable splitting that adapts traditional Gaussian noise-based…
We study the rate of decay of the probability of error for distinguishing between a sparse signal with noise, modeled as a sparse mixture, from pure noise. This problem has many applications in signal processing, evolutionary biology,…
Many machine learning problems can be characterized by mutual contamination models. In these problems, one observes several random samples from different convex combinations of a set of unknown base distributions and the goal is to infer…
Consider discrete values of functions shifted by unobserved translation effects, which are independent realizations of a random variable with unknown distribution $\mu$, modeling the variability in the response of each individual. Our aim…
Denoising Score Matching estimates the score of a noised version of a target distribution by minimizing a regression loss and is widely used to train the popular class of Denoising Diffusion Models. A well known limitation of Denoising…
While deep learning offers powerful capabilities for scientific research, its application is often hindered by a lack of quantitative reliability. To address this, we introduce a probabilistic denoising framework that simultaneously…
Most existing image denoising approaches assumed the noise to be homogeneous white Gaussian distributed with known intensity. However, in real noisy images, the noise models are usually unknown beforehand and can be much more complex. This…
In this paper we study the high-dimensional super-resolution imaging problem. Here we are given an image of a number of point sources of light whose locations and intensities are unknown. The image is pixelized and is blurred by a known…
We consider a standard distributed optimization problem in which networked nodes collaboratively minimize the sum of their locally known convex costs. For this setting, we address for the first time the fundamental problem of design and…
Unsupervised transfer learning-based change detection methods exploit the feature extraction capability of pre-trained networks to distinguish changed pixels from the unchanged ones. However, their performance may vary significantly…
Linear regression without correspondences concerns the recovery of a signal in the linear regression setting, where the correspondences between the observations and the linear functionals are unknown. The associated maximum likelihood…
We consider an unsupervised bilevel optimization strategy for learning regularization parameters in the context of imaging inverse problems in the presence of additive white Gaussian noise. Compared to supervised and semi-supervised metrics…
Low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the case when each instance has a fixed,…
Given samples (x_1,...,x_m) and (z_1,...,z_n) which we believe are independent realizations of random variables X and Z respectively, where we further believe that Z=X+Y with Y independent of X, the problem is to estimate the distribution…
In many real-world classification problems, the labels of training examples are randomly corrupted. Most previous theoretical work on classification with label noise assumes that the two classes are separable, that the label noise is…
If a functional in an inverse problem can be estimated with parametric rate, then the minimax rate gives no information about the ill-posedness of the problem. To have a more precise lower bound, we study semiparametric efficiency in the…
We consider the problem of recovering two unknown vectors, $\boldsymbol{w}$ and $\boldsymbol{x}$, of length $L$ from their circular convolution. We make the structural assumption that the two vectors are members of known subspaces, one with…