Related papers: Deconvolution with Unknown Error Distribution Inte…
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 refine and extend an earlier MDL denoising criterion for wavelet-based denoising. We start by showing that the denoising problem can be reformulated as a clustering problem, where the goal is to obtain separate clusters for informative…
In many learning applications, data are collected from multiple sources, each providing a \emph{batch} of samples that by itself is insufficient to learn its input-output relationship. A common approach assumes that the sources fall in one…
This paper considers the problem of adaptive estimation of a mean pattern in a randomly shifted curve model. We show that this problem can be transformed into a linear inverse problem, where the density of the random shifts plays the role…
In this paper, we propose a fully convolutional networks for iterative non-blind deconvolution We decompose the non-blind deconvolution problem into image denoising and image deconvolution. We train a FCNN to remove noises in the gradient…
In this paper, we study sparse spike deconvolution over the space of complex-valued measures when the input measure is a finite sum of Dirac masses. We introduce a modified version of the Beurling Lasso (BLasso), a semi-definite program…
Image deblurring is an ill-posed problem with multiple plausible solutions for a given input image. However, most existing methods produce a deterministic estimate of the clean image and are trained to minimize pixel-level distortion. These…
Matrix decomposition is a popular and fundamental approach in machine learning and data mining. It has been successfully applied into various fields. Most matrix decomposition methods focus on decomposing a data matrix from one single…
Ptychography is a computational imaging technique that aims to reconstruct the object of interest from a set of diffraction patterns. Each of these is obtained by a localized illumination of the object, which is shifted after each…
Conditional density estimation (CDE) is the task of estimating the probability of an event conditioned on some inputs. A neural network (NN) can also be used to compute the output distribution for continuous-domain, which can be viewed as…
We propose self-diffusion, a novel framework for solving inverse problems without relying on pretrained generative models. Traditional diffusion-based approaches require training a model on a clean dataset to learn to reverse the forward…
This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines…
We study a stochastic optimization problem in which the sampling distribution depends on the decision variable, and the available samples are generated through an iterate-dependent Markov chain. Such settings arise naturally in problems…
We develop a data-driven approach for signal denoising that utilizes variational mode decomposition (VMD) algorithm and Cramer Von Misses (CVM) statistic. In comparison with the classical empirical mode decomposition (EMD), VMD enjoys…
Situations in many fields of research, such as digital communications, nuclear physics and mathematical finance, can be modelled with random matrices. When the matrices get large, free probability theory is an invaluable tool for describing…
Density deconvolution deals with the estimation of the probability density function $f$ of a random signal from $n\geq1$ data observed with independent and known additive random noise. This is a classical problem in statistics, for which…
In this paper the elicitation of probabilities from human experts is considered as a measurement process, which may be disturbed by random 'measurement noise'. Using Bayesian concepts a second order probability distribution is derived…
This paper demonstrates a practical method that can correct spatial varying blur from a set of images of the same object. The algorithm jointly estimates the object and local point spread functions~(PSF). The method prioritizes sections…
Computational sensing strategies often suffer from calibration errors in the physical implementation of their ideal sensing models. Such uncertainties are typically addressed by using multiple, accurately chosen training signals to recover…
In this work we introduce a novel stochastic algorithm dubbed SNIPS, which draws samples from the posterior distribution of any linear inverse problem, where the observation is assumed to be contaminated by additive white Gaussian noise.…