Related papers: Atomic Norm Denoising for Complex Exponentials wit…
The goal of blind image deblurring is to recover a sharp image from a motion blurred one without knowing the camera motion. Current state-of-the-art methods have a remarkably good performance on images with no noise or very low noise…
Background noise in many fields such as medical imaging poses significant challenges for accurate diagnosis, prompting the development of denoising algorithms. Traditional methodologies, however, often struggle to address the complexities…
Many interesting tasks in image restoration can be cast as linear inverse problems. A recent family of approaches for solving these problems uses stochastic algorithms that sample from the posterior distribution of natural images given the…
The blind deconvolution problem aims to recover a rank-one matrix from a set of rank-one linear measurements. Recently, Charisopulos et al. introduced a nonconvex nonsmooth formulation that can be used, in combination with an initialization…
Motivated by recent work on two dimensional (2D) harmonic component recovery via atomic norm minimization (ANM), a fast 2D direction of arrival (DOA) off-grid estimation based on ANM method was proposed. By introducing a matrix atomic norm…
This work concerns noise reduction for one-dimensional spectra in the case that the signal is corrupted by an additive white noise. The proposed method starts with mapping the noisy spectrum to a partial circulant matrix. In virtue of…
During the image acquisition process, noise is usually added to the data mainly due to physical limitations of the acquisition sensor, and also regarding imprecisions during the data transmission and manipulation. In that sense, the…
Optimization algorithms for solving nonconvex inverse problem have attracted significant interests recently. However, existing methods require the nonconvex regularization to be smooth or simple to ensure convergence. In this paper, we…
Blind deconvolution is a technique to recover an original signal without knowing a convolving filter. It is naturally formulated as a minimization of a quartic objective function under some assumption. Because its differentiable part does…
Regularized methods have been widely applied to system identification problems without known model structures. This paper proposes an infinite-dimensional sparse learning algorithm based on atomic norm regularization. Atomic norm…
This paper proposes a new technique based on nonlinear Adaptive Median filter (AMF) for image restoration. Image denoising is a common procedure in digital image processing aiming at the removal of noise, which may corrupt an image during…
We propose an effective method for removing thermal vibrations that complicate the task of analyzing complex dynamics in atomistic simulation of condensed matter. Our method iteratively subtracts thermal noises or perturbations in atomic…
Atomic norm minimization is a convex optimization framework to recover point sources from a subset of their low-pass observations, or equivalently the underlying frequencies of a spectrally-sparse signal. When the amplitudes of the sources…
We propose several new nonsmooth Newton methods for solving convex composite optimization problems with polyhedral regularizers, while avoiding the computation of complicated second-order information on these functions. Under the…
This paper is concerned with the regularization of large-scale discrete inverse problems by means of inexact Krylov methods. Specifically, we derive two new inexact Krylov methods that can be efficiently applied to unregularized or…
Sparse channel estimation for massive multiple-input multiple-output systems has drawn much attention in recent years. The required pilots are substantially reduced when the sparse channel state vectors can be reconstructed from a few…
Being one of the oldest and most basic problems in image processing, image denoising has seen a resurgence spurred by rapid advances in deep learning. Yet, most modern denoising architectures make limited use of the technical knowledge…
Circle- and sphere-valued data play a significant role in inverse problems like magnetic resonance phase imaging and radar interferometry, in the analysis of directional information, and in color restoration tasks. In this paper, we aim to…
We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on the discrepancy principle. We formulate the problem as an equality constrained optimization problem, where the…
Whenever we use devices to take measurements, calibration is indispensable. While the purpose of calibration is to reduce bias and uncertainty in the measurements, it can be quite difficult, expensive, and sometimes even impossible to…