Related papers: Guaranteed Blind Sparse Spikes Deconvolution via L…
Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear…
In this report, a novel efficient algorithm for recovery of jointly sparse signals (sparse matrix) from multiple incomplete measurements has been presented, in particular, the NESTA-based MMV optimization method. In a nutshell, the jointly…
Sparse blind deconvolution is the problem of estimating the blur kernel and sparse excitation, both of which are unknown. Considering a linear convolution model, as opposed to the standard circular convolution model, we derive a sufficient…
Point-spread function (PSF) estimation in spatially undersampled images is challenging because large pixels average fine-scale spatial information. This is problematic when fine-resolution details are necessary, as in optimal photometry…
Sparse dictionary coding represents signals as linear combinations of a few dictionary atoms. It has been applied to images, time series, graph signals and multi-way spatio-temporal data by jointly employing temporal and spatial…
Super-resolution techniques overcome the diffraction-limit and get very high resolutions. A category of these techniques, e.g., STED achieves this by creating an illumination spot smaller than the Airy Disk. As a result, points are…
We consider the multichannel blind deconvolution problem where we observe the output of multiple channels that are all excited with the same unknown input. From these observations, we wish to estimate the impulse responses of each of the…
This article analyzes the recovery performance of two popular finite dimensional approximations of the sparse spikes deconvolution problem over Radon measures. We examine in a unified framework both the L1 regularization (often referred to…
A considerable amount of research in harmonic analysis has been devoted to non-linear estimators of signals contaminated by additive Gaussian noise. They are implemented by thresholding coefficients in a frame, which provide a sparse signal…
We propose a new point-spread function (PSF) deconvolution algorithm for images of galaxies hosting an active galactic nucleus (AGN), designed to simultaneously enhance the spatial resolution of the host galaxy and remove the bright central…
A point-spread function describes the optics of an imaging system and can be used to correct collected images for instrumental effects. The state of the art for deconvolving images with the point-spread function is the Richardson-Lucy…
This paper introduces a novel approach for recovering sparse signals using sorted L1/L2 minimization. The proposed method assigns higher weights to indices with smaller absolute values and lower weights to larger values, effectively…
This paper proposes a precise signal recovery method with multilayered non-convex regularization, enhancing sparsity/low-rankness for high-dimensional signals including images and videos. In optimization-based signal recovery, multilayered…
Spike and Slab priors have been of much recent interest in signal processing as a means of inducing sparsity in Bayesian inference. Applications domains that benefit from the use of these priors include sparse recovery, regression and…
Suppose the signal x is realized by driving a k-sparse signal u through an arbitrary unknown stable discrete-linear time invariant system H. These types of processes arise naturally in Reflection Seismology. In this paper we are interested…
Shuffled regression and unlinked regression represent intriguing challenges that have garnered considerable attention in many fields, including but not limited to ecological regression, multi-target tracking problems, image denoising, etc.…
Many large-scale constrained optimization problems can be formulated as bilevel distributed optimization tasks over undirected networks, where agents collaborate to minimize a global cost function while adhering to constraints, relying only…
The removal of blur from a signal, in the presence of noise, is readily accomplished if the blur can be described in precise mathematical terms. However, there is growing interest in problems where the extent of blur is known only…
Accurate signal recovery or image reconstruction from indirect and possibly undersampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. Inspired by…
This note considers the spectral estimation problems of sparse spectral measures under unknown noise levels. The main technical tool is the eigenmatrix method for solving unstructured sparse recovery problems. When the noise level is…