Related papers: A unified method for super-resolution recovery and…
Blind source separation is one of the major analysis tool to extract relevant information from multichannel data. While being central, joint deconvolution and blind source separation (DBSS) methods are scarce. To that purpose, a DBSS…
This work develops a multiscale solution decomposition (MSD) method for nonlocal-in-time problems to separate a series of known terms with multiscale singularity from the original singular solution such that the remaining unknown part…
Multiview super-resolution image reconstruction (SRIR) is often cast as a resampling problem by merging non-redundant data from multiple low-resolution (LR) images on a finer high-resolution (HR) grid, while inverting the effect of the…
We address the problem of simultaneously recovering a sequence of point source signals from observations limited to the low-frequency end of the spectrum of their summed convolution, where the point spread functions (PSFs) are unknown. By…
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…
Modern scientific simulations, observations, and large-scale experiments generate data at volumes that often exceed the limits of storage, processing, and analysis. This challenge drives the development of data reduction methods that…
The image deblurring problem consists of reconstructing images from blur and noise contaminated available data. In this AMS Notices article, we provide an overview of some well known numerical linear algebra techniques that are use for…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
We consider the problem of reconstructing an infinite set of sparse, finite-dimensional vectors, that share a common sparsity pattern, from incomplete measurements. This is in contrast to the work [17], where the single vector signal can be…
We consider the problem of super-resolving the line spectrum of a multisinusoidal signal from a finite number of samples, some of which may be completely corrupted. Measurements of this form can be modeled as an additive mixture of a…
Super-resolution is the problem of recovering a superposition of point sources using bandlimited measurements, which may be corrupted with noise. This signal processing problem arises in numerous imaging problems, ranging from astronomy to…
Spatial mode demultiplexing was proved to be a successful tool for estimation of the separation between incoherent sources, allowing for sensitivity much below the Rayleigh limit. However, with the presence of measurement's noise,…
We present a rigorous mathematical solution to photometric redshift estimation and the more general inversion problem. The challenge we address is to meaningfully constrain unknown properties of astronomical sources based on given…
We propose a learning-based method to recover normals, specularity, and roughness from a single diffuse image of a material, using microgeometry appearance as our primary cue. Previous methods that work on single images tend to produce…
Methods based on convolutional neural network (CNN) have demonstrated tremendous improvements on single image super-resolution. However, the previous methods mainly restore images from one single area in the low resolution (LR) input, which…
We address the problem of super-resolution of point sources from binary measurements, where random projections of the blurred measurement of the actual signal are encoded using only the sign information. The threshold used for binary…
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 give an overview of recent developments in the problem of reconstructing a band-limited signal from non-uniform sampling from a numerical analysis view point. It is shown that the appropriate design of the finite-dimensional model plays…
Recovering images corrupted by multiplicative noise is a well known challenging task. Motivated by the success of multiscale hierarchical decomposition methods (MHDM) in image processing, we adapt a variety of both classical and new…
A linear inverse problem is proposed that requires the determination of multiple unknown signal vectors. Each unknown vector passes through a different system matrix and the results are added to yield a single observation vector. Given the…