Related papers: Super-resolution multi-reference alignment
Super-resolution is the process of obtaining a high-resolution image from one or more low-resolution images. Single image super-resolution (SISR) and multi-frame super-resolution (MFSR) methods have been evolved almost independently for…
In signal processing and data recovery, reconstructing a signal from quadratic measurements poses a significant challenge, particularly in high-dimensional settings where measurements $m$ is far less than the signal dimension $n$ (i.e., $m…
Mismatches between samples and their respective channel or target commonly arise in several real-world applications. For instance, whole-brain calcium imaging of freely moving organisms, multiple-target tracking or multi-person contactless…
We provide a new methodology for statistical recovery of single linear mixtures of piecewise constant signals (sources) with unknown mixing weights and change points in a multiscale fashion. We show exact recovery within an…
This paper proposes an Any-time super-Resolution Method (ARM) to tackle the over-parameterized single image super-resolution (SISR) models. Our ARM is motivated by three observations: (1) The performance of different image patches varies…
Reconstructing a signal on a graph from noisy observations of a subset of the vertices is a fundamental problem in the field of graph signal processing. This paper investigates how sample size affects reconstruction error in the presence of…
The theory of Compressed Sensing, the emerging sampling paradigm 'that goes against the common wisdom', asserts that 'one can recover signals in Rn from far fewer samples or measurements, if the signal has a sparse representation in some…
Rotation averaging (RA) is a fundamental problem in robotics and computer vision. In RA, the goal is to estimate a set of $N$ unknown orientations $R_{1}, ..., R_{N} \in SO(3)$, given noisy measurements $R_{ij} \sim R^{-1}_{i} R_{j}$ of a…
Let $M(\mathbb{T}^d)$ be the space of complex bounded Radon measures defined on the $d$-dimensional torus group $(\mathbb{R}/\mathbb{Z})^d=\mathbb{T}^d$, equipped with the total variation norm $\|\cdot\|$; and let $\hat\mu$ denote the…
Subsampling is one of the popular methods to balance statistical efficiency and computational efficiency in the big data era. Most approaches aim at selecting informative or representative sample points to achieve good overall information…
We explore a fundamental problem of super-resolving a signal of interest from a few measurements of its low-pass magnitudes. We propose a 2-stage tractable algorithm that, in the absence of noise, admits perfect super-resolution of an…
We consider the problem of reconstructing a sparse signal $x^0\in\R^n$ from a limited number of linear measurements. Given $m$ randomly selected samples of $U x^0$, where $U$ is an orthonormal matrix, we show that $\ell_1$ minimization…
We consider the decomposition of a signal over an overcomplete set of vectors. Minimization of the $\ell^1$-norm of the coefficient vector can often retrieve the sparsest solution (so-called "$\ell^1/\ell^0$-equivalence"), a generally…
The problem of estimating a sparse signal from low dimensional noisy observations arises in many applications, including super resolution, signal deconvolution, and radar imaging. In this paper, we consider a sparse signal model with…
In the problem of multiple support recovery, we are given access to linear measurements of multiple sparse samples in $\mathbb{R}^{d}$. These samples can be partitioned into $\ell$ groups, with samples having the same support belonging to…
Modern high-dimensional methods often adopt the "bet on sparsity" principle, while in supervised multivariate learning statisticians may face "dense" problems with a large number of nonzero coefficients. This paper proposes a novel…
Owing to the edge preserving ability and low computational cost of the total variation (TV), variational models with the TV regularization have been widely investigated in the field of multiplicative noise removal. The key points of the…
Consider the regression problem where the response $Y\in\mathbb{R}$ and the covariate $X\in\mathbb{R}^d$ for $d\geq 1$ are \textit{unmatched}. Under this scenario, we do not have access to pairs of observations from the distribution of $(X,…
Clinical routine and retrospective cohorts commonly include multi-parametric Magnetic Resonance Imaging; however, they are mostly acquired in different anisotropic 2D views due to signal-to-noise-ratio and scan-time constraints. Thus…
The linear inverse source and scattering problems are studied from the perspective of compressed sensing, in particular the idea that sufficient incoherence and sparsity guarantee uniqueness of the solution. By introducing the sensor as…