Related papers: Functional Multi-Reference Alignment via Deconvolu…
We describe a new multi-scale deconvolution algorithm that can also be used in multi-frequency mode. The algorithm only affects the minor clean loop. In single-frequency mode, the minor loop of our improved multi-scale algorithm is over an…
Multi-reference alignment entails estimating a signal in $\mathbb{R}^L$ from its circularly-shifted and noisy copies. This problem has been studied thoroughly in recent years, focusing on the finite-dimensional setting (fixed $L$).…
The signal demixing problem seeks to separate a superposition of multiple signals into its constituent components. This paper studies a two-stage approach that first decompresses and subsequently deconvolves the noisy and undersampled…
This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…
We present a new approach for representing and reconstructing multidimensional magnetic resonance imaging (MRI) data. Our method builds on a novel, learned feature-based image representation that disentangles different types of features,…
Multiple rotation averaging (MRA) is a fundamental optimization problem in 3D vision and robotics that aims to recover globally consistent absolute rotations from noisy relative measurements. Established classical methods, such as L1-IRLS…
In recent years, there is a growing need for processing methods aimed at extracting useful information from large datasets. In many cases the challenge is to discover a low-dimensional structure in the data, often concealed by the existence…
We consider a joint multiple-antenna radar-communications system in a co-existence scenario. Contrary to conventional applications, wherein at least the radar waveform and communications channel are known or estimated \textit{a priori}, we…
Multivariate time-series forecasting holds immense value across diverse applications, requiring methods to effectively capture complex temporal and inter-variable dynamics. A key challenge lies in uncovering the intrinsic patterns that…
Deconvolution is a statistical inverse problem to estimate the distribution of a random variable based on its noisy observations. Despite the extensive studies on the topic, deconvolution with unknown noise distribution remains as a…
We study the dihedral multi-reference alignment problem of estimating the orbit of a signal from multiple noisy observations of the signal, acted on by random elements of the dihedral group. We show that if the group elements are drawn from…
This paper considers the blind deconvolution of multiple modulated signals, and an arbitrary filter. Multiple inputs $\boldsymbol{s}_1, \boldsymbol{s}_2, \ldots, \boldsymbol{s}_N =: [\boldsymbol{s}_n]$ are modulated (pointwise multiplied)…
Diffusion-weighted magnetic resonance imaging (DW-MRI) is a critical imaging method for capturing and modeling tissue microarchitecture at a millimeter scale. A common practice to model the measured DW-MRI signal is via fiber orientation…
We study the problem of signal recovery in the dihedral multi-reference alignment (MRA) model, where a signal is observed under random actions of the dihedral group and corrupted by additive noise. While previous has shown that cyclic…
In the multireference alignment model, a signal is observed by the action of a random circular translation and the addition of Gaussian noise. The goal is to recover the signal's orbit by accessing multiple independent observations. Of…
In many experimental contexts, it is necessary to statistically remove the impact of instrumental effects in order to physically interpret measurements. This task has been extensively studied in particle physics, where the deconvolution…
We focus on an alignment-free method to estimate the underlying signal from a large number of noisy randomly shifted observations. Specifically, we estimate the mean, power spectrum, and bispectrum of the signal from the observations. Since…
In the present paper we consider the problem of estimating a periodic $(r+1)$-dimensional function $f$ based on observations from its noisy convolution. We construct a wavelet estimator of $f$, derive minimax lower bounds for the $L^2$-risk…
Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…
Automated sensing instruments on satellites and aircraft have enabled the collection of massive amounts of high-resolution observations of spatial fields over large spatial regions. If these datasets can be efficiently exploited, they can…